CS302 Assignment 2 Solution and Discussion

Digital Logic Design (CS302)
Assignment # 02

Total marks = 20

Deadline Date
27 Nov 2019

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Topic Covered:
Expression Simplification
Quine-McCluskey Simplification Method

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Question Marks (20)
Consider the below given canonical sum:

∑_(A,B,C,D,E)▒〖(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30)〗

Write the SOP expression for the given sum.
Find the prime implicants from given minterms using Quine-McCluskey simplification method.
Extract the simplified expression.

Note: Perform all steps of this method. In case of missing steps, marks will be deducted.

ASSIGNMENT NO:2
Course: CS302
1: Write the SOP expression for the given sum.

Sol:
A B C D E
0 0 0 0 0
0 0 0 0 1
0 0 0 1 0
0 0 0 1 1
0 0 1 0 0
0 0 1 0 1
0 0 1 1 0
0 0 1 1 1
0 1 0 0 0
0 1 0 0 1
0 1 0 1 0
0 1 0 1 1
0 1 1 0 0
0 1 1 0 1
0 1 1 1 0
0 1 1 1 1
1 0 0 0 0
1 0 0 0 1
1 0 0 1 0
1 0 0 1 1
1 0 1 0 0
1 0 1 0 1
1 0 1 1 0
1 0 1 1 1
1 1 0 0 0
1 1 0 0 1
1 1 0 1 0
1 1 0 1 1
1 1 1 0 0
1 1 1 0 1
1 1 1 1 0
1 1 1 1 1

A B C D E OUTPUT
(F)
0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 1 0 1
0 0 0 1 1 0
0 0 1 0 0 1
0 0 1 0 1 0
0 0 1 1 0 1
0 0 1 1 1 0
0 1 0 0 0 1
0 1 0 0 1 0
0 1 0 1 0 1
0 1 0 1 1 0
0 1 1 0 0 1
0 1 1 0 1 0
0 1 1 1 0 1
0 1 1 1 1 0
1 0 0 0 0 1
1 0 0 0 1 0
1 0 0 1 0 1
1 0 0 1 1 0
1 0 1 0 0 1
1 0 1 0 1 0
1 0 1 1 0 1
1 0 1 1 1 0
1 1 0 0 0 1
1 1 0 0 1 0
1 1 0 1 0 1
1 1 0 1 1 0
1 1 1 0 0 1
1 1 1 0 1 0
1 1 1 1 0 1
1 1 1 1 1 0
FOR SOP WE FOCUS ON 1 VALUE.
A B C D E MINTERM
0 0 0 1 0

0 0 1 0 0

0 0 1 1 0

0 1 0 0 0

0 1 0 1 0

0 1 1 0 0

0 1 1 1 0

1 0 0 0 0

1 0 0 1 0

1 0 1 0 0

1 1 1 0 0

1 1 0 0 0

1 1 0 1 0

1 1 1 0 0

1 1 1 1 1 ABCDE

SOP EXPRESSION:
SUM OF PRODUCT EXPRESSION

2: Find Prime Implicant of minterm using QuineMcculsky method.

Step-1
00010 2
00100 4
01000 8
10000 16
00110 6
01010 10
01100 12
10010 18
10100 20
11000 24
01110 14
10110 22
11010 26
11100 28
11110 30

Step-2
2,6(00-10) 2,10(0-010) 2,18(-0010)
4,12(0-100) 4,6(001-0) 4,20(-0100)
8,10(010-0) 8,24(-1000)
16,18(100-0) 16,20(10-00) 16,24(10-00)
6,14(0-110) 6,22(-0110)
10,14(01-10)10,26(-1010)
12,14(011-0) 12,28(-1100)
18,26(1-010) 18,22(10-10)
20,22(101-0) 20,22(1-100)
24,26(110-0) 24,28(11-00)
14,30(-1110) 22,30(1-110) 26,30(11-10) 28,30(111-0)
Step-3
2,6,18,22(-0-10) 2,6,10,14( 0–10)2,10,18,26(–010)2,18,6,22(-0-10)
2,18,10,26(–010)4,12,6,14(0-1-0) 4,6,12,14 (0-1-0)
4,6,20,22(-01-0)4,20,6,22(-01-0) 4,20,12,28(–100) 8,10,12,14(01–0) 8,24,10,26(-10-0) 8,24,12,28 (-1-00)
6,14,22,30 (–110) 6,22,14,30(–110) 10,14,26,30(-1-10) 10,26,14,30(-1-10) 12,14,28,30(-11-0) 12,14,28,30(-11-0)
18,26,22,30(1–10) 18,22,26,30(1–10) 20,22,28,30(1-1-0)
20,22,22,30(1-1-0) 24,26,28,30(11–0) 24,28,26,30(11–0)
Step-3
2,6,18,22(-0-10) 4,6,20,22(-01-0)
2,18,10,22(-0-10) 4,20,6,22(-01-0)
2,10,18,26(–010) 4,12,6,14(0-1-0)
2,18,6,22(–010) 4,6,12,14 (0-1-0)
4,20,12,28(–100) 10,14,26,30(-1-10)
6,14,22,30 (–110) 10,26,14,30(-1-10)
12,14,28,30(-11-0) 18,26,22,30(1–10)
12,14,28,30(-11-0) 18,22,26,30(1–10)
20,22,28,30(1-1-0) 24,26,28,30(11–0)
20,22,22,30(1-1-0) 24,28,26,30(11–0)
6,22,14,30(–110)
8,10,12,14(01–0)
8,24,12,28 (-1-00)
8,24,10,26(-10-0)
Step-4
2,6,8,22(-0-10) 4,6,20,22(-01-0)
2,10,18,26(–010) 4,12,6,14(0-1-0)
4,20,12,28(–100) 10,14,26,30(-1-10)
12,14,28,30(-11-0) 18,26,22,30(1–10)
20,22,28,30(1-1-0) 24,26,28,30(11–0)
6,22,14,30(–110) 8,10,12,14(01–0)
8,24,12,28 (-1-00) 8,24,10,26(-10-0)
These are the prime implicates
cs302-assign 2.docx