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Intel Software Hardware

Historians Recreate Source Code of First 4004 Application 159

Posted by Zonk
from the really-hard-to-dig-through-bits-and-bytes dept.
mcpublic writes "The team of 'digital archaeologists' who developed the technology behind the Intel Museum's 4004 microprocessor exhibit have done it again. 36 years after Intel introduced their first microprocessor on November 15, 1971, these computer historians have turned the spotlight on the first application software ever written for a general-purpose microprocessor: the Busicom 141-PF calculator. At the team's web site you can download and play with an authentic calculator simulator that sports a cool animated flowchart. Want to find out how Busicom's Masatoshi Shima compressed an entire four-function, printing calculator into only 1,024 bytes of ROM? Check out the newly recreated assembly language "source code," extensively analyzed, documented, and commented by the team's newest member: Hungary's Lajos Kintli. 'He is an amazing reverse-engineer,' recounts team leader Tim McNerney, 'We understood the disassembled calculator code well enough to simulate it, but Lajos really turned it into "source code" of the highest standards.'"
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Historians Recreate Source Code of First 4004 Application

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  • Volume in drive C is NTSWIM100
      Volume Serial Number is 1CB0-998C

      Directory of c:\WINDOWS\system32

    08/23/2001 10:00 AM 114,688 calc.exe
                                  1 File(s) 114,688 bytes
                                  0 Dir(s) 50,615,652,352 bytes free
    • Re: (Score:3, Interesting)

      by jfengel (409917)
      The original lacked a gui.

      And scientific functions.

      And the ability to convert hex.

      And store/recall.

      The original had 4 functions. This one has at least 40. Would you rather the MS guys spend time seeing if they can force their 114k application down into 10k, or perhaps writing an operating system that doesn't suck?
      • by DragonWriter (970822) on Thursday November 15, 2007 @08:01PM (#21372317)

        Would you rather the MS guys spend time seeing if they can force their 114k application down into 10k, or perhaps writing an operating system that doesn't suck?


        It'd be an improvement if MS did either.
      • Re: (Score:3, Funny)

        by geekoid (135745)
        I'm pretty sure it had a GUI. I'f I were to guess, I'd say it was buttons...possibly with numbers on them.
      • Re: (Score:1, Interesting)

        by Anonymous Coward
        A lot of people don't know this, but Windows' Calc.exe actually implements arbitrary precision math. Don't believe me? Calculate 20000!, or calculate 1/3 and repeatedly multiply by 10 and subtract 3.

        Try that in 1024 bytes :)
        • by megaditto (982598)
          I kind of wish their Excel could do at least 200!
          Or at least that it would do "=(10.1)-10-0.1" properly
          • Re:Only 1024? (Score:5, Interesting)

            by TDRighteo (712858) on Thursday November 15, 2007 @11:57PM (#21374353)
            Floating-point math doesn't fix itself. Let's not be hard on Microsoft when:

            Python 2.5.1 (r251:54863, Oct 30 2007, 13:54:11)
            [GCC 4.1.2 20070925 (Red Hat 4.1.2-33)] on linux2
            Type "help", "copyright", "credits" or "license" for more information.
            >>> 10.1-10-0.1
            -3.6082248300317588e-16
            and...

            $ perl
            printf("%s\n", 10.1-10-0.1);
            -3.60822483003176e-16
            and...

            $ php
            <?php
            echo (10.1-10-0.1);
            ?>
            -3.6082248300318E-16
            Note that the answers vary across languages too...
            • Wow, I didn't know this was so widespread.
            • by tkw954 (709413)
              Same on Matlab and Octave.
            • by raddan (519638)
              The important question is, why is Excel using floating-point for Math? There are plenty of decimal math libraries out there, and I'm sure Microsoft could bang out a pretty good one themselves if they cared enough to do so.
              • by mollymoo (202721)
                Commodity CPUs have hardware support for floating point operations but not decimal operations, which means floating point is much faster than decimal.
                • by raddan (519638)
                  True, but-- we're talking about a spreadsheet. How much number-crunching capability do people need? I suspect that anyone whose computational requirements are sufficient enough to require real numerical horsepower already understands the limitations of floating-point math. Very few normal Excel users do, and I think, for them, a program that meets their expectations-- that is, a program that does arbitrary precision decimal math, accurately-- is more important than speed.
          • Just did that in Ubuntu 7.04's default GNOME calculator and got the answer "-0". Minus Zero. Cool!

