**Realizing a Function Using a 16-to-1 Multiplexer**In this task, we aim to realize the function \( f(a, b, c, d, e) = \sum m(6, 7, 9, 11, 12, 13, 16, 17, 18, 20, 21, 23, 25, 28) \) using a 16-to-1 multiplexer with control inputs \( b, c, d, \) and \( e \). Each data input should be either 0, 1, \( a \), or \( a' \).**Instructions:**- **Step 1: Minterm Expansion** Begin by expanding the given function into its mintermd forms. A minterm represents an expression where an output is '1' for a unique combination of inputs.- **Step 2: Combine Minterms** Once expanded, identify and combine minterms to simplify the function. The goal is to eliminate the variables \( a \) and \( a' \) where possible, optimizing the utilization of the multiplexer.**Tips:**- The approach of using a multiplexer effectively reduces the complexity of the function by employing control inputs. The control lines (\( b, c, d, e \)) directly select the data inputs (0, 1, \( a \), or \( a' \)), dictating the output based on the binary value they represent.- Look for opportunities to group the minterms strategically to minimize the use of variables, particularly \( a \) and \( a' \), in your final configuration. This consolidation process helps in achieving the desired function with reduced complexity and increased efficiency.This guide is aimed at understanding the application of multiplexers in function realization, which is key in digital logic design and optimization.

The multiplexer is a device which combines 'n' input into single output and the output will be based on the selection line.Truth Table: a b c d e f MUX input 0 0 0 0 0 0 a I0 0 0 0 0 1 0 a I1 0 0 0 1 0 0 a I2 0 0 0 1 1 0 0 I3 0 0 1 0 0 0 a I4 0 0 1 0 1 0 a I5 0 0 1 1 0 1 a' I6 0 0 1 1 1 1 1 I7 0 1 0 0 0 0 0 I8 0 1 0 0 1 1 1 I9 0 1 0 1 0 0 0 I10 0 1 0 1 1 1 a' I11 0 1 1 0 0 1 1 I12 0 1 1 0 1 1 a' I13 0 1 1 1 0 0 0 I14 0 1 1 1 1 0 0 I15 1 0 0 0 0 1 a I0 1 0 0 0 1 1 a I1 1 0 0 1 0 1 a I2 1 0 0 1 1 0 0 I3 1 0 1 0 0 1 a I4 1 0 1 0 1 1 a I5 1 0 1 1 0 0 a' I6 1 0 1 1 1 1 1 I7 1 1 0 0 0 0 0 I8 1 1 0 0 1 1 1 I9 1 1 0 1 0 0 0 I10 1 1 0 1 1 0 a' I11 1 1 1 0 0 1 1 I12 1 1 1 0 1 0 a' I13 1 1 1 1 0 0 0 I14 1 1 1 1 1 0 0 I15 Design:

Engineering

Electrical Engineering

Realize the function f(a, b, c, d, e) = [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 fand combine minterms to eliminate a and a' where possible.)

Realize the function f(a, b, c, d, e) = [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 fand combine minterms to eliminate a and a' where possible.)

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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