# CS302 Assignment 2 Solution 2021 - Digital Logic Design Assignment

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CS302 ASSIGNMENT 2 SOLUTION SPRING 2021

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CS402 Assignment 1 Solution 2021

Question 1:

Consider the following Canonical Sum:

A,B,C,D,E,F(0,1,3,5,7,17,18,19,24,25,33,37,39,41,47,48,55,59,60,62)

Simplify the stated expression using the Quine McClusky method of Boolean Expression simplification.

SOLUTION:

All the Minterms are listed below in the tabular form.

 Minterms A B C D E F 0 0 0 0 0 0 0 1 0 0 0 0 0 1 3 0 0 0 0 1 1 5 0 0 0 1 0 1 7 0 0 0 1 1 1 17 0 1 0 0 0 1 18 0 1 0 0 1 0 19 0 1 0 0 1 1 24 0 1 1 0 0 0 25 0 1 1 0 0 1 33 0 1 1 0 0 1 37 1 0 0 1 0 1 39 1 0 0 1 0 1 41 1 0 1 0 0 1 47 1 0 1 1 1 1 48 1 1 0 0 0 0 55 1 1 0 1 1 1 59 1 1 1 0 1 1 60 1 1 1 1 0 0 62 1 1 1 1 1 0

The Table of Minterms is rearranged in groups of minterms having 0,1,2,3,4 and 5 Is table is given below

 Minterms A B C D E F Used 0 0 0 0 0 0 0 ✔ 1 0 0 0 0 0 1 ✔ 3 0 0 0 0 1 1 ✔ 5 0 0 0 1 0 1 ✔ 17 0 1 0 0 0 1 ✔ 18 0 1 1 0 0 0 ✔ 24 0 1 1 0 0 0 ✔ 33 1 0 0 0 0 1 ✔ 48 1 1 0 0 0 0 ✔ 7 0 0 0 1 1 1 ✔ 19 0 1 0 0 1 1 ✔ 25 0 1 1 0 0 1 ✔ 37 1 0 0 1 0 1 ✔ 41 1 0 1 0 0 1 ✔ 39 1 0 0 1 1 1 ✔ 60 1 1 1 1 0 0 ✔ 47 1 0 1 1 1 1 ✔ 55 1 1 0 1 1 1 ✔ 59 1 1 1 0 1 1 ✔ 62 1 1 1 1 1 0 ✔

All pair in the above table of minterms which can be compared together to eliminate a variable is marked as used.

 Minterm A B C D E F Used 1,3 0 0 0 0 - 1 ✔ 1,5 0 0 0 - 0 1 ✔ 1,17 0 - 0 0 0 1 ✔ 1,33 - 0 0 0 0 1 ✔ 3,7 0 0 0 - 1 1 3,19 0 - 0 0 1 1 ✔ 5,37 - 0 0 1 0 1 ✔ 17,19 0 1 0 0 - 1 ✔ 17,25 0 1 - 0 0 1 18,19 0 1 - 0 0 - 24,25 0 1 1 0 0 - 33,37 1 0 0 - 0 1 ✔ 33,41 1 0 - 0 0 1 7,39 - 0 0 1 1 1 ✔ 39,47 1 0 - 1 1 1 39,55 1 - 0 1 1 1 60,62 1 1 1 1 - 0

From the above table eliminating a single variable from each term

 Minterm A B C D E F Used 1,3,17,19 0 - 0 0 - 1 ✔ 1,5,33,37 - 0 0 - 0 1 ✔ 1,17,3,19 0 - 0 0 - 1 ✔ 1,33,5,37 - 0 0 - 0 1 ✔ 5,37,7,39 - 0 0 1 - 1 ✔

From the above table, I compared and removed two variables

Prime implicant Chart:

 1 3 5 7 17 19 33 37 39 AC DF x x x x BC EF x x x x AC DF x x x x BC EF x x x x BC DF x x x x

The simplified expression is AC DF + BC EF + BC DF

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CS302 Assignment 2 Solution 2021
CS302 Assignment 2 Solution Spring 2021