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## Multiplexer (MUX)

An MUX has N inputs and one output. Under the control of selection signals, one of the inputs is passed on to the output.

First consider the truth table of a 2x1 MUX with three inputs , and and only one output :

This truth table can be simplified by allowing Don't-cares in the table:

Finally, if we allow variables in the truth table (variable-entered map VEM), the truth table can be further simplified to be

A 4x1 MUX has inputs , , and , and selections and . Its output is one of the four inputs depending on the selections. The truth table for a 4x1 MUX:

This truth table can be simplified by the VEM:

We see that each minterm of the two selection bits corresponds to an input:

where is the ith minterm of .

This approach can be generalized to any MUX of inputs with selections.

Note: The AND gates used here can be conceptively considered as guarded gates. To see this, consider an AND function :

Only when both signals and are 1, will the output be the same as input signal . In other words, only when both guards'' and agree, can the signal go through the gate.

Next: MUX for combinational logic Up: Combinational Circuits Previous: Full Adder
Ruye Wang 2014-02-28