Question

Simplify the following Boolean expressions algebraically.


1)
XY + XYZ’ + XYZ’ + XZY






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Answer 1

Answer:

a) xy + xy′ = x ( y+y′)= x.1 = x

b) (x+y)(x+y′) = xx + xy′ + yx+yy′ = x + xy′ + xy + 0 = x (1+ y′ + y) = x.1= x

Also (x+y)(x+y′) =x+ yy′ = x + 0 = x

c) xyz + x′y + xyz′ = xy(z+z′) + x′y = xy +x′y = y(x+x′)=y

d) (A+B)′(A′+B′)′= (A′B′).(AB)

Explanation: