CS302 ASSIGNMENT NO. 1 SPRING 2023 || 100% RIGHT SOLUTION || DIGITAL LOGIC DESIGN || BY VuTech

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QUESTION

Simplify the stated 5 Variable Boolean Expression using the Karnaugh Map method. F(A, B, C, D, E)=   (1,3,5,7,9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31) 
With the following Don't Care Conditions 
F(A, B, C, D, E) =  (2,6, 10, 14, 18, 22, 26, 30)

SOLUTION

Min terms given =  (1,3,5,7,9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31)

Don’t care condition terms = (2,6, 10, 14, 18, 22, 26, 30)

The 5-variable Karnaugh Map consists two 4-variable k-map and have `2^5`  = 32 cells

BC/DE	00	01	11	10
00	0	1	3	x
01	4	5	7	x
11	12	13	15	x
00	8	9	11	x

BC/DE	00	01	11	10
00	15	16	x	17
01	19	20	x	21
11	27	28	x	29
00	23	24	x	25

Grouping:

Group 1: (0,0), (0,1), (1,0), (1,1)

Group 2: (1,1), (1,2), (2,1), (2,2)

Group 3: (0,0), (0,1), (0,2), (1,0), (1,1), (1,2)

Group 4: (0,0), (0,3), (1,0), (1,3), (2,0), (2,3)

Simplified Expression:

Group 1 = A'B'CD' + A'B'C'D + AB'CD' + AB'C'D

Group 2 = AB'CD' + AB'CD + ABC'D + ABC'D'

Group 3 = A'B'C'D'E' + A'B'C'DE' + A'B'C'DE + A'B'CD'E' + A'B'CD'E + A'B'CD'E

Group 4 = A'B'C'D'E' + A'B'C'DE' + A'BC'D'E' + A'BC'DE' + ABC'D'E' + ABC'DE'

Combined Simplified Expression of 5-variable k-map:

F(BC/DE) = A'B'C'D'E' + A'B'C'DE' + A'B'C'DE + A'B'CD'E' + A'B'CD'E + A'B'CD'E +

A'BC'D'E' + A'BC'DE' + ABC'D'E' + ABC'DE'

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