6 An 8x1 multiplexer has inputs A B And C connected to the s

6. An 8x1 multiplexer has inputs A, B, And C connected to the selection inputs S2, S1, and S0, respectively. The data inputs I0 through I7 are as follows I1 = I2 = 0, I3 = I7 = 1; I4 = I5 = D; and I0 = I6 = D’; Determine the Boolean function that the multiplexer implements.

Solution

Answer :-

A 16-to-1 multiplexer can be constructed from two 8-to-1 multiplexers having an ENABLE input. The ENABLE input is taken as the fourth selection variable occupying the MSB position.

The complete logic circuit diagram. IC 74151 can be used to implement an 8-to-1 multiplexer. The circuit functions as follows. When S3 is in logic ‘0’ state, the upper multiplexer is enabled and the lower multiplexer is disabled.

If we recall the truth table of a four-variable Boolean function, S3 would be ‘0’ for the first eight entries and ‘1’ for the remaining eight entries.

Therefore, when S3 = 0 the final output will be any of the inputs from D0 to D7, depending upon the logic status of S2, S1 and S0. Similarly, when S3 = 1 the final output will be any of the inputs from D8 to D15, again depending upon the logic status of S2, S1 and S0. The circuit therefore implements the truth table of a 16-to-1 multiplexer.