Question

Simplify the following Boolean expression :

(i)  AB + AB’+ A’C + A’C’

(ii)  XY + XYZ’ + XYZ’ + XZY

(iii)  XY(X’YZ’+ XY’Z’+ XY’Z’)

Answer 1

(i)  AB + AB’ + A’C + A’C’ 

= A(B + B’) + A’(C + C’)    (B + B’ =1, C + C’ = 1)

= A + A’ (A + A’ = 1) = 1

(ii)  XY + XYZ’ + XYZ’ + XZY 

= XY(Z’) + XY(Z’ + Z) (Z + Z’ =1) 

= XY(Z’) + XY = XY(Z’ + 1) (Z’ + 1 = 1) 

= XY

(iii)  XY(X’YZ’ + XY’Z’ + XY’Z’) 

= XY[Z’(X’Y + XY’ + XY’)] 

= XY[Z’(X’Y + XY’(1 + 1)] 

= XY[Z’(X’Y + XY’)] 

= XYZ’(X’Y + X Y’)