            Looks like a lot of software has issues with that equation.

      • The KDE guys have gotten theirs to about 5k with a somewhat more functionality than Window's.
        • by belmolis (702863)

          Yeah, but I bet they do that by relying on shared libraries. The size of the executable doesn't really tell us much these days

          • Whats your point? Windows suddenly doesnt have shared libraries?
            Or is there a reason why the Windows calculator cant use them but the KDE one can? :P
            • by belmolis (702863)

              My point is that executable size is not by itself a useful basis for comparison of the resources used by a program or how easy it was to write. If you compare two stand-alone programs, you can reasonably say that one is more compact than the other, and it will very likely be true that the smaller program required greater skill to write. If you compare a program that makes extensive use of libraries with one that doesn't, you can't make the same comparison. The shorter program was very likely the easier one

          • Re: (Score:3, Informative)

            by ppc_digger (961188)
            They put all the actual code in a shared library:

            # ldd /usr/bin/kcalc
            libkdeinit_kcalc.so => /usr/lib/libkdeinit_kcalc.so (0x00002b1351db8000)
            ...

            # ls -lh /usr/lib/libkdeinit_kcalc.so
            -rw-r--r-- 1 root root 436K 2007-07-03 19:15 /usr/lib/libkdeinit_kcalc.so
  • Those were fun (Score:5, Interesting)

    by certsoft (442059) on Thursday November 15, 2007 @07:46PM (#21372181) Homepage
    Somewhere around 1975 or 1976 I wrote software for a 4004 (using a teletype connected to a modem connected to a mainframe someplace that had the assembler) to run a X-Y table. You would place a wafer with thick-film resistors on it and it would test each one to make sure it was within tolerance and if it wasn't it would mark it with magnetic ink. I think we were probably still using the infamous 1702 EPROMs but there might have been something newer at that time.
    • Re: (Score:3, Interesting)

      by jacquesm (154384)
      somewhere around 1982 a buddy of mine and myself disassembled and commented microsoft's basic for the trs-80 color computer. Then we improved it with tons of new statements via the hook in ram. Documenting a bloody calculator is childs play compared to that and we weren't especially proud of it, just curious.

      • Re: (Score:3, Funny)

        by PopeRatzo (965947) *

        somewhere around 1982 a buddy of mine and myself disassembled and commented microsoft's basic for the trs-80 color computer.
        And you lived to tell the tale.
      • by belmolis (702863)

        Remain where you are. The Software Police will be there momentarily.

      • by Simonetta (207550)
        Thousands of people now and in the future would be interested in studying this code. Please dig up and post this work. Perhaps to one of the 'vintage computer' websites.

        People are still writing assembler code for tiny microprocessors. However now it is being done for very inexpensive microcontrollers like the Atmel AVR and the Microchip PIC. This ICs have all their major components integrated (like program ROM, limited RAM, UARTs, and ADC) and sell for about $1-$2. This business is moving
        • by jacquesm (154384)
          sorry for losing track of the conversation for a while... I don't have any stuff from before roughly
          the middle of '86, and by that time I was well underway in programming in C. Also the storage medium of the day (compact cassette tape) does not lend itself to easy backing up or transfer to new media. A friend of mine (Henri Groeneweg) may have some stuff stashed away from those days but I certainly don't. Two intercontinental moves and a pretty hectic life have parted me with most of my belongings older tha
    • In 1970 the PDP series from DEC, e.g. PDP-8, had an interpreted (and used interactively) language called FOCAL, arrays (even sparse ones), real numbers, usual math and other functions, for loops, if statements blah blah blah... all the usual stuff - the entire interpreter *and* runtime was programmed in a total of 2K instructions (and they were primitive instructions). That was normal for the time.
      • Re: (Score:2, Interesting)

        by cburley (105664)

        However, the PDP-8 was a 12-bit-word minicomputer that was designed for inexpensive general-purpose computing, whereas the 4004 was (IIRC) a "tiny" 4-bit-word microchip designed mainly for numerical control applications.

