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4 to 1 MUX

It is simple to produce a Boolean expression for any input MUX, we just need enough states of S. This is accomplished by having n select lines for 2n input lines.

Here we have 4 inputs lines so we need 2 select lines.

If we put the requirements for this MUX into words we would simply say E will be the same as A if both S0 and S1 are low, the same as B if S0 is low and S1 is high, the same as C if S0 is high and S1 is low and the same as D if both S0 and S1 are high. Therefore the Boolean expression for it will be:

The symbol for this MUX would be:

Instead of having lots of different input MUXs we can use 2-input ones hierarchically.

Using three two-input multiplexers as in the diagram above we can produce a 4-input MUX.

We input A and B into one MUX and C and D into another. We control the output of both of those MUXs with with signal S0.

  • If S0 is low then the output of the first hierarcical layer will be A in the upper multiplexer and C in the lower one.
  • If S0 is high then the output will be B and D.

The output of those two multiplexers forms the inputs into a further MUX that has its output contolled by the choice of signal S1

The state of S1 will determine which of the outputs from the first wave of multiplexers finally gets through. If it is low the output will be from the topmost MUX and if it is high it will be from the bottom one.

I told you it was 'Simples!'