Archive-name: hp/hp48-faq/part3 Last-modified: 5/16/1999 Version: 4.59 Posting-Frequency: Every 14 days or so -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 post72 9.1. ASC Functions Note: Although this document mentions SX only, ASC\-> and \->ASC work on both the SX and GX. From: Bill Wickes ASCII Encoding HP48 SX Objects Sending an HP48 SX object via electronic mail can be difficult if the object does not have an ASCII form, such as is the case for library objects. There are various encoding schemes available on different computer systems, but these require that the sender and receiver have similar computers, or at least compatible encode/decode schemes. The programs listed below perform the encoding and decoding on the HP48 SX itself, which has the advantage of being completely independent of any computer. The programs are nominally called \->ASC and ASC\->. The former takes an object from the stack and converts it to a string, in which each nibble of the object and its checksum is converted to a character 0-9 or A-F. (The object must be in RAM, otherwise a "ROM Object" error is returned.) For sake of easy inclusion in e-mail letters, the string is broken up by linefeed characters after every 64 characters. ASC\-> is the inverse of \->ASC: it takes a string created by \->ASC and converts it back into an object. When you transmit the encoded strings, be sure not to change the string; ASC\-> uses the checksum encoded in the string to verify that the decoding is correct. An "Invalid String" error is returned if the result object does not match the original object encoded by \->ASC. When you upload a string to your computer, use HP48 translate mode 3 so that the HP48 will convert any CR/LF's back to LF's when the string is later downloaded. Two versions of ASC\-> are included here. The first (P1) is in HP48 user language, using SYSEVALs to execute system objects. P2 is a string that the setup program uses P1 to decode into an executable ASC\-> - then P1 is discarded. The second version is more compact than the first, and also uneditable and therefore safer (but it can't be transmitted in ASCII form, which helps to make the point of this exercise). Here are the programs, contained in a directory (if you have problems with this and you are using the HTML version of the FAQ, you may wish to try the plain text version or download a binary copy of the program): %%HP: T(3)A(D)F(.); DIR P1 @ ASC\-> Version 1. \<< IF DUP TYPE 2 \=/ THEN "Not A String" DOERR END RCWS \-> ws \<< 16 STWS #0 NEWOB SWAP DUP SIZE IF DUP 4 < THEN DROP SWAP DROP "Invalid String" DOERR END DUP 65 / IP - 4 - # 18CEAh SYSEVAL "" OVER # 61C1Ch SYSEVAL SWAP # 6641F8000AF02DCCh # 130480679BF8CC0h # 518Ah SYSEVAL # 19610313418D7EA4h # 518Ah SYSEVAL # 7134147114103123h # 518Ah SYSEVAL # 5F6A971131607414h # 518Ah SYSEVAL # 12EA1717EA3F130Ch # 518Ah SYSEVAL # 280826B3012808F4h # 518Ah SYSEVAL # 6B7028080BEE9091h # 518Ah SYSEVAL # BE5DC1710610C512h # 518Ah SYSEVAL # 705D00003431A078h # 518Ah SYSEVAL # 3D8FA26058961431h # 518Ah SYSEVAL # 312B0514h # 518Ah SYSEVAL # 18F23h SYSEVAL DUP BYTES DROP 4 ROLL IF == THEN SWAP DROP ELSE DROP "Invalid String" DOERR END ws STWS \>> \>> P2 @ ASC\-> Version 2. To be converted by ASC\-> version 1. "D9D20D29512BF81D0040D9D20E4A209000000007566074726636508813011920 140007FE30B9F060ED3071040CA1304EC3039916D9D2085230B9F06C2A201200 094E66716C696460235472796E676933A1B21300ED30FD5502C230C1C1632230 CCD20FA0008F14660CC8FB97608403104AE7D814313016913213014117414317 414706131179A6F5C031F3AE7171AE214F8082103B6280821909EEB0808207B6 215C0160171CD5EB870A13430000D50713416985062AF8D341508813044950B9 F06BBF06EFC36B9F0644230C2A201200094E66716C696460235472796E676933 A1B2130B21300373" P3 @\->ASC. To be converted by ASC\->. "D9D20D2951881304495032230FD5502C230A752688130ADB467FE30322306AC3 0CB916E0E30CBD30F6E30C1C1632230CCD20DC0008F14660CC8FB97608403104 AE7D8143130169174147061741431311534AC6B4415141534946908D9B026155 4A6F53131F3AE731A014C161AE215F08082103A6280821939EEC08082170A621 4C161170CD56B870A18503430000D5071351796A9F8D2D02639916D9D2085230 C2A209100025F4D402F426A6563647933A1B2130A2116B213033C0" SETUP @Automatic setup program \<< P2 P1 'ASC\->' STO P3 ASC\-> '\->ASC' STO { P1 P2 P3 SETUP } PURGE \>> END Installation instructions: 1. Save the above text into a text file named CONV (for example). Be sure that you leave the strings exactly as entered above, with no extra spaces or other invisible characters at the beginnings or ends of the lines. 2. Set the HP48 SX into ASCII transfer mode. 3. Using Kermit, download CONV text file to the 48, verify its checksum (6C8Ah). 4. Execute CONV to make it the current directory. 5. Execute SETUP. 6. The directory CONV now contains ASC\-> and \->ASC, ready to use. To archive the decoded versions of ASC\-> and \->ASC back on your computer, be sure to set the HP48 SX in binary transfer mode before uploading. Disclaimers: o Use the programs at your own risk. Any time you delve into the SYSEVAL world, there are increased dangers. Archive your 48 memory before experimenting with these programs! Also, verify the checksums of objects defined above to make sure they have been downloaded correctly, before executing ASC\->. o I will not answer questions about how the programs work. This is not because of any great secrecy, but rather because it's hard to give any answer that doesn't lead to more questions, and more, and more... o 48 hackers are welcome to mine any nuggets they can from the programs, and from the fact that \->ASC is a convenient way to decompile an object. 9.2. OBJFIX When a binary object received by Kermit on the HP-48 is left as a string beginning with HPHP48, OBJFIX will extract the HP-48 object if the only problem is that extra bytes got appended to the end. OBJFIX takes a variable name in stack level 1 and modifies the contents of the variable if no other problems are detected. Note: This is like FIXIT by Horn and Heiskanen on Goodies Disk 8, but this one is by HP and so I suppose it's more reliable. Although it fails the test cases included with FIXIT, that may be because they were artificially contrived cases. Try both on real-world downloads that need fixing. Which do you like better? OBJFIX.ASC %%HP: T(3)A(D)F(.); "D9D202BA81D9F81B2040D9D20F2A26DA91629C8145126489162C23072C80CCD2 0BD0008FB9760147108134164142C2818F24D534501008B2F41643150D73B840 58405438314A161966D2BF6BF6A6F5BE16314213114334CF8208A6F58F235A04 55136D7D4EA494D231A1CA101110131CA130DBE284F8FC0760D41198F29960D4 130142119EA1408F5E0108D341503223072D70B2130B21301460" 9.3. FIXIT From: Joe Horn and Mika Heiskanen PURPOSE: Converts a badly uploaded string into the original object. THEORY: A lot of folks upload HP48 objects poorly, such that when you download them, you just get strings full of garbage that look something like this: "HPHP48-E#c&r$a%p@!*!..." [looks familiar, eh?] That's because they uploaded it using XMODEM, or managed to screw it up some other way. The following FIXIT program takes such a string and extracts the actual HP48 object that they originally intended to upload (if at all possible). Such object extraction can be done by hand, but it's too dangerous. FIXIT minimizes the danger of Memory Clear. It checks whether the extracted object is a valid one, and if not, drops it from the stack before the HP48 attempts to display it. All of the many bad downloads I've archived over the years are fixed by FIXIT, whereas about half of them cause a Memory Clear when extracted manually. No guarantees, however. Use at your own risk. The actual extraction is done by a "Code object" written by Mika Heiskanen. The User RPL "shell" around this code object is what minimizes the danger of Memory Clear; it was written by Joe Horn. INSTRUCTIONS: BACKUP YOUR MEMORY, just in case the string contains a logic bomb. Place the bad download on the stack (see "HPHP48-...") and run FIXIT. Possible results: o No error: the object was extracted successfully and is on level 1. o "Bad Argument Type" error: you didn't have a string on level 1. o "Bad Argument Value" error: the string wasn't of the proper form; it must be an "HPHP48-..." downloaded string. o "Invalid Definition" error: the object was mangled in transmission so badly that its end was lost; the object cannot be extracted. o "Undefined Result" error: there is no HP48 object in the string. o "Recover Memory? YES/NO": the string contained a bomb, and FIXIT detonated it. Press YES to sift through the shrapnel and rubble in a feeble attempt to resurrect the dead. Press NO to bury them. EXAMPLES: To do the following examples, download the FIXIT directory to your HP48 and get into it. o Press HI. See "HPHP48-E...", a badly uploaded download. Before pressing FIXIT to fix it, try doing what we all used to do: press EDIT to see if we can recognize anything (usually a futile attempt). We see: "HPHP48-E... << Melancholy Baby >>" But looks can be deceiving; press ON to exit the editor, and then press FIXIT to extract the intended upload: << Happy Camper >> o Press WTAV; see another garbage download. But EDIT refuses; the string contains null characters. Press FIXIT; see successfully extracted directory. o Press BAD1. Notice that it looks exactly like WTAV. (Press WTAV, compare, then DROP). But its ending is all messed up; manually extracting WTAV from BAD1 can cause Memory Clear. Press FIXIT and see "Error: Invalid Definition" indicating that the object inside BAD1 is so mangled that its end cannot be located. o Press BAD2. Looks like WTAV again. But its body is messed up; manually extracting it would create an External object that could cause Memory Clear if evaluated. Press FIXIT and see "Error: Undefined Result" indicating that there is nothing recognizable inside BAD2. FIXIT.ASC %%HP: T(3)A(D)F(.); "69A20FF7CE20000000402414442340C2A203B000840584054383D25403A20FF7 2500000000403535947440D9D20E16329C2A2DBBF13013216DF1406A1C42328D BF193632B213034000407545146540D9D20E163292CF1EFFB1DBBF1EBFB150FA 193632B2130003030303034C000402414441340C2A203B000840584054383D25 469A20FF72500000000403535947440D9D20E16329C2A2DBBF13013216DF1406 A1C42328DBF193632B213034000407545146540D9D20E163292CF1EFFB1DBBF1 