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2-input MUX

Let us consider a 2-to-1 multiplexer where:

  • A and B are the two inputs,
  • S0 is the selector input, and
  • C is the output.

We want S to choose A as the output when it is low and B when it is high. That means that C should be the same as A when S is low and the same as B when it is high.

Let us draw a truth table to show that:

S A B C
0 1 1 1
1 0 1
0 1 0
0 0 0
1 1 1 1
1 0 0
0 1 1
0 0 0

We can produce a Boolean expression for this truth table by making an equation that expresses the relationship of the input combinations that produce a high output.

Each input combination has to be ANDed together and then those combinations are ORed together (as any one of them will give a high output).

Boolean laws are then used to simplify the expression.

This 2-to-1 multiplexer would need to be wired up using 2 AND gates, an OR gate, and a NOT gate.

If we put the Boolean expression for this MUX into words it simply says C will be the same as A if S is low and the same as B if the input of S in high. It is therefore simple to produce an expression for any input MUX, we just need enough states so S. This is accomplished by having n select lines for 2n input lines.

See here for a 4-input MUX