        I programmed both, the latter for a friend of mine when I was about 15 years old (he later basically got me my first "real" job as a Software Engineer at Pr1me), and the -8 was definitely much easier to program, with a much more powerful instruction set — the code my friend needed wri

        • Re: (Score:2, Interesting)

          I don't remember the 4004 being all *that* primitive but perhaps I'm thinking of the 8008. But even the 4004 was easier to program than an old Univac machine I used that used patch boards to set up the program - LOL. Regardless I wasn't comparing the relative difficulty between the two machines. I was just making the general observation that people were able to put quite sophisticated software on very primitive machines in what today would be considered microscopic amounts of memory. As for Fortran that act
      • Re: (Score:3, Interesting)

        by FrenchSilk (847696)
        And I once wrote a full-featured symbolic assembler in 1579 bytes. Besides symbolic labels, it supported address expressions with +=/* and logical AND/OR, hex and text strings, and a lot more. To the best of my knowledge it is the smallest symbolic assembler ever written. I published and sold it as The Assembler for the VIC-20.
  • but... (Score:1, Offtopic)

    by malraid (592373)
    does it run linux? ... lame!
    • No: 4-bit devices are outside the range of Linux.
      • by sqrt(2) (786011)
        That sounds like a dare to me.
        • Here's a real dare: have linux work on a 1-bit turing machine that has no registers
          • Re: (Score:3, Funny)

            by Anonymous Coward
            Did it, but the ATI drivers still sucked.
            • by McGiraf (196030)
              whah! ah! ah! ah! ah! ah!

              Your comment violated the "postercomment" compression filter. Try less whitespace and/or less repetition. Comment aborted.
  • by Dusty (10872) on Thursday November 15, 2007 @07:53PM (#21372247) Homepage
    You can still run it on the latest Intel x86 chips. ;)
  • "Historians Recreate Source Code of First 404 Error Message"

    (truth be told, quick scanning the headlines, that's what my brain registered)
    • by MooUK (905450)
      That was my first thought too.

      My second was related to a highly rated Bash joke about plums.
  • by gatekeep (122108) on Thursday November 15, 2007 @07:55PM (#21372271)
    "...an authentic calculator simulator..."

    What the hell is an authentic simulator?
  • by Eberlin (570874) on Thursday November 15, 2007 @08:07PM (#21372365) Homepage
    Quick, someone send this over to the folks who wrote Excel!
  • Hello world!
  • by geekoid (135745) <dadinportland.yahoo@com> on Thursday November 15, 2007 @08:11PM (#21372405) Homepage Journal
    58008
    • Re: (Score:1, Funny)

      by Anonymous Coward
      Better than 55318008
  • Commander Keen (Score:5, Interesting)

    by QuantumG (50515) <qg@biodome.org> on Thursday November 15, 2007 @08:16PM (#21372451) Homepage Journal
    I once reverse engineered the classic id software game Commander Keen. John Carmack did some cool stuff in that code.. each sprite had two function pointers in it, one was called when the sprite came into contact with another sprite, the other was called every frame to animate the sprite (he called it the "think" function). When you killed a monster the sprite was replaced with a "body" which was just like a sprite but had a few less fields (so it took up less memory). One of the neatest things he did was use this exact same framework of sprites and bodies to animate the "static" parts of the game. For example, the color coded doors that you have to get the key cards to open were sprites with a contact function that checked if the player had the right key card, at which time they would "die" and be replaced by a body that had a think function would make them slide out of the way.

