Question

Computer Engineering

3. (3 points) Simplify the following POS expression, giving the result in SOP form. Hint: Use K-maps) Out- (AtB+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)

Answer 1

Given
Out = (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)
M1 = 0001 = (A+B+C+D')
M2 = 0010 = (A+B+C'+D)
M5 = 0101 = (A+B'+C+D')
M6 = 0110 = (A+B'+C'+D)
M14 = 1110 = (A'+B'+C'+D)
M9 = 1001 = (A'+B+C+D')
M10 = 1010 = (A'+B+C'+D)

F (A, B. C. D)-TT M (1, 2, 5, 6, 9, 10, 14) K-map B+C+D' C'+D CD 00 01 1.1 AB A+C+D' 01 4 5 6 12 11:8 i1% 10 l.l 10

The Simplified POS form of F (A, B, C, D) = = (B+C+D’)(C’+D)(A+C+D’)

From the above the minterms of F (A, B, C, D) = ​ m (0, 3, 4, 7, 8, 11, 12, 13, 15)

F (A, B. C, D)- 2m (0, 3, 4,7, 8, 11,12, 13,15) C'D' CD K-map 10 CD 01 AB 1 1 1 01 6 4 ABC 11 13 15 14 12 10 10

The SOP form of F (A, B, C, D) = = ABC’+C’D’+CD