Formula & Analytical Engine by Charles Babbage — Translation, notes and first computer program by Ada Lovelace, 1843
| Op | Nature | Act on | Receive | Result |
|---|
Superscript indicates how many times a variable has been written — Ada's own notation: 1V₄ is the first value given to V₄.
Charles Babbage designed the Analytical Engine (1837) as a steam-powered general-purpose calculator. It possessed a Store for holding numbers on 25 columns of wheels (V₀–V₂₄) and a Mill for arithmetic. Operations were directed by punched cards, after Jacquard looms.
Babbage derived the formula for generating Bernoulli numbers recursively, but never completed the machine. He gave Ada the bare mathematical series to test the Engine's capabilities.
In translating Menabrea's memoir, Ada Lovelace appended Note G — a complete, step-by-step trace of how the Engine would compute the 7th Bernoulli number. She introduced a looping structure, conditional branching, and the concept that a machine could manipulate symbols, not merely numbers.
Her table of 25 operations is recognized as the first published computer program. By following it, the Engine would, without human intervention, produce B₇ = −1/30, demonstrating software's power over hardware.