Page 1094 - Basic Electrical Engineering

AC + ABC + ACD = AC, (here the factor AC is present in all the terms,
and hence the other terms are neglected)
Consensus theorem: If in a Boolean expression, one term contains a

variable and the second term contains the complement of this variable, then
in the expression a third term can be added without effecting the value of the

expression, e.g. if X = AC + B where
is the complement of C. We can add another term in the expression as

To prove we write

16.10 UNIVERSAL GATES

As mentioned earlier NAND and NOR gates are known as universal gates
because they can be used to build any logic circuit. The logic function of
NOT, OR, and AND can be performed using either NAND or NOR gates.

First we shall see how a NAND gate, functions as NOT, AND, and OR gates
respectively. A NAND gate with its two inputs tied together is a single input

NAND gate.

16.10.1 Use of NAND Gate to Form the Three Basic Gates

i. NAND gate as NOT gate

ii. NAND gate as AND gate