EBFB150FA193632B2131313131313134C000407545146540C2A203B000840584 054383D25469A20FF72500000000403535947440D9D20E16329C2A2DBBF13013 216DF1406A1C42328DBF193632B213034000407545146540D9D20E163292CF1E FFB1DBBF1EBFB150FA193632B2130003030303034C00020849420C2A20570008 40584054383D254D9D20E163284E2050841607079784E20603416D6075627936 32B2130A0BA02D456C616E63686F6C697022416269702BB28000506494859445 50D9D20E16323CE2278BF168BC1ED2A2167E1AFE22D9D203CE2278BF19C2A274 3A2C58C1C2A2031000840584054383D2167E1AFE22D9D2078BF18B9C1DBBF1AA F028DBF1CCD201200014713717917F137145142164808C5BF22D9D2033920200 0000000005150933A1B21305DF22B21305BF22D9D20339202000000000004150 933A1B21305DF223CE2278BF168BC1D8DC1167E1AFE22D9D203FBF1339202000 000000002770933A1B21305DF223CE2278BF19D1A1DBBF18DBF1E0CF1D5CE1AF E22D9D208DBF1339202000000000000030933A1B21305DF22CB2A193632B2130 B21303D4F" 9.4. LASTX The LASTX function is useful in calculations where a number occurs more than once. By recovering a number using LASTX, you do not have to key that number into the calculator again. Note however that LASTX uses the built in last argument feature, so if you use LASTX you will lose the contents of your LASTARG. For example, calculate: 96.704 + 52.394706 -------------------- 52.394706 Keystrokes: Stack: ----------------- -------------------- 96.704 ENTER 96.704 52.304706 + 149.098706 LASTX 149.098706 52.304706 / 2.84568265351 @ This is a version of LASTX for the HP48 @ %%HP: T(3)A(D)F(.); \<< DEPTH \-> n \<< LASTARG DEPTH n - DUP \-> s \<< ROLLD s 1 - DROPN \>> \>> \>> 9.5. Compact Data Storage From: Jim Donnelly A simple length-encoding technique can be put to use for a free- format, very compact multi-field data storage system. Two tiny programs, SUBNUM and STRCON are here to help the process, and are listed near the end of this note. At the end of the note is a directory that may be downloaded into the HP48 that contains the examples. The principle is to store starting indices in the beginning of a string that point to fields stored subsequently in the string. The indices are stored in field order, with an additional index at the end to accommodate the last field. There are several small points worth mentioning: o Fields may be 0-length using this technique. o The execution time is uniform across all fields. o This technique saves about 4 bytes per field after the first field, because the string prologue and length are omitted for fields 2 -> n. EXAMPLE: Indices | Fields Character | 1 11111111 12222222222 Position : 1 2 3 4 |567890 12345678 90123456789 +--+--+--+--+------+--------+-----------+ String : | 5|11|19|30|Field1| Field2 | Field 3 | +--+--+--+--+------+--------+-----------+ This is a string that contains 3 fields, and therefore 4 index entries. The first field begins at character 5, the second field begins at character 11, and the third field begins at character 19. To keep the pattern consistent, notice that the index for field 4 is 30, which is one more than the length of the 29 character data string. To extract the second field, place the string on the stack, use SUBNUM on character 2 to extract the starting position, use SUBNUM on character 3 to extract the (ending position +1), subtract 1 from the (ending position+1), then do a SUB to get the field data. NOTE: The index for field 1 is stored as char. data 5, NOT the string "5"! To place the field index for field 1 in the string, you would execute "data" 1 5 CHR REPL. PROGRAM: The following program accepts an encoded data string in level 2 and a field number in level 1: DECODE "data" field# --> "field" << --> f << DUP f SUBNUM ; "data" start --> OVER f 1 + SUBNUM ; "data" start end+1 --> 1 - ; "data" start end --> SUB ; "field" --> >> >> DATA ENCODING: The following program expects a series of 'n' strings on the stack and encodes them into a data string suitable for reading by the first example above. The programs SUBNUM and STRCON are used to assemble the indices. ENCODE field n ... field 1 n --> "data" << DUP 2 + DUP 1 - STRCON --> n data << 1 n FOR i data i SUBNUM OVER SIZE ; ... field index fieldsize + data SWAP ; ... field "data" index' i 1 + SWAP CHR REPL ; ... field "data"' SWAP + 'data' STO ; ... NEXT data ; "data" >> >> In this example, four strings are encoded: Input: 5: "String" 4: "Str" 3: "STR" 2: "STRING" 1: 4 Output: "xxxxxSTRINGSTRStrString" (23 character string) (The first five characters have codes 6, 12, 15, 18, and 24) VARIATION: The technique above has a practical limit of storing up to 254 characters of data in a string. To overcome this, just allocate two bytes for each field position. The code to extract the starting index for becomes a little more busy. In this case, the index is stored as two characters in hex. Indices | Fields Character | 11111 11111222 22222223333 Position : 12 34 56 78|901234 56789012 34567890123 +--+--+--+--+------+--------+-----------+ String : |09|0F|17|21|Field1| Field2 | Field 3 | +--+--+--+--+------+--------+-----------+ << --> f << DUP f 2 * 1 - ; "data" "data" indx1 --> SUBNUM 16 * ; "data" 16*start_left_byte --> OVER f 2 * SUBNUM + ; "data" start OVER f 2 * 1 + SUBNUM ; "data" start end_left_byte --> 16 * 3PICK f 1 + 2 * SUBNUM + 1 - ; "data" start end --> SUB ; "field" --> >> >> TWO VERY TINY HELPFUL PROGRAMS: SUBNUM "string" position --> code << DUP SUB NUM >> STRCON code count --> "repeated string" << --> code count << "" code CHR 'code' STO 1 count START code + NEXT >> >> Alternative Solution to the Problem: From: Matjaz Vencelj <[email protected]> Jim allocates two bytes for each index entry (to handle longer strings), but on the other side obviously only uses values 00...FF for index dublets, which just doesn't make sense. He's at a 16*16 = 255 chars limit again! I have put together a working set of commands which support up to 65K strings, using two-byte indexing. The encoder (Encode) is User-RPL program which calls the binary N2C which converts the level 1 real into a 2 character string: @*** Encode *** %%HP: T(3)A(R)F(.); \<< IF DUP TYPE 0 = THEN 514 DOERR END \-> N \<< N 1 + 2 * #18CEAh SYSEVAL #45676h SYSEVAL 1 N FOR I I 2 * 1 - OVER SIZE 1 + N2C REPL SWAP + NEXT N 2 * 1 + OVER SIZE 1 + N2C REPL \>> \>> @*** N2C, cksum=#8919h *** %%HP: T(3)A(R)F(.); "D9D202BA812BF819FF30D9D20AEC8111920001007FE3057A50C57463223057A5 0EE250B2130B21307206" ASCII download them with translate code 3, then call program 'Encode' with data strings in levels 2..n+1 and a real n in level 1 indicating the number of strings. The string decoder (Decode), which is usually speed-critical, is the following \->ASC encoded binary: @*** Decode, cksum=#38E1h *** %%HP: T(3)A(R)F(.); "D9D20D8A81D9F811192013000D9D20AEC8113D26CA130F6E30CA130E0E305080 311920001002CE30CAF0650803CBD30CAF06FED30F6E30CA130E0E3050803119 20001002CE30CAF0650803CBD30E0E3033750B2130B21309534" It takes a `database' string on level 2 and a real (record position) on level 1, then comes back with the appropriate substring (record). 9.6. HP82240B Printer Codes From: Jarno Peschier Size of physical row One printed row is either 24 normal characters, 12 expanded characters or 168 pixels wide. This means that one normal character has a width of 7 pixels. Any printed data "falling off the row" will be truncated and ignored by the printer. Reset ESC 255d This resets the printer to the following state: Roman8 character set (watch out: the power-up character set is ECMA94), both expanded and underline printing off, buffer cleared. Self test ESC 254d This causes the printer to print a selftest pattern. This mainly consists of a printout of the Roman8 character set. Expanded printing ESC 253d This turns expanded printing on. This means that from this code on all characters that are printed will be printed at twice the normal character width because each column of pixels is printed twice. Has no effect if expanded printing is already on. ESC 252d This turns expanded printing off. This means that from this code on all characters that are printed at normal character width again. Has no effect if expanded printing is already off. Underlined printing ESC 251d This turns underlined printing on. This means that from this code on all characters that are printed will be underlined because the bottom-most pixel in each columns of pixels is now always on. Has no effect if underlined printing is already on. ESC 250d This turns underlined printing off. This means that from this code on all characters that are printed will not be underlined anymore. The bottom-most pixel in each columns of pixels is printed as it is defined for the printed character. Has no effect if underlined printing is already off. Character sets ESC 249d This switches the printer to use the ECMA94 character set. This set is 100% identical to the character set used in HP48 calcula- tors. This is the power up default of the printer. Has no effect if ECMA94 is the current character set already. ESC 248d This switches the printer to use the Roman8 character set. This set is different than the character set used in HP48 calculators in the 128 last characters. As far as I know this set is used by older printers like the HP82240A and by HP28 calculators (hence the need for the OLDPRT command in HP48 calculators if you are printing to a HP82240A). This character set is turned on if you reset the printer with the reset code. Has no effect if Roman8 is the cur- rent character set already. Graphics ESC n data (with n between 1 and 247) This causes the printer to print graphics specified by the speci- fied data (one byte per pixel column). The value n specifies the number of bytes of data that follow the printer code that will be interpreted as graphics data. Any data after pixel column 168 will be truncated and ignored. 10. Appendix B: GX Specific Information 10.1. What's new in the HP48 G/GX? From: Joe Horn AUTOMATIC LIST PROCESSING Almost all commands that did not accept list(s) as their arguments can do so now. Here are just a few examples: { 1 2 3 } SF sets flags 1, 2, and 3 { 1 2 3 } SQ --> { 1 4 9 } { 2 4 } 10 / --> { .2 .4 } 10 { 2 4 } / --> { 5 2.5 } { 10 12 } { 2 4 } / --> { 5 3 } { .1 .2 .5 } ->Q --> { '1/10' '1/5' '1/2' } { freq freq ...