23. Multiplexers (Mux): Data Selectors

A Multiplexer (Mux) is a combinational circuit that selects one of several input lines and directs it to a single output line. It acts like a digitally controlled switch.

Mux Terminology

An $N$-to-1 Mux requires $S$ select lines, where $N = 2^S$.

• Input Lines ($D_0, D_1, \dots$): The data lines being selected.
• Select Lines ($S_0, S_1, \dots$): Determines which input is chosen.
• Output Line (Y): The selected input data appears here.

2-to-1 Multiplexer Design

This is the simplest Mux, requiring one select line ($S$).

Logic Equation: $$Y = \overline{S} D_0 + S D_1$$

This circuit requires two AND gates, one inverter (for $\overline{S}$), and one OR gate.

Key Application

Muxes are essential for routing data in CPUs, allowing different components (registers, memory) to share a common bus (data highway).