Page 53 - Computer science 868 Class 12
P. 53
A A' A + A' (A + A')
0 1 1 0
1 0 1 0
4. Given the Boolean function F(A, B, C, D) = S(2, 3, 6, 7, 8, 10, 12, 14, 15).
Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).
[ISC 2023]
Ans. F(A, B, C, D) = S(2, 3, 6, 7, 8, 10, 12, 14, 15)
C'.D' C'.D C.D C.D'
A'.B' 1 1
A'.B 1 1
A.B 1 1 1
A.B' 1 1
Quad 1: (2, 3, 6, 7) = A'.C
Quad 2: (6, 7, 14, 15) = B.C
Quad 3: (8, 10, 12, 14) = A.D'
F(A, B, C, D) = A'C + BC + AD'
5. Given the Boolean function F(A, B, C, D) = p(0, 1, 2, 4, 5, 8, 10, 11, 14, 15).
Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).
[ISC 2023]
Ans. F(A, B, C, D) = p(0, 1, 2, 4, 5, 8, 10, 11, 14, 15)
C+D C+D' C'+D' C'+D
A+B' 0 0 0
A+B' 0 0
A'+B' 0 0
A'+B 0 0 0
Quad 1: (0, 1, 4, 5) = A + C
Quad 2: (10, 11, 14, 15) = A’ + C’
Quad 3: (0, 2, 8, 10) = B + D
F(A, B, C, D) = (A + C) . (A’ + C’) . (B + D)
6. Verify the following expression by using the truth table: [ISC 2023]
(A ⊕ B)' = (A ⊕ B)
Ans.
A B No of I's A 9 B (A 9 B') A ⊕ B
0 0 0 1 0 0
0 1 1 0 1 1
1 0 1 0 1 1
1 1 2 1 0 0
Hence proved
7. Convert the following cardinal expression to its canonical form: [ISC 2023]
F(P, Q, R) = p(0, 1, 3, 4)
Ans. F(P, Q, R) = (P + Q + R).(P + Q + R’).(P + Q’ + R’).(P’ + Q + R)
8. The Boolean equation which holds true for the Involution Law is: [ISC 2022]
(a) A' + 1 = 1 (b) ((A + B)' )' = A + B
(c) (A + B)' = A'. B' (d) A.(B + C) = (A + B).C
Ans. (b)
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Boolean Algebra 51