} { dur dur ... } BEEP can play a song with no audible hiccup between tones. Since + has always been used to concatenate lists, a new ADD func- tion exists to add the elements of two lists, like this: { 1 2 3 } { 4 5 6 } ADD returns { 5 7 9 }, whereas { 1 2 3 } { 4 5 6 } + returns { 1 2 3 4 5 6 } as it did before. The only commands which do not have automatic list processing are: o those which never get a Bad Argument Type error (like DUP), o meta-object commands (like ROLL), o program branch structures (like FOR), and o commands that specifically work on lists (like GET). Sometimes the results are non-obvious, for example: 5 { A B C } STO --> A=5, B=5, C=5 { 5 6 7 } 'A' STO --> A={ 5 6 7 } (same as on SX) { 5 6 7 } { A B C } STO --> A=5, B=6, C=7 List processing is only recursive for ->Q and ->Qpi. PORTS AND MEMORY The HP48 G, like the 48 S, only has 32K RAM. The GX, unlike the SX, has 128K RAM built-in. Card slot 1 can contain another 128K (maximum), but card slot 2 can contain up to 4 megabytes of RAM. Only port 1 can be merged in the GX. Card slot 2, which is intended for large-capacity RAM cards, is permanently "free", and is automatically divided up into 128K "ports", each of which becomes Port 2, Port 3, Port 4, etc. Up to 4 Megabytes can be plugged into slot 2, which would then become Port 2 through Port 33. (Although the FREE and MERGE commands were kept for HP48 SX compatibility, GX users will prefer the new FREE1 and MERGE1 commands). Therefore the maximum amount of merged main memory is 256K (unlike the SX which allowed up to 288K) after MERGE1; the maximum amount of fully online free independent memory is 4224K after FREE1. LOCAL VARIABLES Variable names prefixed with a <- (backarrow character) are compiled as local (temporary) variable name objects even if they're not explicitly after FOR or ->. This allows programs to share values through local variables, which is much faster than sharing values through global variables, and they get purged automatically. SPEED CPU clock speed is double the S/SX's, but throughput is estimated to be only 40% faster, primarily due to the fact that all RAM & ROM is now bankswitched (on the S/SX only a 32K portion of the ROM required bank switching), and it still has the same 4-bit bus bottleneck. IMPROVED COMMANDS: o AXES can now also specify the spacing of the tick marks. o DEPND can now also specify the initial values and tolerance for the new DIFFEQ plot type. o REPL and SUB now work on arrays. HP SOLVE EQUATION LIBRARY CARD COMMANDS: o AMORT, amortization calculations o CONLIB, starts Constants Library catalog o CONST, returns value of a named CONLIB constant o DARCY, calculates Darcy friction factor o EQNLIB, starts Equation Library catalog o F0lambda, calculates black-body power fraction o FANNING, calculates Fanning friction factor o LIBEVAL is a generalized form of the EQ card's ELSYSEVAL; it executes any XLIB by its library number o MCALC, marks an MSOLVR variable as "not user-defined" o MINEHUNT, starts the "Minehunt" video game o MINIT, initializes Mpar from 'EQ' for MSOLVR o MITM, customizes title & menu of MSOLVR's screen o MROOT, solve for variable(s) in MSOLVR o MSOLVR, shows Multiple Equation Solver menu o MUSER, marks an MSOLVR variable as "user-defined" o SIDENS, density of silicon as function of temperature o SOLVEQN, starts solver for specified EqLib equation(s) o TDELTA, subtracts temperatures like "-" ought to but doesn't o TINC, adds temperatures like "+" ought to but doesn't o TVM, shows the financial calculator (Time Value of Money) menu o TVMBEG, sets payments-at-beginning-of-periods mode o TVMEND, sets payments-at-end-of-periods mode o TVMROOT, solves for a TVM variable o ZFACTOR, calculates gas compressibility factor Z Note: The EQ Card's Periodic Table and Tetris game are not in the HP48 G/GX, but the EQ Card can be used in the GX if those applications are needed. Tetris was not included because no agreement on royalty was reached. The Periodic Table is available separately as freeware on HPCVBBS. NEW ARRAY COMMANDS: o COL+, inserts a column vector into a matrix or a number into a vector (like INSCOL/PUTCOL in Donnelly's Tool Library) o COL-, deletes a column from a matrix or number from a vector (identical to DELCOL in Donnelly's Tool Library) o COL->, combines multiple column vectors into a matrix o ->COL, breaks a matrix into multiple column vectors (like repeated GETCOL in Donnelly's Tool Library) o COND, column norm condition number of a square matrix o CSWP, swaps two columns in a matrix (like EXCOL in Donnelly's Tool Library) o ->DIAG, returns vector of major diagonal elements of a matrix o DIAG->, creates matrix with specified diagonal elements o EGV, eigenvalues and right eigenvectors of a square matrix o EGVL, eigenvalues of a square matrix o FFT, discrete Fourier transform o IFFT, inverse discrete Fourier transform o LQ, returns the LQ factorization of a matrix o LSQ, minimum norm least-squares solution to an ill-determined system of linear equations o LU, returns the Crout LU decomposition of a square matrix o PCOEF, returns polynomial with given roots (inverse of PROOT) o PEVAL, evaluates polynomial at x o PROOT, finds all roots of polynomial (inverse of PCOEF) o QR, returns QR factorization of a matrix o RANK, rank of a rectangular matrix (uses flag -54) o RANM, creates matrix with random elements o RCI, multiplies elements in one row of a matrix by a scalar o RCIJ, does RCI then adds the result to a row o ROW+, inserts a row vector into a matrix or a number into a vector (like INSROW/PUTROW in Donnelly's Tool Library) o ROW-, deletes a row from a matrix or number from a vector (identical to DELROW in Donnelly's Tool Library) o ROW->, combines multiple row vectors into a matrix o ->ROW, breaks a matrix into multiple row vectors (like repeated GETROW in Donnelly's Tool Library) o RSWP, swaps two rows in a matrix (identical to EXROW in Donnelly's Tool Library) o SCHUR, computes the Schur decomposition of a square matrix o SNRM, spectral norm of an array o SRAD, spectral radius of a square matrix o SVD, singular value decomposition of a matrix o SVL, computes the singular values of a matrix o TRACE, sum of diagonal elements of a square matrix GRAPHICS and PLOTTING COMMANDS: o ANIMATE, displays grobs on the stack sequentially. You can use the defaults, or specify your own delay between frames (can be very fast), the number of times to repeat the sequence, and even the pixel coordinates. It's just like a ROLL REPL loop... except very fast. Note: Charlie Patton converted 17 seconds of the Apollo moon-walk video into HP48 GROBs and ran them with ANIMATE, and it looked very good! o ATICK, specifies tick spacing on plot axes o EYEPT, specifies the eye-point coordinates in a perspective plot o GRIDMAP, selects the new "gridmap" plot type o PARSURFACE, selects the new "parametric surface" plot type o PCONTOUR, selects the new "pcontour" plot type o PICTURE, same as GRAPH command o SLOPEFIELD, selects the new "slopefield" plot type o WIREFRAME, selects the new "wireframe" plot type o XVOL, sets the width of the 3D plotting volume o XXRNG, sets the width of the 3D target mapping range for gridmap and parametric surface plots o YSLICE, selects the new "yslice" plot type o YVOL, sets the depth of the 3D plotting volume o YYRNG, sets the depth of the 3D target mapping range for gridmap and parametric surface plots o ZVOL, sets the height of the 3D plotting volume USER-INTERFACE COMMANDS: o CHOOSE, displays a point-and-click menu "dialog box" o INFORM, formatted multi-line input with named fields (nice!!) o MSGBOX, displays text in a centred box with shadow, then WAITs o NOVAL, placeholder for unspecified values in INFORM argument list LIST PROCESSING COMMANDS: o ADD, adds lists element-wise (see section above) o DOLIST, evals an object on multiple lists o DOSUBS, evals a program or command taking arguments from a list o ENDSUBS, returns the number of loops the current DOSUBS will do o HEAD, first element in a list or first char in a string (identical to CAR in Donnelly's Tool Library) o DeltaLIST, list of first finite differences of list objects o SigmaLIST, sum of the elements in a list o PiLIST, product of the elements in a list o NSUB, returns the current list pointer value during a DOSUBS o REVLIST, reverses the order of the objects in a list (like REVERSE in Donnelly's Tool Library) o SEQ, list of results from repeated execution of an object (like a FOR/STEP loop but the results go into a list) o SORT, sorts elements in a list into ascending order, or sorts a list of lists using each list's first element as the key (can be done with LSORT/QSORT in Donnelly's Tool Library) o STREAM, executes an object on first two elements of a list, then again on the result and the 3rd element, etc. Allows easy creation of things similar to SigmaLIST and PiList. o TAIL, returns a decapitated list or string (see HEAD above) (identical to CDR in Donnelly's Tool Library) SYSTEM COMMANDS: o CLTEACH, clears the 'EXAMPLES' directory created by TEACH o CYLIN, sets polar/cylindrical coordinate mode o FREE1, like 1 FREE (see section above) o MERGE1, like 1 MERGE (see section above) o PINIT, port initialize, esp. important for 4-Meg RAM card users o RECT, sets rectangular coordinate mode o SPHERE, sets polar/spherical coordinate mode o TEACH, loads the Owner's Manual examples into a dir in HOME o VERSION, returns the operating system ROM version string and a copyright notice, like this: 2: "Version HP48-R" <-- means version "R" 1: "Copyright HP 1993" o XRECV, X-Modem protocol receive (binary mode only) o XSEND, X-Modem protocol send (binary mode only) MATH COMMANDS: o LININ, tests whether an equation is linear in a given variable o NDIST, normal probability density o PCOV, population covariance of SigmaDAT o PSDEV, population standard deviation of SigmaDAT o PVAR, population variance of SigmaDAT o RKF, solves initial value problem using Runge-Kutta-Fehlberg o RKFERR, change in solution and absolute error using RKF o RKFSTEP, next solution step with given error tolerance using RKF o RRK, solves initial value problem using Rosenbrock & RKF o RRKSTEP, next solution