Page 64 - Computer science 868 Class 12
P. 64
= CA' + A'B + B'C + AB'D'
= A'C + A'B + B'C + AB'D'
47. Given the Boolean function F(P, Q, R, S) = π(0, 1, 2, 4, 5, 6, 8, 10). [ISC 2017]
Reduce the above expression by using the 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).
Ans. F(P, Q, R, S) = π (0, 1, 2, 4, 5, 6, 8, 10)
CD
AB C+D C+D' C'+D' C'+D
A+B 0 0 0
0 1 3 2
A+B' 0 4 0 5 7 0 6
A'+B' 12 13 15 14
A'+B 0 0
8 9 11 10
= (A + C)(A + D)(B + D)
48 A school intends to select candidates for an Inter-School Essay Competition as per the criteria are given below: [ISC 2017]
The student has participated in an earlier competition and is very creative.
OR
The student is very creative and has excellent general awareness, but has not participated in any competition earlier.
OR
The student has excellent general awareness and has won a prize in an inter-house competition. The inputs are:
Inputs
A participated in a competition earlier
B is very creative
C won a prize in an inter-house competition
D has an excellent general awareness
(In all the above cases 1 indicates yes and 0 indicates no).
Output: X [1 indicates yes, 0 indicates no for all cases]
Draw the truth table for the inputs and outputs given above and write the POS expression for X(A, B, C, D).
Ans. A B C D X
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 0
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 1
POS Expression: X (A, B, C, D) = R (0, 1, 2, 4, 6, 8, 9, 10)
6262 Touchpad Computer Science-XII

