Security Techniques

Reversing Sinclair’s amazing 1974 calculator hack

Reversing Sinclair’s amazing 1974 calculator hack: In a hotel room in Texas, Clive Sinclair had a big problem. He wanted to sell a cheap scientific calculator that would grab the market from expensive calculators such as the popular HP-35. Hewlett-Packard had taken two years, 20 engineers, and a million dollars to design the HP-35, which used 5 complex chips and sold for $395. Sinclair’s partnership with calculator manufacturer Bowmar had gone nowhere. Now Texas Instruments offered him an inexpensive calculator chip that could barely do four-function math. Could he use this chip to build a $100 scientific calculator?
Texas Instruments’ engineers said this was impossible – their chip only had 3 storage registers, no subroutine calls, and no storage for constants such as π. The ROM storage in the calculator held only 320 instructions, just enough for basic arithmetic. How could they possibly squeeze any scientific functions into this chip?

Fortunately Clive Sinclair, head of Sinclair Radionics, had a secret weapon – programming whiz and math PhD Nigel Searle. In a few days in Texas, they came up with new algorithms and wrote the code for the world’s first single-chip scientific calculator, somehow programming sine, cosine, tangent, arcsine, arccos, arctan, log, and exponentiation into the chip. The engineers at Texas Instruments were amazed.

How did they do it? Up until now it’s been a mystery. But through reverse engineering, I’ve determined the exact algorithms and implemented a simulator that runs the calculator’s actual code.