The 2-to-1 MUX

Choosing between two inputs

Figure: A trapezoid 2-to-1 MUX symbol with two data inputs a and b stacked on the left, one output y on the right

A multiplexer (MUX) is a selector switch built from gates. The 2-to-1 MUX is the smallest one:

• Two data inputs, a and b.
• One select line, s.
• One output, y.

The rule: when s = 0 the output copies a, and when s = 1 it copies b. Selection shows up everywhere in a processor, choosing which value flows next, so this block is worth knowing cold.

Select picks the source

Because the MUX ignores one input at a time, the behaviour compresses to two rows:

Written as a full truth table over all three inputs:

The x is a don't care: when s = 0 the value of b cannot change the output, and when s = 1 the value of a cannot.

From table to equation

You already have the tool to turn that table into gates. Take the two rows where $y = 1$ and write a product for each:

• Route a: the term $a \cdot \overline{s}$ passes a while s = 0.
• Route b: the term $b \cdot s$ passes while .