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