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Logic Gates
The Inverter
The inverter (NOT circuit) performs the operation called inversion or complementation.
Standard logic symbols:
1
1input output input output
Inverter Truth Table & Logic Expression
Input Output
LOW (0) HIGH (1)
HIGH (1) LOW (0)
0 1
1 0
A X = A
The AND Gate & Its Operation The AND gate is composed of two or more
inputs and a single output.
For a 2-input AND gate: Output X is HIGH only when inputs A and B are
HIGH X is LOW when either A or B is LOW, or when
both A and B are LOW.
&A
BX
A
BX
AND Gate Truth Table
The total number of possible combinations of binary inputs to a gate is determined by:
N = 2n
Therefore: 2 bits (n=2) = 4 combinations 3 bits = 8 combinations 4 bits = 16 combinations
INPUTS OUTPUT
A B X
0 0 0
0 1 0
1 0 0
1 1 1
A
BX
AND Gate – Logic Expressions Use either:
X = A · B ,or X = AB
If there are more than 2 inputs, do as below:
A
BX
X= ABC
X= ABCD
ABC
ABCD
The OR Gate
Like AND gate, an OR gate has two or more inputs and one output.
For a 2-input OR gate: output X is HIGH when either input A or input B is
HIGH, or when both A and B are HIGH. X is LOW only when both A and B are LOW.
A
BX
≥ 1A
B
X
OR Gate Truth Table
INPUTS OUTPUT
A B X
0 0 0
0 1 1
1 0 1
1 1 1
A
BX
OR Gate – Logic Expressions
Use the operator + for OR operation X = A + B If there are more than 2 inputs, do as below:
X= A+B+C
X= A+B+C+D
ABC
ABCD
The NAND Gate
NAND = NOT-AND
For a 2-input NAND gate: Output X is LOW only when inputs A and B are
HIGH X is HIGH when either A or B is LOW, or when
both A and B are LOW
&A
BX
A
BX
A
BX
NAND Gate Truth Table & Logic Expression
INPUTS OUTPUT
A B X
0 0 1
0 1 1
1 0 1
1 1 0
A
BX
The Boolean expression for the output of a 2-input NAND gate is
X = AB
Negative-OR Equivalent Op of a NAND For a 2-input NAND gate performing a
negative-OR operation Output X is HIGH when either input A or input B is
LOW or when both A and B are LOW
NAND Negative-OR
The NOR Gate
NOR = NOT-OR
For a 2-input NOR gate: Output X is LOW when either input A or input B is
HIGH, or when both A and B are HIGH X is HIGH only when both A and B are LOW
A
BX
A
BX
≥ 1A
BX
NOR Gate Truth Table & Logic Expression
INPUTS OUTPUT
A B X
0 0 1
0 1 0
1 0 0
1 1 0
A
BX
The Boolean expression for the output of a 2-input NOR gate is
X = A+B
Negative-AND Equivalent Op of a NOR For a 2-input NOR gate performing a
negative-AND operation Output X is HIGH only when both inputs A and B
are LOW
NOR Negative-AND
The XOR and XNOR Gates
Exclusive-OR and Exclusive-NOR gates are formed by a combination of other gates already discussed.
Because of their fundamental importance in many applications, these gates are often treated as basic logic elements with their own unique symbols.
The XOR Gate
For a 2-input exclusive-OR gate: Output X is HIGH when input A is LOW and input
B is HIGH, or when input A is HIGH and input B is LOW
X is LOW when A and B are both HIGH and both LOW
= 1A
B
X
A
BX
XOR Gate Truth Table & Logic Expression
INPUTS OUTPUT
A B X
0 0 0
0 1 1
1 0 1
1 1 0
A
BX
The Boolean expression for the output of a 2-input XOR gate is
X = A+B
The XNOR Gate
For a 2-input exclusive-NOR gate: Output X is LOW when input A is LOW and input
B is HIGH, or when input A is HIGH and input B is LOW
X is HIGH when A and B are both HIGH and both LOW
= 1A
B
X
A
BX
XNOR Gate Truth Table & Logic Expression
INPUTS OUTPUT
A B X
0 0 1
0 1 0
1 0 0
1 1 1
A
BX
The Boolean expression for the output of a 2-input XNOR gate is
X = A+B
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