ECE 275: Digital Design I

Class 3

More Theorems

Problem 1

F = (A + B)' (A' + B')' F = (A' B') (A B) F = A' B' A * B F = 0

Problem 2

F = A'BC + ABC' + ABC + A'BC' F = B(A'C + AC' + AC + A'C') F = B(C(A + A') + C'(A + A')) F = B(C(1) + C'(1)) F = B(C + C') F = B(1) F = B

Problem 3

F = (W' + X) (Y + Z') + (W' + X)' (Y + Z') F = AB + A'B F = B(A + A') F = B F = Y + Z'

Problem 4

F = ((A' * A) + B') + (B' + B') F = (0 + B') + (B' + B') F = B' + (B' + B') F = B' + B' F = B'

Problem 5

X = (A B) + C F = X' D (X + D) F = X'DX + X'DD F = 0 + X'D F = (AB+C)' D

Problem 6

1 OR Gate (Any # of inputs) 3 AND Gate (Only 2 inputs)

F = ABC + A'BC + AB'C + ABC' F = BC(A + A') + AC(B + B') + AB(C + C') F = BC(1) + AC(1) + AB(1) F = BC + AB + AC

Image

Problem 7

2 OR Gates (Only 2 inputs) 2 AND Gates (Only 2 inputs)

F = (A + B + C) (A + C + D) (A + E) X = A + C F = (T + B) (T + D) (A + E) F = (T + BD) (A + E) F = (A + C + BD) (A + E) F = A + E(C + BD)