• Ken Shirriff on Clive Sinclair's passing

    From Eli the Bearded@21:1/5 to All on Fri Sep 17 19:08:38 2021
    Ken Shirriff's reverse engineering of chips has been discussed here
    before. This particular exercise is not recent, but is now timely
    with the passing of Clive Sinclair this week.

    Most of these have one or more images, view on twitter to see them.

    https://twitter.com/kenshirriff/status/1438660221493153792
    Sir Clive Sinclair, the English entrepreneur responsible for
    computers such as the ZX81, has passed away. One of his most
    interesting products was the budget Sinclair Scientific calculator
    (1974). I wrote a simulator that runs the calculator's actual code.

    The Sinclair Scientific calculator was an amazing hack, repurposing a
    4-function calculator chip with 320 words of code to implement trig
    and logs. My favorite part is the constants like π and e printed on
    the case since there wasn't room in ROM to hold them.

    I reverse-engineered the calculator chip from Visual6502 and
    @johndmcmaster's photos, reading out the bits of the code that
    implemented the operations. From this, I reverse-engineered what
    the code was doing.
    https://siliconpr0n.org/archive/doku.php?id=mcmaster:ti:tmc0805nc

    The secret to the calculator's compact code was that the algorithms
    were very slow and inaccurate. For example, trig worked by rotating a
    vector by .001 radians until the proper angle was achieved. The
    larger the angle, the slower the operation.
    A diagram showing a vector on a circle, rotated through an angle,
    yielding cos and sin coordinates.

    Log and exponentiation used another trick, basing them on powers of
    .99. This is efficient since X*.99=X-X/100; dividing by 100 is just a
    shift on a decimal calculator. Again, this was slow and inaccurate,
    but used very little code.

    At a time when the HP-35 calculator sold for $395, the Sinclair
    Scientific originally sold for under $120, and a £9.95 kit by the end
    of the year. Despite being very slow and inaccurate, the calculator
    was hugely popular. But at those prices, Sinclair Radionics collapsed
    by 1979.

    The calculator was built around Texas Instruments' TMS0805 chip. This
    strange chip had 11-bit customizable opcodes so I had to
    reverse-engineer the instruction set too, helped by the patent.
    More details at my simulator page: https://righto.com/ti

    The calculator chip patent contained a chip schematic, inconveniently
    chopped into many pages. I made the schematic below by tediously
    pasting them back together.

    That's the story of how Sinclair and team took a calculator chip with
    just 320 words of ROM that could barely support 4-function
    arithmetic, and amazingly crammed trig, log, and exp into it to make
    a budget scientific calculator.
    For more: https://righto.com/sinclair

    Elijah
    ------
    Sir Clive's daughter has said Clive preferred a slide rule

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