step with given error tolerance using RRK o RSBERR, change in solution and absolute error using Rosenbrock MENU NUMBERS and KEY CODES Many menu numbers have changed, so software that uses # MENU or # TMENU may not work the same as in the HP48 S/SX. (Specifically, only menu numbers 0-3, 28, 30, and 42-59 are the same). Likewise, almost all of the shifted keycodes correspond to new commands and menus, which programmers must take into account; for example, the "RAD" key on the S/SX had the keycode 82.2, but it's 21.2 on the G/GX. The left-shift key, which was orange on the S/SX, is now purple [officially "lavender"], and the right-shift key which was blue on the S/SX is now green [officially "teal"] on the G/GX. Also, the digit-key menus can be activated by both shift keys; left-shift gives the softkey menus like in the S/SX, but the right-shift gives the new user- friendly full-screen menus. The unshifted keys remain identical to the S/SX, except for a cosmetic colour change to match the very dark green of the calculator case. MANUALS The G/GX comes with two manuals, a "Quick Start Guide" for beginners, and a cost-cutting, slimmer owner's manual called the "User's Guide" which has only 21 pages about programming, since HP figures that the huge majority of all 48 owners never program it anyway. The power users can buy the optional "Advanced Users Reference Manual" (similar to the S/SX's "Programmer's Reference Manual") which covers programming and the many commands that are not mentioned in the User's Guide. There is no "Quick Reference Guide" like the S/SX came with, although the case still has a pocket for one. Jim Donnelly has marketed a nice pocket guide, but it's too wide to fit in the case's pocket. The User's Guide is not spiral bound, but is made to open fully and last a long time, since it's not just glued but has sewn signatures like real books, and is printed on quality paper. Another possibility is "The HP 48G/GX Pocket Guide" by Chris Coffin and Thomas Dick (Grapevine Publications). It's 80 pages long, contains a complete command reference (with input/output stack diagrams), alpha keyboard description, system flag description, as well as examples of how to use various calculator features. This guide is designed to fit nicely in the pocket of the HP case. FLAGS Some previously "unused" flags are now used. They are: -14 Clear = end-of-period payment mode (for TVM calculations) Set = beginning-of-period payment mode -27 Clear = display symbolic complex numbers in coordinate form e.g. '(X,Y)' Set = display symbolic complex numbers using 'i' e.g. 'X+Y*i' -28 Clear = plot multiple equations like the S/SX does (serially) Set = plot multiple equations simultaneously -29 Clear = include axes in plots (like the S/SX does) Set = omit axes from 2D and statistics plots -30 is no longer used (it never did anything useful anyhow) -54 Clear = tiny matrix elements get rounded to zero Set = leaves matrix elements alone The default setting of all these flags is Clear (as in the S/SX). FLAG BROWSER There is a System Flag browser which shows the flag number, shows whether it's set or clear, lets you toggle it, and shows in English what the current setting means. CHARACTER BROWSER While programming, if you want to type any character at all, press CHARS and a screenful of ASCII characters is displayed that you can browse with the arrow keys, and not only does the screen also show the ASCII code (NUM value) and even the shortcut keyboard key sequence (if any) for each character, but if you press ECHO, it will be "typed" into your program. There's no need any more for the alpha keyboard table. DIRECTORY MAINTENANCE Press right-shift VAR to launch a Variable Browser which is a complete memory manager. You can tag multiple objects and copy, move, or delete them all with a single keystroke; there's even a Mark All and an Unmark All, like a real computer. It's slow, however, and has been obsoleted by the very fast PCT library. FRACTIONAL UNIT POWERS The S/SX only handled integer powers of units correctly, but the G/GX can use any real number as a unit power. NAME PLATE The case has a rectangular indentation in the back like the HP 95LX and 100LX, and it comes with an adhesive metal nameplate that you can get engraved with your name. XLIB NAMES All of the new commands in the GX are XLIB names, and therefore take 5.5 bytes in programs. The commands common to the SX and GX take 2.5 bytes each, as they did in the SX. INPUT FORMS and CHOOSE BOXES Many operations have two menu types: the old SX style, and a new "drop-down" menu and "input forms" that have the feel of computer dialog boxes. Especially useful for the HP48 beginner. ENHANCED PRECISION The internal precision of at least some of the matrix routines has been improved; INV gets better answers on square matrices than the SX did. HP has not released information about which routines were improved, how, and by how much. IMPROVED DISPLAY The LCD introduced with revision M of the G/GX is easier to read since it has higher contrast between on/off pixels. It has a slower cycle response time, however, making it difficult to use for rapid-motion video games or any other rapid animation. 10.2. Examples of INFORM, CHOOSE, and MSGBOX From: Jarno Peschier Some examples of INFORM, CHOOSE and MSGBOX on the HP48 GX. Just download the entire directory to your calculator and try the programs, change them, modify them and do everything else with them you can think of. SIMPLE: This program will demonstrate a simple INFORM input screen with 3 fields (one without type restrictions, one for real or complex numbers and one for strings) with some additional layout. MSGBOX and CHOOSE (with the third parameter equal 0) are used to show what the results of the INFORM command are. The list the INFORM command returns is left on stack so you can see what it looks like. ANGLE: This program will demonstrate the use of CHOOSE. It lets you choose between the three possible angle modes (DEG, RAD, GRAD) and when you choose one of them, the corresponding mode is set by evaluating a tiny program containing the right command. ISOLATE: This program will demonstrate the use of INFORM in ways that it is used in the calculator itself. It is a very simple shell around the ISOL command (isolation of a variable from an algebraic). It remembers it's settings in a variable called IPAR and the next time the program is run this will be the default values of the INFORM command, so you can isolate for a different variable using the same algebraic you used before, without retyping it. MSGBOX is used for error messages. TYPELIST: This program will again demonstrate the use of CHOOSE. It extracts the names of all the internal types of the HP48 GX from ROM and shows them in a CHOOSE-box (alphabetically sorted by name). If you choose one of them, its TYPE number is shown in a MSGBOX. MATHQUIZ: This final program will demonstrate the use of INFORM with variable field descriptions and default/reset values. It's will show you 8 fields that are simple math questions for you to solve (addition and subtraction). You can enter all the results and then you will see if your answers were correct (in a MSGBOX). You must fill all the fields. Hint: you can cheat by resetting a field (or all fields). %%HP: T(3)A(D)F(.); DIR SIMPLE \<< IF "AN EXAMPLE OF INFORM" { { } { } { } { "OBJECT:" "ALL OBJECTS ARE ALLOWED HERE" } { } { "NUM:" "ENTER A (COMPLEX) NUMBER" 0 1 } { "NAME:" "ENTER YOUR FULL NAME" 2 } { } { } } { 3 1 } { \<< 440 1 BEEP \>> (0,1) "JARNO PESCHIER" } { NOVAL 0 "N.N." } INFORM THEN DUP "YOU ENTERED:" SWAP 0 CHOOSE DROP "The list that INFORM produced is still on the stack." ELSE "You cancelled the INFORM." END MSGBOX \>> ANGLE \<< IF "ANGLE MEASURE" { { "Degrees" DEG } { "Radians" RAD } { "Grads" GRAD } } 1 CHOOSE THEN EVAL END \>> ISOLATE \<< IF "A VERY SIMPLE VARIABLE ISOLATOR" { { } { "EXPR:" "ENTER THE EXPRESSION" 9 } { "VARIABLE:" "ENTER VARIABLE TO ISOLATE" 6 } } { } { } IF 'IPAR' VTYPE 5 \=/ THEN { } ELSE 'IPAR' RCL END INFORM THEN DUP 'IPAR' STO IF DUP NOVAL POS THEN DROP "You must enter an expression and a variable!" MSGBOX ELSE OBJ\-> DROP IFERR ISOL THEN DROP2 "Error: " ERRM + MSGBOX END END END \>> TYPELIST \<< IF "ALL HP48 TYPES (IN ROM)" 0 27 FOR msg IFERR msg 263 + DOERR THEN ERRM END msg 2 \->LIST NEXT 28 \->LIST SORT 1 CHOOSE THEN "That one has type number " SWAP + "." + MSGBOX END \>> MATHQUIZ \<< IF "A SIMPLE MATH QUIZ" 1 8 FOR i "'" RAND 100 * IP + IF RAND 0.75 < THEN "+" ELSE "-" END + RAND 100 * IP + "'" + "ENTER RESULT #" i + 0 3 \->LIST NEXT 8 \->LIST DUP \<< \-> X \<< X HEAD 2 OVER SIZE 1 - SUB "=" + X 1 ROT PUT \>> \>> DOLIST SWAP \<< \-> X \<< X HEAD OBJ\-> EVAL \>> \>> DOLIST 3 ROLLD { 2 5 } 4 PICK { } INFORM THEN IF DUP NOVAL POS THEN DROP2 "You didn't fill all the blanks." ELSE IF SAME THEN "All answers were correct!" ELSE "Not all answers were correct." END END MSGBOX ELSE DROP END \>> END 10.3. Some useful LIBEVALs From: Joe Horn Note well: backup memory before using any of the following! LIBEVAL can clear memory if used incorrectly. Warning to the clueless: LIBEVAL, NOT SYSEVAL!!! If you don't know what a "bint" is, don't use the ones that mention bints. Example usage: "OUT OF RANGE Try Again" #B0091h LIBEVAL. Try it! -----------------------------------------------------+---------- Function | LIBEVAL -----------------------------------------------------+---------- Displays message box with grob | #B1000h CMD last command window | #B2000h CHARS application | #B2001h MODES application input form | #B41C1h flag browser (returns t/f to level 1, just drop it) | #B41CFh MEMORY application (aka variable browser) | #B41D7h SOLVE application choose box | #B4000h solve equation input form | #B4001h solve difeq input form | #B4017h solve polynomial input form | #B402Ch solve linear systems of equations input form | #B4033h solve TVM input form | #B4038h PLOT input form | #B4045h SYMBOLIC application choose box | #B4113h integrate input form | #B4114h differentiate input form | #B4122h Taylor polynomial expansion input form | #B412Bh Isolate a variable input form | #B412Dh solve quadratic input form | #B4130h