Gray Code Table Generator

In ordinary binary counting, going from 7 to 8 changes four bits at once: 0111 becomes 1000. In a real circuit those bits do not switch at the same instant, and during the transition the reading can be anything — including a number matching neither value. Gray code removes the problem at the root: between two consecutive values, exactly one bit changes.

Choose the number of bits, from 1 to 8, and the page builds the full table with the decimal, ordinary binary and matching Gray value. The conversion is surprisingly simple: take the exclusive-or of the number with itself shifted one bit right. The way back is less direct, because each bit of the result depends on all the more significant bits already decoded.

Where this genuinely matters is in a rotary encoder, the disc reporting a shaft's position. With ordinary binary, reading at the wrong instant returns an absurd position; with Gray, the worst case is reading a neighbour. The same idea appears in Karnaugh maps, where Gray ordering makes adjacent cells differ in a single variable, and in analogue-to-digital converters.