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7.21 Realize the following function as a minimum two-level NAND-gate circuit and as a minimum two-level NOR-gate circuit. (f) f(a,b,c,d) = M(1, 3, 10, 11, 13, 14, 15).IID(4,6)

7.21 Realize the following function as a minimum two-level NAND-gate circuit and as a minimum two-level NOR-gate circuit. (f) f(a,b,c,d) = M(1, 3, 10, 11, 13, 14, 15).IID(4,6)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Problem Statement 7.21 Realize the following function as a minimum two-level NAND-gate circuit and as a minimum two-level NOR-gate circuit. ### Function Details \[ f(a, b, c, d) = \prod M(1, 3, 10, 11, 13, 14, 15) \cdot \prod D(4, 6) \] #### Explanation This function is expressed in terms of maxterms (denoted by \( \prod M \)) and don't-care conditions (denoted by \( \prod D \)). - **Maxterms \(\prod M\)**: These represent the product of sums for the binary inputs, where the function output is '0'. In this case, the function should be '0' for binary representations of the numbers 1, 3, 10, 11, 13, 14, and 15. - **Don't-Care Conditions \(\prod D\)**: These are conditions where the function can be either '0' or '1', providing flexibility for optimization. The don't-care conditions here are for the numbers 4 and 6. This expression needs to be implemented using both NAND-gate and NOR-gate logic circuits at a minimum of two levels, considering the constraints provided by the maxterms and don't-care conditions.
Transcribed Image Text:### Problem Statement 7.21 Realize the following function as a minimum two-level NAND-gate circuit and as a minimum two-level NOR-gate circuit. ### Function Details \[ f(a, b, c, d) = \prod M(1, 3, 10, 11, 13, 14, 15) \cdot \prod D(4, 6) \] #### Explanation This function is expressed in terms of maxterms (denoted by \( \prod M \)) and don't-care conditions (denoted by \( \prod D \)). - **Maxterms \(\prod M\)**: These represent the product of sums for the binary inputs, where the function output is '0'. In this case, the function should be '0' for binary representations of the numbers 1, 3, 10, 11, 13, 14, and 15. - **Don't-Care Conditions \(\prod D\)**: These are conditions where the function can be either '0' or '1', providing flexibility for optimization. The don't-care conditions here are for the numbers 4 and 6. This expression needs to be implemented using both NAND-gate and NOR-gate logic circuits at a minimum of two levels, considering the constraints provided by the maxterms and don't-care conditions.
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