manipulate expression input form | #B4131h TIME application choose box | #B4137h Set alarm input form | #B4138h Set time and date input form | #B415Bh Alarm browser (aka alarm catalog) | #B416Eh STAT application choose box | #B4175h single-var stat input form | #B4176h frequencies input form | #B417Dh fit data input form | #B417Fh summary stat input form | #B418Fh I/O application choose box | #B4192h Send to HP48 input form | #B4193h Print input form | #B4197h Transfer input form | #B41A8h Get from HP48 (immediate) | #B50FFh recalls the contents of the reserve variable Mpar | #E4012h -----------------------------------------------------+---------- LIBEVAL : stack diagram / what it does ------- ----------------------------------------------------------- #B0091h : $ --> makes a message box with an alert symbol in it #E0044h : $ --> displays a title line, top center (follow with 1 FREEZE if you want it to stay there after program ends) #B2000h : launches the Last Command choose-box #B2001h : launches the CHARS application; returns nothing if user does not press ECHO #B2002h : launches the CHARS application; returns "" if user does not press ECHO #B41CFh : launches Flag Browser; leaves a True or False on stack, so follow this LIBEVAL with a DROP. #B50A3h : --> current time as hour, min, sec separately, plus an XLIB that represents AM/PM/24-hr (just DROP it) #B50A4h : hh.mmss --> hh mm ss xlib (the xlib represents AM,PM, or 24-hr mode; just DROP it) #B50A6h : --> current date as month, day, year (always that order, and a two-digit year) #B50A7h : mm.ddyyyy (or dd.mmyyyy) --> month, day, yr #B50A9h : #month #yr --> #days_in_that_month (inputs and output are bints; year is two digits, interpreted as between 1991 & 2090 only) #B50AAh : #yr --> %0.00yyyy (input is two-digit bint interpreted as between 1991 and 2090; output is a real number) #B50ABh : #mon #day #yr --> #day_of_week (inputs & output are bints; year is two digits interpreted as between 1991 & 2090; Sunday is #7; if you're in DMY mode, then the input order is #day #mon #yr) #B50B2h : --> { 1 2 3 ... 59 } (not very fast) #B50B3h : --> { 1 2 3 ... 10 } (very fast) #B50B4h : --> { 0 1 2 ... 23 } (very fast) #B50B9h : --> { " 1 January" " 2 February" ... "12 December" } #B50D5h : --> number of alarms currently set (as a bint) #E3063h : hxs --> grob (this is an RLL packed-grob uncompressor, used by EQ LIB and MINEHUNT; for example, try this: #E202Bh LIBEVAL 3 GET #E3063h LIBEVAL PICT STO PICTURE) #E202Bh : the first of the packed EQ LIB grobs (see above) #E2069h : the last of the packed EQ LIB grobs (see above) #E7039h : MINEHUNT packed grob (left screen border) #E703Ah : MINEHUNT packed grob (right screen border) #E801Eh : obj --> obj T/F (tests whether object is in temporary memory or not; returns System-RPL True or False) 11. Appendix C: Details of Bugs 11.1. The EquationWriter Bug From: Joe Horn Rev E Behaviour Clear flag -53 first (the Precedence Flag). On a Rev E, put '((1+2)/(3+4))^5' on the stack and press down- arrow. You'll see: 5 / 1+2 \ | --- | (A) \ 3+4 / which is as it should be. But now press [orange-shift] [+]; see the message "Implicit () off" momentarily; press [left-arrow] (not backspace), then press the [EXIT] softkey. The expression gets mangled into this: 1+2 ----------- (B) (5) (3+4) which is not equal to expression (A) above! Bug, yes? Press ON to abort the process. Now set flag -53, then repeat the above procedure. First you see: 5 / 1+2 \ | --- | (C) \ 3+4 / which is the same as (A) above; but continuing as before, you see: (5) / 1+2 \ | ----- | (D) \ (3+4) / which is equal to the original. Thus the bug can be worked around by keeping flag -53 set (not a pleasant solution). Rev J Behaviour Major difference: after pressing down-arrow, Rev J goes directly into graphic mode, so you have to press ON and then EXIT to get into the equation editor (which Rev E goes directly into). But that's petty cash compared to the following big change. The same sequence of operations, first with flag -53 clear, then set, exactly as detailed above, yields these four displays in a Rev J: 5 / (1+2) \ | ----- | (A') \ 3+4 / (notice the extra parentheses?) and then: 5 / (1+2) \ | ----- | (B') \ (3+4) / which is equal to (A'); nothing at all like expression (B) above! and then: 5 / (1+2) \ | ----- | (C') \ 3+4 / which is the same as (A') above; and then: 5 / (1+2) \ | ----- | (D') \ (3+4) / which is also equal to (A'). No bug in Rev J. SUMMARY: Rev A-E have a bug in the EquationWriter that can mangle expressions if flag -53 is clear (the default) and if "Explicit Paren- theses" mode is toggled. This bug has been fixed in Rev J. Unfortunately (as you can see above) Rev J always puts parentheses around polynomial numerators. It is therefore impossible to use the ->GROB command on a Rev J to create a GROB that looks like expression (A) above; the simplest that can be had is expression (A'). Another minor change, while I'm at it: Rev A-E don't change the menu when you press REPL; Rev J automatically flips to the appropriate RULES menu. 11.2. Rotation Rate to Angular Frequency Conversion Bug About the Bug: From: Wlodek Mier-Jedrzejowicz <[email protected]> There is a rotation rate conversion bug in the HP48 G/GX which I have not seen reported here before, so after discussion with the folks at Corvallis I am posting this description. Warning: it is 159 lines long! First - an example. Put the unit object 60_rpm in level 2 and the unit object 1_r/s in level 1, then execute the command CONVERT. You are asking the HP48 to convert a rotation rate of 60 revolutions per minute into an angular frequency in radians per second. 60 rpm is 1 revolution per second, or 2pi radians per second. No HP48 G/GX will give this answer! Not everyone uses rpm or is even aware of the existence of this unit - it is one of the extra units in the UTILS menu of the Equation Library - so here is a second example - add 2pi radians per second to one Hertz. Put 6.2832_r/s in level 1, 1_Hz in level 1, and add. You are adding an angular frequency of two pi (one cycle) per second to a rotation rate of one per second, so the result should be a frequency of two Hertz. On an HP48 S/SX that is the answer. On an HP48 G/GX it is not. When units are converted, by CONVERT, or during arithmetic on unit objects, the level 2 object is first turned into "base units", and then the result is converted into the units of the level 1 object. On the HP48 S/SX, the "base unit" of angles is one rotation (or a "unit circle" or a revolution or a cycle). So, the angle unit of rpm (a revolution) or of Hz (a cycle if Hz is treated as a rotation rate) is already in base units - conversions to angles involving rpm and Hz automatically work correctly. On the HP48 G/GX, the "base unit" of angles is the current angle mode (DEG, RAD or GRAD) - so any conversion from rpm or Hz (or any formula which works in cycles, rotations, revolutions, unit circles) to angles should be preceeded by a conversion from the unit circle to the current angle. Apparently no-one noticed this would be necessary, because it all worked automatically on the HP48 S/SX. So, when you convert 60_rpm to units of _r/s, an HP48 G/GX converts not 60 rotations but 60 "base angle units" per minute to radians/second. In RAD mode, you get 1 radian per second. In DEG mode you get 1 degree per second, and in GRAD mode you get 1 grad per second (in each case expressed in radians). That's three different answers, none of which is correct! Exactly the same happens if you convert 1_Hz to angles per second, and the inverse mistake is made if you convert angles per time to cycles or rotations divided by time. I first learned of this bug from a member of HPCC (the British club for users of HP handhelds), Peter Embrey. He describes his troubles in articles in the first two 1994 issues of our club journal, DATAFILE (in Volume 13 number 1 pages 12 to 14 and V13n2p6). He was calculating the energy stored by a flywheel - given by the formula (1/2)*I*omega^2 and after a time he decided the answers had to be much too big when he CONVERTed from kg*m^2*(r/s)^2 to W*h on an HP48 GX. It turns out that (r/s) are the correct units to get the right answer, but the GX was converting to degrees per second as it was in DEG mode, so his answer was too large by a factor of (360/2pi)^2 - a factor of about 3,300. In this case, his HP48 SX was not much better, since it converted from radians to unit circles. The way to get the correct answer is to use an HP48 G or GX in RAD mode - or to divide out the radians from the formula before using CONVERT. This is not yet a bug, but needs as much care as does use of temperature units on the HP48. But when Peter tried to deal with the problem by working in rpm, he came upon the bug described above. My thanks to Peter for putting me on the trail! Apparently this bug not been reported before - at least my friends in HP tell me that it was not on their list of known problems until I told them of it. (This means it is not fixed in the new revision R.) Why not - does everyone know about it and work around it without thinking to tell anyone else? Or does no- one use their HP48 to do calculations on rotating bodies - or do most people do calculations with rotating bodies in such a way that they do not encounter this problem? Could there be hundreds of students and engineers out there calculating and designing things on their HP48 G/GX and getting wildly inaccurate results? Has anyone built a disk drive or a jet engine which rotates far too fast and will disintegrate because of this? No, of course not, all engineers know that any design calculation absolutely must be repeated on two entirely separate calculators or computer programs! :-| Maybe some students have lost marks in exams because of this though - but please, this is not intended to restart the discussion as to whether calculators should be allowed in exams! I want to underline again that apparently no-one has reported this before - which must mean that few people have been affected by it. It is therefore not a good reason to throw away your HP48 G/GX or get on a high horse and demand that HP replace