Question

A combinational circuit is specified by the following three Boolean functions:

F1(A,B,C)=Σ(1,4,6)F2(A,B,C)=Σ(3,5)F3(A,B,C)=Σ(2,4,6,7)\begin{aligned} &F_{1}(A, B, C)=\Sigma(1,4,6)\\ &\begin{array}{l} F_{2}(A, B, C)=\Sigma(3,5) \\ F_{3}(A, B, C)=\Sigma(2,4,6,7) \end{array} \end{aligned}

Implement the circuit with a decoder constructed with NAND gates and NAND or AND gates connected to the decoder outputs. Use a block diagram for the decoder. Minimize the number of inputs in the external gates.

Solutions

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Requirements: It is required to implement the circuit specified by the following Boolean functions:

F1(A,B,C)=(1,4,6)F2(A,B,C)=(3,5)F3(A,B,C)=(2,4,6,7)\begin{aligned} F_1 (A,B,C) &= \sum (1,4,6)\\ F_2(A,B,C) &= \sum (3,5)\\ F_3 (A,B,C) &= \sum (2,4,6,7) \end{aligned}

using a decoder constructed with NAND gates (similar to Fig. 4.19) and NAND or AND gates connected to the decoder outputs.

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