    For anyone who would like to take a look, I've put the re-engineered source code [insomnia.org] up.
    • Re: (Score:1, Funny)

      by Anonymous Coward
      How dare you learn something without authorization! This is a clear DMCA violation. Mr. Carmack's lawyers are on the way to your house now to execute you...errr, I mean execute their warrant to take all your computers and reclaim the code you stole. And you're distrubuting it too! Well now you're also a pirate. You're going away for a long time.
      • by QuantumG (50515)
        Ha! What in the world makes you think Carmack still has copyright over this code? Last I heard, Tom Hall had the rights.

    • Re:Commander Keen (Score:5, Interesting)

      by Cheesey (70139) on Thursday November 15, 2007 @08:52PM (#21372789)
      Carmack's code is always interesting. Most famously, there's the infamous square root approximation from Quake [codemaestro.com]. But I'm still impressed by the original Doom render loop, with it's self-modifying code.

      The loop is drawing columns (vertical slivers of wall). It needs to interpolate between two things: the input wall texture, and the output part of the screen. Carmack uses something like Bresenham's line drawing algorithm to do this, but because the 386 has such a limited register set, he stores the fractional increment in an immediate attached to the "addl" instruction:

      doubleloop:
          movl ecx,ebp // begin calculating third pixel
      patch1:
          addl ebp,12345678h // advance frac pointer
          movb [edi],al // write first pixel
          shrl ecx,25 // finish calculation for third pixel
          movl edx,ebp // begin calculating fourth pixel
      patch2:
          addl ebp,12345678h // advance frac pointer
          movl [edi+SCREENWIDTH],bl // write second pixel
          shrl edx,25 // finish calculation for fourth pixel
          movb al,[esi+ecx] // get third pixel
          addl edi,SCREENWIDTH*2 // advance to third pixel destination
          movb bl,[esi+edx] // get fourth pixel
          decl [loopcount] // done with loop?
          movb al,[eax] // color translate third pixel
          movb bl,[ebx] // color translate fourth pixel
          jnz doubleloop
      and elsewhere... :)

      movl ebx,[_dc_iscale]
          shll ebx,9
          movl eax,OFFSET patch1+2 // convice tasm to modify code...
          movl [eax],ebx
      A similarly impressive trick is used to draw floors, where 3D interpolation is required because each texture needs to be crossed diagonally, not vertically. I never understood how Doom drew floors until I looked at the code, and I still think it's deep magic. And that's without even mentioning the BSP code!
      • Would you mine annotating this a bit more? I'm not that familiar with 386 assembly, thanks.
        • by Cheesey (70139)
          The self-modifying code parts have already been described by Hal Porter, but he didn't explain how the algorithm actually works.

          Registers: ebp holds a fixed point integer which represents a position within the column. 25 bits hold the fractional part. For each pixel, esi holds the memory offset of the column texture. eax and ebx hold the memory offset of the colour translation table, which is used for lighting effects. This address has to be aligned to a 256 byte boundary for reasons that will become clear.
      • "Carmack's code is always interesting. Most famously, there's the infamous square root approximation from Quake."

        That is indeed impressive code, but John claims he didn't write it. In fact, nobody at id has claimed authorship of it. It was speculated that perhaps Michael Abrash wrote it, but he denies authorship as well. My speculation is that it was a cool snippet of code floating around the public domain, and somebody at id had the good judgment to realize that it was significantly faster than the stan
    • by pragma_x (644215)
      Now that's an interesting tidbit. So I guess in a sense Keen can claim some amount of intellectual heritage to Quake?

      Here's what I'm driving at: I did a rather deep survey of some Quake2 code about 10 years ago and found that it too called the animation control routines "think" functions. Same kind of hackery there too: structs with functions attached.

      The part I liked the most (in Q2) was where the save routine simply copied the entire array of game entities to disk as one big slab of bits, taking care to
  • by compumike (454538) on Thursday November 15, 2007 @08:26PM (#21372543) Homepage
    Take a look at this set of videos from MIT's 6.004 Computation Structures [mit.edu] class. They basically walk through the design of a simple 32-bit CPU from transistors, to gates, to functional blocks, to a full processor.

