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NPP

328 Fundamentals of Computers NPP

(d) Y = Σ m ( 3,2 ) 5 , 4 ,
(e) F = Σ m ( 1,0 , 9 , 7 , 3 , 15 )
(f) Y = π M (0, 2, 6, 7 )

(g) F = π M (1, 4, 6,9,12,13,15 )
3. Minimize the following Boolean expressions using K-map method K

(a) F = Σm (2, 4, 6) + d (1, 7)
(b) Y = πM (2, 4, 7).d (0, 1, 6)
(c) F = m + m + m + m + m .X + m .X
0 1 5 7 2 3
(d) F = Σm (0, 1, 3, 7, 9) + d (2, 6, 12, 13, 15)
(e) F = πM (1, 2, 4, 7, 8, 10) . d(0, 3, 9, 13, 15)

(f) F = M . M . M . M 7
0
1
4
(g) F = Σm (0, 1, 3, 7, 8) + d (2, 4, 5, 6, 9, 12)
(h) F = πM (1, 3, 6, 7, 12, 13) . d (0, 2, 11, 15)
4. Simplify the following Boolean Functions in SOP and POS Forms. Implement using Uni-
versal Gate (SOP POS
(a) A = Z . Y . X + Z . Y . X + Z . Y . X

(b) F = (A+ B+ C ) (A. + B+ C ) (A. + B+ C ) (A. + B+ C )
(c) Q = Σ m ( 4,2 ) 7 , 6 ,
(d) F = π M (0,1, 4, 6, 8, 12, 15 )
(e) F = π M (0,3, 7 )
(f) F = Σ m ( 2,0 ) 7 , 5 , + d ( ) 1
)
(g) F = π M (0,3, 4,5, 7,9,10,11 * d (8,13,15 )
(h) Q = D . C . B . A + D . C . B . A + C . B . A + B . A
(i) F = C . B . A + C . B . A + C . B . A + D . C . B . A

5. Simplify the following Boolean function using variable mapping method (

(a) F = C . B . A + C . B . A + . B . A CD
(b) F = C . B . A + C . B . A + D . C . B . A + C . B . A D

(c) Q = D . C . B . A + C . B . A D + D . C . B . A + D . C . B . A

(d) F = C . B . A + C . B . A + C . B . A + C . B . A + C . B . A