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