    Anyway, reading about how hard it was to recreate the source code from the 4004 makes me wonder how easily we could find source code for some apps from even a decade ago. Lots of companies have gone bankrupt / discontinued products / been sold / etc, and we all know that lots of people aren't good about backing up their code. It's neat to go to the Linux Kernel Archives and look at the Historic Linux sources [kernel.org].

    --
    Educational microcontroller kits for the digital generation. [nerdkits.com]
    • Re: (Score:1, Offtopic)

      by Danny Rathjens (8471)
      Can you please put your advertisement in the proper signature field in your preferences instead of pasting it into the body of your message with the fake -- delimiter to fool people(search engines?) into thinking it is a normal sig?
      Those of us with signature viewing disabled will still see the link to your website above your comment.
    • Simple -- buy a wire wrap tool, a breadboard kit and the TTL Handbook.

      Can't find them? Should be on the shelf there somewhere. There must be a lot of old kit you can use to desolder TTL circuit components. You may need to build a Heathkit http://en.wikipedia.org/wiki/Heathkit/ [wikipedia.org] dual-trace CRO first though.

      Geez I'm getting old.

  • Amazing! (Score:5, Insightful)

    by Reality Master 101 (179095) <RealityMaster101@NOSpam.gmail.com> on Thursday November 15, 2007 @08:28PM (#21372557) Homepage Journal

    'He is an amazing reverse-engineer,' recounts team leader Tim McNerney, 'We understood the disassembled calculator code well enough to simulate it, but Lajos really turned it into "source code" of the highest standards.'

    No disrespect to Lajos, but have we really fallen so far in programming standards that it's considered "amazing" to disassemble a 1024 byte program? Back in my day (and stay the hell off my lawn!) we used to disassemble programs all the time. I reverse engineered the operating system for a computer I developed for because we wanted to hook into places that weren't accessible.

    Disassembly is apparently a lost art in these decadent days of some programmers never using anything but scripting languages (e.g., Java, Python, Perl) and having no clue what goes on under the hood.

    • No disrespect to Lajos, but have we really fallen so far in programming standards that it's considered "amazing" to disassemble a 1024 byte program?

      Good question. Lets look at the excerpt from TFA included in TFS:

      'He is an amazing reverse-engineer,' recounts team leader Tim McNerney, 'We understood the disassembled calculator code well enough to simulate it, but Lajos really turned it into "source code" of the highest standards.'

      Sure looks to me that what Lajos is being credited with isn't the disassembl

      • 'He is an amazing reverse-engineer,' recounts team leader Tim McNerney, 'We understood the disassembled calculator code well enough to simulate it, but Lajos really turned it into "source code" of the highest standards.' [...] Sure looks to me that what Lajos is being credited with isn't the disassembly, at all.

        I disagree, McNerney seems to be saying that they understood the machine language well enough to simulate the calculator, but Lajos disassembled and commented the source code so that they underst

        • Re:Amazing! (Score:4, Insightful)

          by be-fan (61476) on Thursday November 15, 2007 @09:44PM (#21373275)
          "Programs must be written for people to read, and only incidentally for machines to execute." - Abelson & Susman

          From a theoretical point of view, assembly knowledge isn't particularly useful because it doesn't lend itself to rigorous analysis (the "science" part of "computer science"). From a practical point of view, since very few programs are written in assembly language anymore, knowledge of it has limited utility. Further, from a practical point of view, I'd much rather deal with a programmer who can explain his work in terms of data structures and algorithms than one that is stuck thinking in terms of registers and memory locations.

          There is certainly a place for assembly knowledge*. It's just a niche, and not a particularly important one anymore. Meanwhile, there are lots and lots of diverse applications for the theory they teach you in those classes instead of assembly. In my own work, I've had to bust out the graph theory way more often than I've had to bust out my knowledge of asm tricks for fast line-rendering...

