Question

12. Show that xz = (x + y)(x + y’)(x’ + z)

b) Using Boolean identities

The Essentials Of Computer Organization And Architecture - Chapter 3 - PROB 12E

Note: It seems the Chegg solutions for the textbook are sometimes not correct, need an expert. Will thumbs up any helpful answers. Typed is better.

Answer 1

Ans

Taking RHS,

(x+y)(x+y')(x'+z)

And last two terms,

(x+y)(xx' + xz + y'x' + y'z)

xx' = 0 (And with complement is 0)

(x+y)(xz + y'x' + y'z)

(xxz + xy'x' + xy'z + yxz + yy'x' + yy'z)

Anding with same variable result in variable i.e AA = A

AND is commutative so xy' = y'x, yx = xy

(xz + y'xx' + xy'z + xyz + yy'x' + yy'z)

Now xx'=0, yy'=0 (AND with complement)

(xz + xy'z + xyz)

(xz + xzy' + xzy)

AND is distributive

(xz + xz(y' + y))

y'+y = 1 ( or with complement is 1)

(xz+xz)

or with same term result in same

xz

= LHS

If any doubt ask in the comments.