One output, two sources
A processor constantly chooses between values: the result of an add or the result of a subtract, data from cache or data from memory. The circuit that chooses is the multiplexer, or MUX.

A 2-to-1 MUX has:
- Two data inputs,
aandb - One select input,
s - One output,
y
The rule: s = 0 routes a to the output. s = 1 routes b.