          *) Interestingly enough, one of those places is inside the language runtimes of high-level languages. There are usually lots of neat tricks inside those things (eg: using the NaN space of double-precision floats to store unions of floats and 51-bit integers without extra variant tags!)
        • McNerney seems to be saying that they understood the machine language well enough to simulate the calculator


          Its odd that he would say "disassembled code" if he meant "machine language".
      • Re:Amazing! (Score:4, Interesting)

        by dmonahan (957638) on Thursday November 15, 2007 @09:31PM (#21373175)
        Sometime in the early 70s, a Honeywell division, one of our steady clients, called with a strange request. They had built a small number of special machines for the Navy. Now the Navy wanted more. Honeywell had the circuit drawings and the bootable tape (which they got from the Navy). They had no documentation (not even the instruction set). They asked us to rebuild the code. We did. Dick.
    • No disrespect to Lajos, but have we really fallen so far in programming standards that it's considered "amazing" to disassemble a 1024 byte program?

      I dunno. I'm certain I could look at any given one kilobyte program and tell you "that opcode is adding the results of those two", but it takes a certain kind of cleverness to figure out why it's using opcodes for constants and how they manage to pack a shift-right-branch-if-odd into two bytes plus an index register.

      See also "The Story Of Mel" [pbm.com]. Now imagine being tasked with turning that into readable, understandable code. That's the real accomplishment.

      • by Jay L (74152)
        Now imagine being tasked with turning that into readable, understandable code.

        Don't have to imagine. Well, that's not quite true; I've never done anything on the scale of drum timing. But "disassembly" isn't just "opcode 53 adds X to the accumulator"; that part's (nearly) always been easy and automated. The hard part is going through, figuring out what every single memory location is for, making up your own consistent label for it, understanding the self-modifying part of the code, etc. Disassembly is a
        • Been there, done all of that. And no, what he did isn't extremely difficult or novel, but I still give him credit for pulling off nice work.

    • Re: (Score:2, Funny)

      by Juliemac (892781)
      The company I work for hired 4 programmers (from out of country) to re-work existing code and clear out known bugs. As a result, the log in no longer worked. 2 weeks later, the testers could get in, but none of the drop down boxes worked and more. Problem is they are wizards. They click and drop code with out understanding what the code does. The US trained programmers cant get the time of day from the head of IT.
    • This is not your typical disassembly job.

      If you read the fine source code linked to in the article, you would see that not only is the machine code disassembled, but the virtual machine that it implements is fully described. That's not a trivial exercise.

    • No disrespect to Lajos, but have we really fallen so far in programming standards that it's considered "amazing" to disassemble a 1024 byte program? Back in my day (and stay the hell off my lawn!) we used to disassemble programs all the time. I reverse engineered the operating system for a computer I developed for because we wanted to hook into places that weren't accessible.

      It's one thing to disassemble a 64Kb program handwritten in assembly, or using a compiler from a relatively low-level language (such

  • So you are saying that nobody had the source backed up anywhere? We have come so far, yet haven't gone very far at all...
  • 'leet speak first turned the world upside down as a joke about "BOOBLESS". I wonder if the 4004 could run a softporn text adventure game like that.
  • [reminisce] Back in 1972 I did the first uP project at Cornell using a 4004. No assembler, no emulator, not even a PROM programmer. Just a list of op-codes and a sheet of paper that I wrote H or L for every bit of the PROM. That got sent to a electronics distributor that would program the part. Unfortunately, I can't claim to have done the first OPERATING uP project at Cornell! [/reminisce]
  • by lseltzer (311306) on Thursday November 15, 2007 @09:13PM (#21372967)
    I found a buffer overflow. Exploit code to follow...
  • File version 6.0.6000.16386
    Size: 172 KB (176,128 bytes)

    kinda puts things in perspective, doesn't it?

    ah, "progress"
  • I have the original 4004 reference guide (blue cover), scored during an early Wescon convention in 1970. I looked at this and said -- "Oooh, a whole hexadecimal digit on a single chip. That's going to change things."

