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'