your HP48 G/GX - but I think it is important that people be warned so they can take appropriate avoiding action. The rest of this message goes into more detail - if you never worry about rotation calculations then you can safely ignore the rest - though you might find it interesting, so don't stop yet :-) One way to avoid this would be to add a new unit to the HP48 - call it what you like - the "cycle" or "rotation" or "revolution" or "unit circle". As I wrote above, this is already implied in the HP48 S/SX; to see this on an HP48 S/SX, put 360 degrees in level 1 and execute UBASE - the result is 1, meaning that 360 degrees are equivalent to one base unit of angle measurement, but that there is no named HP48 unit corresponding to this. In contrast, UBASE on an HP48 G/GX considers the base unit of angle measurement to be the radian, even though CONVERT behaves as though the base unit is the current angle mode. There appear to be two different norms for base angle units on the HP48 G/GX! The whole subject gets very little mention in HP's manuals. In the original HP48 SX manual (two volumes, spiral bound), the section on "Dimensionless Units of Angle" in chapter 13, on page 198, warns the reader about the danger of using dimensionless units and states how angle units and scalars are treated. In the later HP48 S and HP48 SX manual (one volume), the same warning is given in "Converting Dimensionless Units of Angle", on page 13-12. The HP48 G Series User's Manual, in "Converting Angular Units" on page 10-7, says that conversion will interpret a scalar according to the current angle mode setting. (A scalar is a pure number with no units.) For a detailed description, look in the HP48 S/SX edition of "HP48 Insights Vol II", section 21.4.3. This book is written by Dr Bill Wickes, who was the design team leader of the HP48 SX, and who wrote the "Insights" books largely to provide the sort of explanations and details that get left out of manuals. A good explanation of angle units is exactly the sort of thing one can find there! He explains the pitfalls and unavoidable contradictions of working with angles in the HP48 units system and points out that the HP48 S/SX make the somewhat arbitrary choice of using 2pi as the base unit of angles, thereby making conversions between angles per time and Hertz work correctly. Maybe no-one on the HP48 G/GX team read this while they were making changes from the HP48 S/SX! Why did they change the base unit at all? Most likely they were trying to deal with another contradiction: the units system lets you add pure numbers to angles, since both are dimensionless. If you add the number 1 in level 2 to the unit object 0_r in level 1 on an HP48 S/SX, the number 1 is treated as 1 base unit, or 2pi radians, and the result is 6.2832_r - but if you take the SIN of the number 1 instead, it is not treated as 2pi, but as 1 unit of the current angle mode. The change made on the HP48 G/GX does resolve this contradiction, but at the cost of introducing the bug described above. As mentioned, a way to resolve the problems involved would be to add the angle unit "cycle" explicitly to the HP48 units system. Hz would then be treated as cycles per second when used in calculations involving rotations - rpm would be treated as cycles per minute, and conversions would go from cycles to the appropriate angle units. This suggestion was made by Peter Embrey in his articles, and the folks at HP accept that this is a good solution - but they have not implemented it yet. In the meantime, be very, very careful when converting between units of rotation rate and units of angular frequency. I would urge everyone who does not yet have a copy of Insights II to buy one and read the relevant section - maybe that will even entice Bill Wickes into publishing his long-awaited HP48 G/GX version of the book! I have not yet mentioned solid angles. In principle there should be no problem - on both the HP48 S/SX and the HP48 G/GX the base unit of solid angle is a "unit sphere", or 4pi steradians. On the HP48 S/SX you can add the pure number 1 to 0_sr and get 12.5664_sr (4pi steradians). The HP48 G/GX manuals imply that exactly the same should happen, but on my (version L) HP48 GX this gives the error message "Inconsistent Units". This is yet another undocumented difference between the Series S and Series G but at least it is no bug! Apologies for making this description so long, I hope most people will agree that a subject like this deserves a careful description! For my next trick - some details on the HP48 Random Number Generator. Addition Insight: From: Eric Haas <[email protected]> Note: The < symbol below is actually the angle character. The angular conversion bug is actually in the definition of the rpm unit. If you put 1_rpm on the stack, and type UBASE, you get 1.66666666667E-2_1/s. Notice that there is no angular unit in the definition. If the rpm unit is instead defined as 6_</s, all conversions to and from rpms will work just fine. As an easy work-around, define the unit RPM as 6_</s and use that instead of the built-in unit. If desired, one could also define the unit HZ as 60_rpm or 360_</s. However, as Hz is sometimes used to describe things other than rotation rates, such a definition would not be appropriate for all circumstances. 12. Appendix D: Hardware Additions 12.1. How to Make a Serial Cable From: Frank Vorstenbosch <[email protected]> Revised by: Andrew Chen Now that you have your HP, you probably want to tap the tremendous amount of programs out there. But how do you do this? You need an HP to PC link. You can buy one, but they tend to be fairly costly. Or you can build your own. The process requires the following parts: Required Parts: o Soldering iron and flux o RS232-9 or RS232-25 shield (serial port shield) o RS232-9 or RS232-25 female connector (serial port connector) o 4 pin HP connector, with sockets spaced 2 mm (NOT 0.1") apart o Some copper wire Of the above list of parts, most are pretty easy to acquire, and you should be able to find them at your local electronics store. However, the 4 pin (i.e. male) HP connector can be a bit harder to find. If you happen to have a broken floppy drive, hard drive, or CD-ROM audio cable lying around, look inside and see if you can find a connector there that will fit the HP48. Do not use a 0.1" connector, as this will damage the pins on your calculator. HP Connector The HP connector part of the cable will be the most frustrating part of the link. The reason is that you will probably not be able to find these at your local electronics store, but you should you should find everything else there. Instead, you can either find the connector at used computer stores or you can create the link yourself. Easy Way Because the former is much easier, I will give you some tips on where one can find the connecter. First, check your yellow pages and look under "computer". You will find a lot of stores, but look specifically for "computer repair" or "computer parts". Call these stores asking for a "CD-ROM audio cable". If the store carries these cables, go to the store and ask to see the requested cable. What you should see is a cable with two ends, each with a 4 socket connector. One end should be spaced a bit larger than the other, and this one will not fit into the HP's pins (don't press too hard, or else you will bend the connector pins). The other side should fit like a charm. Don't be worried about that there are only 3 sockets. This is fine because the empty one is a ground. Once you have this cable, cut off the unusable end, and go to the PC connector section. Hard Way If are unable to find a place that carries CD-ROM audio cables, or you prefer to make your make, it is possible to build the connector yourself. What you can do is buy IC sockets from a local electronics store. You can usually find them in packs of 8 or more. These IC sockets will be bound together in a hard plastic shell, which also places at unusable intervals. Therefore, it is necessary to strip the IC sockets out of the hard plastic shell (don't worry too much about damaging them, the IC sockets are fairly durable and you have 8 of them). Next, solder a 'fork' from thin rigid metal wires, to hold the four IC pins spaced at exactly 2 mm while you glue them together with superglue. Glue a plastic 'handle' to the four IC pins to be able to remove the connector from the HP48. You can also indicate the top side of the connector on this handle. Note that the hole in the HP48 in which the connector should go is not symmetrical; the pins are nearer to the top of the calculator than the bottom, and you can use this to make it difficult to insert the connector the wrong way up. With that done, you can proceed on to the PC side of the connector. PC Connector The PC side of the connector is much simpler than the HP side. All you have to do is make a standard serial connector with the parts you bought. However, don't do it yet because you need to solder the wires from the HP connector into the back of the serial connector first. Making the Connections Now that you have the two sections done, you can begin making the connections for the actual link. Starting with the HP side, put in the connector and mark the top as "UP". If you have a CD-ROM audio cable with one socket missing, make sure that the empty socket connects to pin 1: Connector on HP48 Connector to HP48 ______ ______ |....