Logic Gates
The basic building blocks for a complex digital system are known as logic gates.
A gate is a simple electronic circuit or device that performs logical functions. It has one or more inputs and one output gate and are also called binary logic gates, as 1 and 0 are the inputs and outputs.We shall discuss the three basic gates known as 'AND', 'OR' and 'NOT' gates whose input - output tables are similar to conjunction, disjunction and negation respectively with T = 1 and F = 0.
AND Gate
An 'AND' gate is a Boolean function with two input variables x1, x2, defined by
f(x1, x2) = x1, x2where x1, x2
{0, 1}
Table 10


OR Gate
An 'OR' gate is a Boolean function with two variables defined by
f(x1, x2) = x1 + x2 x1, x2
{0, 1}

Table 11

NOT Gate
A NOT gate is the Boolean function defined by
f(x) = x' x
{0, 1}

Table 12

Example:
Find the output for the given input.
x1 = 1, x2 = 1 from the circuit given in figure.
The Boolean function for the given circuit isS = f(x1, x2) = (x1 . x2)' + x1
If x1 = 1, x2 = 1S = (x1 . x2)' + x1 = (1 . 1)' + 1
= (1)' + 1 = 0 + 1= 1
Combinatorial Circuit
A circuit in which the output is uniquely defined for each combination of inputs x1, x2, x3 is called a combinatorial circuit.
Equivalent Circuit
Two combinatorial circuits, each having inputs x1, x2, x3, x4,……xn and a single output are said to be equivalent if their input/output tables are identical.
Example:
Simplify the combinatorial circuit for the given figure.
The given circuit is x1.x2 + x1'x2 + x1x2'
= x2(x1 + x1') + x1x2' Axiom 4(a)= x2 . 1 + x1x2' Axiom 5(a)
= x2 + x1x2' Axiom 2(b)= x1x2' + x2 Axiom 3(a)
The simplified combinatorial circuit is
