A combinational circuit is defined by F = Σ0, 2, 5, 6, 7. Hardware implement the Boolean function F with a suitable decoder and an external OR/NOR gate having the minimum number of inputs.

Question

A combinational circuit is defined by [latex]F = Σ0, 2, 5, 6, 7[/latex]. Hardware implement the Boolean function F with a suitable decoder and an external OR/NOR gate having the minimum number of inputs.

Accepted Answer

The given Boolean function has five three-variable minterms. This implies that the function can be
implemented with a [latex]3-to-8[/latex] line decoder and a five-input OR gate. Also, [latex]\overline{F}[/latex] will have only three three-variable minterms, which means that [latex]F[/latex] could also be implemented by considering minterms corresponding to the complement function and using a three-input NOR gate at the output. The second option uses a NOR gate with fewer inputs and therefore is used instead. [latex]F=\sum{0,2,5,6,7}[/latex] . Therefore, [latex]\overline{F} =\sum{1,3,4} [/latex]. Figure 8.23 shows the hardware implementation of Boolean function [latex]F[/latex].

Question 8.7: A combinational circuit is defined by F = Σ0, 2, 5, 6, 7. Ha...

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