Page 1080 - Basic Electrical Engineering

In Boolean algebra, the AND operation is represented by multiplication,
since the result of multiplication of a combination of binary numbers 1 and 0
will be equal to 1 only if all its inputs are equal to 1. The Boolean expression

for A and B is A.B.
The OR operation is represented by addition because the only way to

obtain a result of an addition operation equal to 0 is to make all inputs equal
to 0, which basically describes an OR operation. The Boolean expression for

A or B is A + B.
NOT operation means inversion. The Boolean expression for NOT

operation is A = NOT(A) = Ā. NAND operation is an AND operation
followed by a NOT operation. The NOR operation is an OR operation
followed by a NOT operation. Boolean expressions for the three basic gates

are given below.

16.6.1 Boolean Expressions

Boolean expressions are equivalent expressions of logic states of gates. For
example, the Boolean expressions for the basic gates are
a NOT gate with input A and output C, C = NOT A, or C =Ā

The NOT gate

The output of a NOT gate is the inverse of its input. If the input is low, the
output is high, and if the input is high, the output is low. NOT gates can have

only one input and one output. A NOT gate is also called an inverter. The
symbolic representation along with its Boolean expression and truth table are

shown below.