A multiplexer is a logic circuit that

Concept — A multiplexer (MUX), also called a data selector, is a combinational circuit built for many-to-one data steering. It carries 2n data input lines, n select lines and exactly one output line. The binary code applied to the select lines decides which single data line is connected to that output at a given instant; the data lines carry information, the select lines carry the choice.

Application — trace the standard 4-to-1 device:

1. Label the data inputs D0, D1, D2, D3 and the select lines S1, S0.

2. Each select combination enables exactly one AND gate: S1'S0' enables D0, S1'S0 enables D1, S1S0' enables D2, and S1S0 enables D3.

3. The four AND outputs are OR-ed together onto one line, giving Y = S1'S0'D0 + S1'S0D1 + S1S0'D2 + S1S0D3.

4. For any select code exactly one product term survives, so all four data lines share the same single output line.

Cross-check — contrast the neighbouring input/output shapes:

• One input to several outputs is the reverse operation, performed by a demultiplexer, where the select code picks the destination rather than the source.

• Many inputs to many outputs describes a general combinational network such as a decoder array or a code converter, in which every output is its own Boolean function.

• One input to one output describes a single-line element such as a buffer or an inverter, which has no lines to select between.

Result — a multiplexer accepts many inputs and gives one output.