    People used to consider square wave logic charts a programming tool back then, too.

  • by drachenstern (160456) <drachenstern@gmail.com> on Friday November 16, 2007 @01:29AM (#21375075) Journal
    How has no one mentioned this yet? - Don't blame me too much, I just copied and pasted from: http://downlode.org/Etext/power.html [downlode.org]

    The Feeling Of Power
    by Isaac Asimov

    Jehan Shuman was used to dealing with the men in authority on long-embattled earth. He was only a civilian but he originated programming patterns that resulted in self-directing war computers of the highest sort. Generals, consequently listened to him. Heads of congressional committees too.

    There was one of each in the special lounge of New Pentagon. General Weider was space-burned and had a small mouth puckered almost into a cipher. He smoked Denebian tobacco with the air of one whose patriotism was so notorious, he could be allowed such liberties.

    Shuman, tall, distinguished, and Programmer-first-class, faced them fearlessly.

    He said, "This, gentlemen, is Myron Aub."

    "The one with the unusual gift that you discovered quite by accident," said Congressman Brant placidly. "Ah." He inspected the little man with the egg-bald head with amiable curiosity.

    The little man, in return, twisted the fingers of his hands anxiously. He had never been near such great men before. He was only an aging low-grade technician who had long ago failed all tests designed to smoke out the gifted ones among mankind and had settled into the rut of unskilled labor. There was just this hobby of his that the great Programmer had found out about and was now making such a frightening fuss over.

    General Weider said, "I find this atmosphere of mystery childish."

    "You won't in a moment," said Shuman. "This is not something we can leak to the firstcomer. Aub!" There was something imperative about his manner of biting off that one-syllable name, but then he was a great Programmer speaking to a mere technician. "Aub! How much is nine times seven?"

    Aub hesitated a moment. His pale eyes glimmered with a feeble anxiety.

    "Sixty-three," he said.

    Congressman Brant lifted his eyebrows. "Is that right?"

    "Check it for yourself, Congressman."

    The congressman took out his pocket computer, nudged the milled edges twice, looked at its face as it lay there in the palm of his hand, and put it back. He said, "Is this the gift you brought us here to demonstrate. An illusionist?"

    "More than that, sir. Aub has memorized a few operations and with them he computes on paper."

    "A paper computer?" said the general. He looked pained.

    "No, sir," said Shuman patiently. "Not a paper computer. Simply a piece of paper. General, would you be so kind as to suggest a number?"

    "Seventeen," said the general.

    "And you, Congressman?"

    "Twenty-three."

    "Good! Aub, multiply those numbers, and please show the gentlemen your manner of doing it."

    "Yes, Programmer," said Aub, ducking his head. He fished a small pad out of one shirt pocket and an artist's hairline stylus out of the other. His forehead corrugated as he made painstaking marks on the paper.

    General Weider interrupted him sharply. "Let's see that."

    Aub passed him the paper, and Weider said, "Well, it looks like the figure seventeen."

    Congressman Brant nodded and said, "So it does, but I suppose anyone can copy figures off a computer. I think I could make a passable seventeen myself, even without practice."

    "If you will let Aub continue, gentlemen," said Shuman without heat.

    Aub continued, his hand trembling a little. Finally he said in a low voice, "The answer is three hundred and ninety-one."

    Congressman Brant took out his computer a second time and flicked it. "By Godfrey, so it is. How did he guess?"

    "No guess, Congressman," said Shuman. "He computed that result. He did it on this sheet of paper."

    "Humbug," said the general impatiently. "A computer is one thing and marks on a paper are another."

    "Explain, Aub," said Shuman.

    "Yes, Programmer. Well, gentlemen, I write down seventeen, and just undernea
  • 1024 Bytes? Bah! (Score:3, Interesting)

    by LS (57954) on Friday November 16, 2007 @05:01AM (#21376041) Homepage
    How about 256 bytes for a 3D rotating parallax tunnel fly-through [256b.com] !!!

    LS

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