Page 44 - Computer science 868 Class 12
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Let us understand this better with the help of some examples.
Example 7: Minimise a Boolean expression F(A, B, C) = Σ(0, 1, 2, 4, 6)
Solution: B'.C' B'.C B.C B.C'
A' 1 0 1 1 0 3 1 2
A 1 4 0 5 0 7 1 6
Quad 1: m +m +m +m = C'
4
2
0
6
Pair1: m +m = A'.B'
0
1
Reduced SOP expression: A'.B'+C'
Example 8: Given F(P, Q, R, S) = Σ(0, 2, 5, 7, 8, 10, 11, 13, 14, 15)
Reduce the above expression by using a 4 – variable K-map, showing the various groups (i.e., octal, quads and pairs).
[ISC 2010]
Solution: R'.S' R'.S R.S R.S'
P'.Q' 1 0 0 1 0 3 1 2
P'.Q 0 4 1 5 1 7 0 6
P.Q 0 12 1 13 1 15 1 14
P.Q' 1 8 0 9 1 11 1 10
Quad 1: m +m +m +m = Q.S
13
15
7
5
Quad 2: m +m +m +m = P.R
11
15
14
10
Quad 3: m +m +m +m = Q'.S'
10
0
8
2
Reduced SOP expression: Q'.S' + P.R + Q.S
Example 9: Given F(A, B, C, D) = (A+B+C+D).(A+B+C+D').(A+B+C'+D').(A+B+C'+D).(A+B'+C+D').(A+B'+C'+D').(A'+B+C+D).
(A'+B+C'+D).
Reduce the above expression by using a 4 – variable K-map, showing the various groups (i.e., octal, quads and pairs).
[ISC 2010]
C+D C+D' C'+D' C'+D
A+B 0 0 0 1 0 3 0 2
A+B' 1 4 0 5 0 7 1 6
A'+B' 1 12 1 13 1 15 1 14
A'+B 0 8 1 9 1 11 0 10
Quad 1: M .M .M .M = B+D
2
0
10
8
Quad 2: M .M .M .M = A+B
2
1
0
3
Quad 3: M .M .M .M = A+D'
7
1
5
3
Reduced POS expression: (A+B).(B+D).(A+D')
4242 Touchpad Computer Science-XII

