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

CS301 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

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