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Realize the function f(a, b, c, d, e) = Em (6, 7, 9, 11, 12, 13, 16, 17, 18, 20, 21, 23, 25, 28) using a 16-to-1 MUX with control inputs b, c, d, and e. Each data input should be 0, 1, a, or a'. (Hint: start with a minterm expansion off and combine minterms to eliminate a and a' where possible.)

Realize the function f(a, b, c, d, e) = Em (6, 7, 9, 11, 12, 13, 16, 17, 18, 20, 21, 23, 25, 28) using a 16-to-1 MUX with control inputs b, c, d, and e. Each data input should be 0, 1, a, or a'. (Hint: start with a minterm expansion off and combine minterms to eliminate a and a' where possible.)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Problem Statement:** Realize the function \( f(a, b, c, d, e) = \Sigma m(6, 7, 9, 11, 12, 13, 16, 17, 18, 20, 21, 23, 25, 28) \) using a 16-to-1 MUX with control inputs \( b, c, d, \) and \( e \). Each data input should be 0, 1, \( a, \) or \( a' \). **Hint:** Start with a minterm expansion of \( f \) and combine minterms to eliminate \( a \) and \( a' \) where possible. --- **Explanation:** You are tasked with implementing a given Boolean function using a multiplexer (MUX). The function is specified by its minterms, which are the binary combinations of the variables that make the function output 1. The aim is to simplify the logic design by choosing appropriate data inputs for the MUX to minimize complexity. 1. **Understanding Minterms:** A minterm is a specific combination of variables that yields a true output for the Boolean function. For example, \( \Sigma m(6) \) means that when the binary representation of the control inputs equals the decimal number 6, the output should be 1. 2. **Using a 16-to-1 MUX:** A 16-to-1 MUX has 16 data inputs and 4 control inputs, which aligns perfectly with the indices provided (0 to 15 for the control inputs). The challenge is to map each minterm to 0, 1, \( a, \) or \( a' \) in such a way that the function in terms of \( a \) and the selected control inputs is minimized. 3. **Logical Simplification:** The hint suggests starting with the minterm expansion and combining minterms to simplify. Specifically, you will attempt to express certain combinations in terms of \( a \) and \( a' \). 4. **Elimination Strategy:** This involves recognizing patterns where the values of \( a \) and \( a' \) can either directly satisfy the condition or be used to reduce complexity by grouping similar minterms together, focusing on minimizing hardware requirements. 5. **Goal:** Efficiently determine the data inputs for the 16-to-1
Transcribed Image Text:**Problem Statement:** Realize the function \( f(a, b, c, d, e) = \Sigma m(6, 7, 9, 11, 12, 13, 16, 17, 18, 20, 21, 23, 25, 28) \) using a 16-to-1 MUX with control inputs \( b, c, d, \) and \( e \). Each data input should be 0, 1, \( a, \) or \( a' \). **Hint:** Start with a minterm expansion of \( f \) and combine minterms to eliminate \( a \) and \( a' \) where possible. --- **Explanation:** You are tasked with implementing a given Boolean function using a multiplexer (MUX). The function is specified by its minterms, which are the binary combinations of the variables that make the function output 1. The aim is to simplify the logic design by choosing appropriate data inputs for the MUX to minimize complexity. 1. **Understanding Minterms:** A minterm is a specific combination of variables that yields a true output for the Boolean function. For example, \( \Sigma m(6) \) means that when the binary representation of the control inputs equals the decimal number 6, the output should be 1. 2. **Using a 16-to-1 MUX:** A 16-to-1 MUX has 16 data inputs and 4 control inputs, which aligns perfectly with the indices provided (0 to 15 for the control inputs). The challenge is to map each minterm to 0, 1, \( a, \) or \( a' \) in such a way that the function in terms of \( a \) and the selected control inputs is minimized. 3. **Logical Simplification:** The hint suggests starting with the minterm expansion and combining minterms to simplify. Specifically, you will attempt to express certain combinations in terms of \( a \) and \( a' \). 4. **Elimination Strategy:** This involves recognizing patterns where the values of \( a \) and \( a' \) can either directly satisfy the condition or be used to reduce complexity by grouping similar minterms together, focusing on minimizing hardware requirements. 5. **Goal:** Efficiently determine the data inputs for the 16-to-1
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