Multiplexers (MUX)

For logic function realizations, instead of logic gates, Multiplexers can also be used

Consider a boolean function f={1,2,6,7}. Here input variables are A,B,C.

Multiplexer schematic for $8\times 1$ multiplexer is shown in figure 13.1

Figure 13.1: ($8\times 1$) multiplexer implementation of logic function $f$

Depending on the contorl input combination specfic input is connected to the single output of multiplexer.

$$f=\overline{A} \overline{B}C+\overline{A}B\overline{C}+AB\overline{C}+ABC$$ (13.1)

When $8\times 1$ multiplexer is used to implement the above function. We connect boolean logic '1' at the inputs corresponding to control inputs ABC= 1, 2, 4, and 6. For all other input boolean logic '0' is connected.

In case we take a $4\times 1$ multiplexer we can make $BC$ as control input and then determine what should be connected at the inputs of multiplexer as shown below.

$$BC=00 \Rightarrow f=0$$ (13.2)

$$BC=01 \Rightarrow f=\overline{A}$$ (13.3)

$$BC=10 \Rightarrow f=A+\overline{A}=1$$ (13.4)

$$BC=11 \Rightarrow f=A$$ (13.5)

The realization is shown in figure 13.2 using a $4\times 1$ Mux.

Figure 13.2: Multiplexer ($4\times 1$) Implementation