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Using the Karnaugh Map, find the most simplified Boolean Expression of output S. Show process steps...

Using the Karnaugh Map, find the most simplified Boolean Expression of output S. Show process steps and your work clearly such as grouping and how did you obtain the Boolean Expression. A B C D S 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0

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Answer #1

Truth Table:

A B C D S
0 0 0 0 0 0
1 0 0 0 1 0
2 0 0 1 0 0
3 0 0 1 1 1
4 0 1 0 0 1
5 0 1 0 1 1
6 0 1 1 0 0
7 0 1 1 1 1
8 1 0 0 0 0
9 1 0 0 1 0
10 1 0 1 0 0
11 1 0 1 1 1
12 1 1 0 0 1
13 1 1 0 1 1
14 1 1 1 0 1
15 1 1 1 1 0

K-Map layout:

C'D' C'D CD CD'
A'B' 0 1 3 2
A'B 4 5 7 6
AB 12 13 15 14
AB' 8 9 11 10

K-Map:

Groups:

(4,5,12,13) BC'
(3,7) A'CD
(3,11) B'CD
(12, 14) ABD'

Therefore, Simplified boolean expression is: S = BC' + A'CD + B'CD + ABD'

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