EE 311
Digital Hardware Organization
Chapter 2 Homework Solutions (Set 1)
2.1.
The proof is as follows:
(x + y)(x + z) = xx + xz + xy + yz
= x + xz + xy + yz
= x(1 + z + y) + yz
= x(1) + yz
= x + yz
2.2.
The proof is as follows:
(x + y)(x + y ) = xx + xy + xy + yy
= x + xy + xy + 0
= x(1 + y + y) = x(1)
= x
2.3.
Manipulate the left hand side as follows:
xy + yz + xz = xy + (x + x)yz + xz
= xy + xyz + xyz + xz
= xy(1 + z) + xz(y + 1)
= xy(1) + x(1)z
= xy + xz
2.4.
Proof using Venn diagrams:

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