🌡️ Thermometer Code

Thermometer code is a unary-style binary encoding where the number of active bits (1s) directly represents the value

It resembles a rising column in a thermometer——more 1s mean a higher value——thusly named

Notes

Thermometer code is not unary in the purist way since it uses 0s, but it still counts in unary, thusly named unary-style

It always counts in one direction, either up or down i.e. monotonic. Thus, there is no such thing as 0s appearing between 1s

Application is in fast, simple comparisons and analog signal quantization

📘 Definition

A binary vector where the first $N$ bits are $1$, and the remaining bits are $0$, representing the value $N$.

• The 1s form a contiguous block at the start.
• There are no 0s between 1s—gaps are invalid.

It can count up in either direction, left-to-right or right-to-left, it just has to count in a single direction