A logic circuit realizes the function FA B C D A B A C D

A logic circuit realizes the function F(A, B, C, D) = A\' B\' + A\' C D + A C\' D + A B\' D\'. Assuming that A = C never occurs when B = D = 1, find a simplified expression for F.

Solution

As in the question if we assume that B=D so A should never be equal to C

A\' is the complement of A as taken in the sol.

F(A,B,,C,D) = A\'B\' + A\'CD + AC\'D + AB\'D\'

F(A,B,,C,D) = put the val B = D = 1 so B\' or D\' = 0 for sure

F(A,B,C,D) = A\' (0) + A\'C (1) + AC\' (1) + A (1) (0)

A\' . (0)= 0 and A . (1) . (0)=0

F(A,B,C,D) = A\' C + A C\'

and we have assume B=D=1 and A not equal to C but this then is true { A\' = C or A = C\' }