DIGITAL ELECTRONICS

4-to-1 Multiplexer Boolean Function

A multiplexer can implement a Boolean function by wiring its data inputs to fixed logic levels or variables. In this example, A and B are the select inputs of a 4-to-1 multiplexer. The data pattern 0, 1, 1, 0 makes the output high exactly when A and B differ, which is the XOR function. Reading the select combinations as truth-table addresses makes the method straightforward to verify. Change the four fixed data inputs to implement a different two-variable function without changing the multiplexer structure.

UPDATED 2026-09-24

TYPECircuit

EXAMPLE4-to-1 Multiplexer Boolean Function

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CASE ANALYSIS

Scenario

Implementing XOR with a multiplexer truth table.

Key decisions

Select inputs: A and B address the truth table rows.
Fixed data inputs: The 0, 1, 1, 0 pattern encodes XOR.
Function output: F is the resulting Boolean function.

When to reuse this

Use this to show how a MUX can realize a Boolean truth table.

FAQ

Frequently asked questions

How does a MUX implement XOR?01

Its data inputs are wired to the XOR truth-table values 0, 1, 1 and 0.

Which signals act as variables?02

A and B are the select inputs and therefore address the truth-table entries.

Can this implement XNOR?03

Yes, use the inverted data pattern 1, 0, 0 and 1.

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