| |oooo| <-- First is \____/ \____/ null pin 1 pin 4 pin 4 pin 1 If you made the HP connector the hard way, you have to solder the ends of the IC sockets to long pieces of wire, which will eventually connect to the serial connector on the PC side of the cable. With these wires done, you must solder the individual wires into the proper places on the PC side. Use this table of pin connections: HP to PC cable HP48 | RS232-9 | RS232-25 -----+---------+---------- 1 | shield | shield 2 | 2 | 3 3 | 3 | 2 4 | 5 | 7 You can use either a 9 or a 25 pin female sub-D socket for the PC- side of the cable: 9-pin RS232 25-pin RS232 connector (F) connector (F) pin 5 pin 1 pin 13 pin 1 ------------- --------------------------- | o o o o o | | o o o o o o o o o o o o | \ o o o o / \ o o o o o o o o o o o / --------- ----------------------- pin 9 pin 6 pin 25 pin 14 Use flexible 4-wire cable to connect the four contacts of your HP48 connector to the PC connector. Pin 1 of the HP48 should be connected to the metal shield of the RS232 connector. Usually it is not easy to solder this shield; first scratching the shield bare (it has some kind of coating) using a screwdriver or a file will help. If this doesn't work, simply leave pin 1 of the HP48 disconnected. Note that pins 2 and 3 of the RS232 connector must be swapped when you use a 25-pin connector. Before connecting the completed cable to your HP48, check for short-circuits using an ohmmeter or multimeter set to ohms or "diode test". The HP48 has a built in serial loop back test that can be used to test the serial cable (see the question regarding the ON-KEY combinations). After you are done, close the shield and connector, and put in all the screws. You should now have a HP<-->PC link, which functions on COM (serial) ports. Using the Link With the link finished, it is now ready to be tested. Download some programs (such as those in the Best Program List) that you wish to try. At some point you should go to <http://www.columbia.edu/kermit/> to obtain the version of Kermit that suits you best. However, if you have an alternate communications program (for example, Windows 95 comes with HyperTerminal which you can use) you can delay downloading Kermit. However, it is a highly recommended to obtain because certain programs for the HP48 use special features in Kermit (such as server mode) not available in other communications programs. With this done, you can begin the actual transfers. Start your communications program, and set the port to COM1 (or whatever your link is plugged into). In Kermit, you would type "SET PORT COM1" and in HyperTerminal you would set the dialog box with the choice of what modem you want to use to "Direct to COM1". Then change the speeds of the ports to 9600. In Kermit, type "SET SPEED 9600" and in Hyperterminal click on Advanced. On the HP, go to I/O, and go to Transfer. Set the calculator to Wire, 9600 baud, and Kermit (or X-Modem, if you using it instead). Then, get ready for to receive a file. Note that X- Modem is much faster than Kermit in most situations, especially in long transfers. However, it is not available built-in on the S/SX. On the PC start sending, and on the HP, start receiving. You should see the transfer arrow on the upper right of the screen on the HP, and it should be flashing. On the PC, you should see a progress indicator to show how much of the file has been transferred. When the transfer is finished, check that you received what you expected. If it what you expected, your HP<-->PC link works! HP to HP Cable If you want to use 9600 bps communication between two HP48s, then make two HP48 connectors and simply connect the two, swapping pins two and three. HP to HP cable HP#1 | HP#2 -----+----- 1 | 1 2 | 3 3 | 2 4 | 4 Warranty, Disclaimer, etc... Although the serial interface of the HP48 is protected internally, it is possible to damage the calculator when a wrong connection is made. I am not responsible for any errors in this file, or for any mistakes you may make. From: Deborah Lynn Williams I made an HP48 link out of four pieces of speaker wire and serial port plug. The wiring of the plug is available above. The connection to the HP plug is the difficult part. I took 4 pieces of stranded speaker wire and cut them so that the wire and the insulation were even. I then took a paper clip and pushed it into the this open end, making a space between the wire and the insulation. I then had to trim some of the strands that were sticking out. I then just pushed this onto the pins in the HP48 port. It isn't a very strong connection, but it works fine if you don't jostle it. The other ends of these speaker wires I connected to the serial plug. Just remember to label which wires go to which pin, or make them all different lengths. From: John Cutter Another cheap source for cables is the common serial mouse for PC- compatibles. I had a cheap one on which the button gave out after 2 weeks of use, so I opened it up. It had a serial 9 pin cable that disappeared into the mouse. Once open, there was a 4 pin 2 mm connector plugged into the mouse's circuit board. All I had to do was reverse two pins inside the connector, and it's been working fine since. I also noticed that Logitech mice have 6 pin 2 mm connectors, which could also be adapted. No soldering or crimping here! 12.2. Using a modem with the HP48 From: Diego Berge My purpose here is to explain in some detail the steps you need to follow to be able to transmit data via modem with the HP48. Another related document is <http://www.freeweb.org/freeweb/enrico/hp2modem.htm> by Enrico Carta. In order to successfully connect your HP48 calculator to a modem, the first thing you need is a 'Null Modem Cable'. A null modem cable is like a regular serial cable, except that two of its lines are crossed. You might wonder: So why is it different connecting to a PC than connecting to a modem? Well, data communication devices can be classified in two groups: Devices which GENERATE or RECEIVE information, and devices which merely TRANSMIT information. The former are called Data Terminal Equipment (DTE), PCs are an example of DTE; the later is called Data Communication Equipment (DCE), and are primarily modems. Now, when PCs were designed, it seems like they didn't think somebody would ever want to hook two DTEs directly, as a result, in a typical PC all we have (besides the parallel printer port) is an RS-232 port, which is intended for connecting a DCE. So when a machine wants to connect to a PC, its port must be that of a DCE, even if it otherwise acts as a DTE. Within that class of hybrids fall HP48s, Psions, some (or most?) serial printers, mice, and a long etcetera. Remember, the RS-232 communication scheme is: DTE <--- DCE === DCE ---> DTE If you want to link two DTE together, you must 'simulate' a DCE; that's what a Null Modem Cable is for. It's called 'Null' because it (the modem) does not actually exist, and 'Modem' because it acts like if there was one. To build a Null Modem Cable for the 48, assuming that you already have a regular cable, you'll need two MALE RS-232C connectors, at least one of which must be a DB-9 (9-pin), and a short piece of mouse cable or similar (some 3 inches should do) (If you don't have a regular cable, I recommend that you get one). The wiring must be as shown here: CONNECTOR 'A' CONNECTOR 'B' pin#: 3 2 7 (DB-25) pin#: 2 3 5 pin#: 2 3 5 (DB-9) name: TX RX GND name: TX RX GND | | | | | | | | | | | | | | +---------------------------------|---|---+ | | | | ( <<< and | +------------------>>>----------------+ | >>> show | | direction of +----------------------<<<--------------------+ data ) The pin number should be embossed near the pin itself in the connector. Once the physical part is done, which in most cases will be the most critical, you're ready to try out your brand-new, state-of-the-art, $2.25 null modem cable. Plug it between your regular HP48 cable and your modem, turn the modem on (please don't forget this part :), and on the 48 type in: [RightShift]+[""] [alpha] [alpha] AT [ENTER] 13 [LeftShift]+[CHARS] [CHR] [+] In stack level 1 you should have (# is a little black square): 1: "AT#" Now type: [LeftShift]+[I/O] [NXT] [SERIAL] [XMIT] [BUFLEN] [DROP] [SRECV] you should get: 2: "AT###OK##" 1: 1 If this test goes wrong, try two or three more times. If it still fails, check your cable(s), check that the 48 can transmit and receive to/from the PC, do the same with your modem. And when everything else has failed anyway, connect your modem to the PC, crank up a terminal program (as Terminal / Hyperterminal, or Kermit's 'Connect' command), and type: AT&D0 [ENTER] the modem should respond: OK This tells the modem to ignore the DTR signal from the host, which the 48 can't supply. Try again with the calculator, if it works, go back to the terminal and type: AT&W0&Y0 [ENTER] to save the current modem configuration as default. If it has not worked so far, I can't help you. Assuming you've got it to work, now all you have to do is learn a few modem commands to dial and, possibily, hang up. In general, modem commands start with the two-character sequence 'AT' (no quotes) and end with a single <CR> character (dec 13), <LF> is optional. To dial a number use: ATDT12345<CR> where 12345 should be replaced by the actual number. For example: [RightShift]+[""] [alpha] [alpha] ATDT0800890011 [ENTER] 13 [LeftShift]+[CHARS] [CHR] [+] [LeftShift]+[I/O] [NXT] [SERIAL] [XMIT] dials the AT&T Direct access number for the UK. If your line is not connected to a digital switchboard, you may need to dial by pulses, then you should use instead: ATDP12345<CR> Next thing you'll probably ask is: 'How do I know that I'm connected?' If the modem has successfully established a connection, it should respond in most cases with a message like: CONNECT 9600/V34/LAPM/V42BIS/9600:TX/9600:RX or simply "1" if its not in the default verbose mode. Also, if the modem has a 'CD' indicator, it'll usually light up. To find out via the calculator whether it's connected or a problem has occurred, use the following keystrokes: ( [LeftShift]+[I/O] [NXT] [SERIAL] ) [BUFLEN] [DROP] [SRECV] repeatedly until a non-empty string appears in level 2. Some common messages are: verbose: non-verbose: CONNECT 1 NO CARRIER 3 ERROR 4 NO DIALTONE 6 BUSY 7 NO ANSWER 8 DELAYED 24 Once you get the CONNECT message, you're ready to send any data you want to the remote host as you'd usually do. I personally use Kermit this way when I'm not in the office or at home. Finally, when you're done you'll want to hang up the line. The simplest way is turn the modem off, which I recommend. But if you want to instruct the modem to hang up, the process usually is: (wait at least 1 sec without sending any data) [RightShift]+[""] [alpha] [alpha] +++ [ENTER] [LeftShift]+[I/O] [NXT] [SERIAL] [XMIT] (wait at least 1 sec without sending any data) [RightShift]+[""] [alpha] [alpha] ATH [ENTER] 13 [LeftShift]+[CHARS] [CHR] [+] [LeftShift]+[I/O] [NXT] [SERIAL] [XMIT] Note, however, that this, as most of what I have said here about modem commands, might vary depending on each modem's particular brand, model and configuration. You may need to read your modem's manual for more details. Disclaimer: As you'd expect, I take no responsibility for anything you may break, twist, cut, slice, burn, hurt, or otherwise damage while following these instructions. 