Logic Gates – Symbol, Boolean Algebra and Truth Table




Symbol of the Logic Gate

For each gate, the input or inputs are on the left of the symbol. The output is on the right

The Truth Tables

  1. The function of a logic gates can be shown by using the Truth tables.
  2. A truth table lists all possible input together with the corresponding output.

AND gate

Symbol:

Boolean Expression:
X=A•B
Truth Table:

Truth Table
INPUT OUTPUT
0 0 0
0 1 0
1 0 0
1 1 1

Notes:
The output is HIGH (1) only if both the inputs are HIGH (1).

OR gate

Symbol:

Boolean Expression:
X=A+B
Truth Table:

Truth Table
INPUT OUTPUT
0 0 0
0 1 1
1 0 1
1 1 1

Notes:
The output is HIGH (1) only if one or more inputs are HIGH (1).

NOT gate

Symbol:

Boolean Expression:
X= A ¯
Truth Table:

Truth Table
INPUT OUTPUT
0 1
1 0

Notes:
The output is the opposite of the input.

NAND gate

Symbol:

Boolean Expression:
X= A•B ¯
Truth Table:

Truth Table
INPUT OUTPUT
0 0 1
0 1 1
1 0 1
1 1 0

Notes:
The output is LOW (0) only if both the inputs are HIGH (1).

NOR gate

Symbol:

Boolean Expression:
X= A+B ¯
Truth Table:

Truth Table
INPUT OUTPUT
0 0 1
0 1 0
1 0 0
1 1 0

Notes:
The output is HIGH (1) only if both the inputs are LOW (0).