12.3. Additional Information on the HP48 and RS-232 From: John Meyers You can't connect the HP48 to anything else until you have first plugged in its cable, which finally brings the HP48's serial connections out to a DB9 connector. At that point, the HP48, including its attached cable, is clearly configured as DCE (the same as a modem), so you need a "crossover" (such as a "null-modem adapter") to connect the HP48 to a modem. 12.4. Using Non-HP RAM Cards If you use RAM cards that are NOT designed for the HP48, it is possible to severely damage your HP48. If you want to be safe, you should only use RAM cards designed for the HP48. Here is an edited discussion from comp.sys.handhelds. From [email protected] Fri Mar 1 17:00:00 1991 From: [email protected] (Steve Harper) Date: Thu, 10 May 1990 22:46:09 GMT Subject: RE: HP48 SX Memory Card Pricing Organization: Hewlett-Packard Co., Corvallis, OR, USA There has been a substantial amount of comment regarding the memory cards for the HP48 SX and their prices. My purpose in this response is not to attempt to justify any particular price, but rather to present the technical reasons why there is a substantial price difference between the memory cards and other types of expansion memory for PC's, for example, with which users are probably more familiar. Some users have correctly pointed out that the memory in the cards is static RAM rather than dynamic RAM commonly used in PC's. Dynamic RAM uses one transistor and a capacitor for each bit of memory whereas static RAM requires either four transistors and two resistors, or six transistors. The net result is that an equivalent amount of static RAM is much larger and therefore much more expensive than dynamic RAM. The advantage is that static RAM doesn't need to continually be running and drawing current (refresh cycles) to retain the contents of memory. In addition, the static memory used in the cards is not just any static memory, but is specially processed and/or selected for very low standby current. This allows the backup battery in the card to keep memory alive for a very long time, rather than requiring the user to replace it every few months. The special processing and/or special testing to select low current parts adds to the already higher cost of the static RAM chips. The standard molded plastic DIP package used for most integrated circuits, including memory chips, is relatively inexpensive because of its simplicity and the huge volumes. Unfortunately, these packages are too large to put into a memory card. Therefore, the card manufacturer mounts the individual silicon memory chips directly on a special thin PC board together with the memory support chips. Because multiple chips are being placed in a single hybrid package in a special process which has lower volume, yields are lower and this again causes the cost to be higher. Indeed, the yield becomes exponentially worse as the number of chips and interconnections increases in such a packaging process. In addition to the memory chips themselves, two more integrated circuits and several discrete components are required for power and logic control. A bipolar technology chip senses the external voltage and switches the power to the chips from the internal keep-alive battery as needed. A CMOS gate array chip protects the memory address and data lines from glitches/ESD when the card is not plugged in. This chip also generates the proper enabling signals when there are multiple memory chips in the card, as is presently the case with the 128 Kbyte RAM card. These chips must be designed for extremely low current, just as the memory chips are. In addition to the battery and the battery holder, the other mechanical parts are important, too. The molded plastic frame holds the PC board and provides the foundation for the metal overlays and the shutter-and-springs assembly which protects the contacts from ESD and from contaminants. The write-protect switch is also an important feature. It is quite expensive for the manufacturer to make the tools necessary to fabricate each of these parts as well as the tools to assemble and test the complete card. While the volume of memory cards is relatively low this tooling cost represents a significant part of the cost of each card. Admittedly, there are other alternatives, such as those presently used in PC's, to provide a memory expansion capability. To provide that kind of expansion would require the calculator to be much larger than it is and possibly more expensive. This is clearly very undesirable. Other features that were felt to be essential were the ability to distribute software applications and to share and archive/backup user- created programs and data. Other expansion alternatives do not provide these important benefits. The I/O capabilities of the calculator provide these features only to a limited degree. One other item bears repeating here: Memory cards for use in the calculator will clearly indicate that they are for use with the HP48 SX. Other memory cards exist which are mechanically compatible with the HP48 S, but these cards cannot be relied upon to work electrically in the calculator. The HP48 SX cards are designed for a lower supply voltage range. Use of the other cards may cause memory loss, and under certain circumstances may even damage your calculator electrically. From [email protected] Fri Mar 1 17:00:00 1991 From: [email protected] (Steve Harper) Date: Fri, 11 May 1990 16:52:07 GMT Subject: Re: Memory Card: Give Us True Facts! Organization: Hewlett-Packard Co., Corvallis, OR, USA My previous statement that under certain circumstances the calculator may even be damaged electrically is not a ploy. If the calculator's internal power supply voltage happens to be near the low end of the range, say 4.1 V, and the voltage at which the card's voltage control chip shuts it down happens to be near the high end of its range, say 4.2 V (this can and does occasionally occur for the non-HP48 SX cards), then the calculator will start to drive the memory address lines and the card will still have these clamped to ground (that's what it does to protect itself when there is not sufficient system voltage to run). This unfortunate situation may simply trash your memory, or if the calculator tries to drive enough of the lines high at the same time, several hundred milliamps may flow...for awhile that is, until something gives up... On the other hand, your calculator and a particular non-HP48 SX card may work just fine if those voltages happen to be at the other end of their ranges. These voltages are also slightly temperature sensitive. It may work in the classroom or office and not at the beach, or vice versa. The voltage trip point of the HP48 SX cards has been set lower (a different voltage control chip) so that this cannot occur, regardless of part and temperature variations. One other item was brought to my attention yesterday by Preston Brown that I should have included in my original posting here. While most of us recognize that comparing RAM cards to a handful of dynamic RAM chips to plug into your PC is apples and oranges, it may be more interesting to compare the HP48 SX cards with cards for other products, like the Atari Portfolio, the Poquet, the NEC Ultralite, etc. I believe you will find that the prices on the HP48 SX cards are not at all out of line. Steve "I claim all disclaimers..." From [email protected] Fri Mar 1 17:00:00 1991 From: [email protected] (Preston Brown) Date: Thu, 17 May 1990 17:26:53 GMT Subject: Re: Memory Card: Give Us True Facts! Organization: Hewlett-Packard Co., Corvallis, OR, USA When the RAM cards detect that voltage is to low to operate they clamp the address lines to ground. This clamping is done by turning on the output drivers of a custom chip included on the card. The clamping current is specified to be 2mA min at the Vol output level. Since the 48 can be trying to drive the line all the way high even more current is typical. 10mA per fight is not uncommon with totals of several hundred mAs. The VDD power supply is regulated at 4.1 - 4.9 with typical parts at the low end (4.3). The power to the cards is switched through a transistor, creating up to a 0.1V drop. Standard Epson cards have a significant chance of seeing this voltage as to low and shutting down. We have seen cards do this in the lab. When it occurs the calculator locks up with VDD pulled down to about 2.5V and 250mA being drawn from the batteries. This current drain greatly exceeds the ratings for the power supply and can damage your calc. The least that will happen is a loss of memory. Now, why didn't we regulate VDD higher? The 48 has two power supplies VDD at 4.3 and VH at 8.5. VH cannot be regulated higher without exceeding the spec for our CMOS IC process. VH is used as the + voltage for the I/O. In order to meet a +3V output level VH must be more then 3.6V above VDD. (VDD is used as I/O ground). Our power supply system increase the battery life and reduces the cost greatly for the wired I/O. Preston 12.5. Where can one obtain third party RAM cards? If you decide you want to look into the non-mainstream alternatives for RAM cards, you might like to check the following URLs: o <http://www.cynox.de/> o <http://stolte-edv.com/de/> o <http://www.cyberline.de/kkgbr/> o <http://www.Digitalis.de/> o <http://home.t-online.de/home/FFFFF/> o <http://www.geocities.com/Eureka/Enterprises/3190/> -----BEGIN PGP SIGNATURE----- Version: PGPfreeware 5.0i for non-commercial use Charset: noconv iQA/AwUBNz8oQOhzXOws+qC7EQKLNACfdCHbhGSpsjKRoxJB1FlyIgTmU1MAn37G 3ET/SX5Luix7oTUtkKnLB89p =qFFu -----END PGP SIGNATURE-----
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