Logic gates


NOT gate

Description

• The output, X, is 1 if the input A is NOT 1

How to write this

• X = NOT A (logic notation)
• $X=\bar{A}$ (Boolean algebra)

Truth table

Input	Output
A	X
0	1
1	0

AND gate

Description

• The output, X, is 1 if input A is 1 and input B is 1

How to write this

• X = A AND B (logic notation)
• $X=A\cdot B$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	0
1	0	0
1	1	1

OR gate

Description

• The output, X, is 1 if input A is 1 or input B is 1.

How to write this

• X = A OR B (logic notation)

• $X=A+B$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	1
1	0	1
1	1	1

NAND gate

Description

• The output, X, is 1 if input A is NOT 1 or input B is NOT 1.

How to write this

• X = A NAND B (logic notation)

• $X=\overline{A\cdot B}$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	1
0	1	1
1	0	1
1	1	0

NOR gate

Description

• The output, X, is 1 if: input A is NOT 1 and input B is NOT 1

How to write this

• X = A NOR B (logic notation)

• $X=\overline{A+B}$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	1
0	1	0
1	0	0
1	1	0

XOR gate

Description

• The output, X, is 1 if (input A is 1 AND input B is NOT 1) OR (input A is NOT 1 AND input B is 1)

How to write this

• X = A XOR B (logic notation)
• $X=(A\cdot \bar{B})+(\bar{A}\cdot B)$ (Boolean algebra)

(Note: this is sometimes written as: $(A+B)\cdot \overline{(A\cdot B)}$)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	1
1	0	1
1	1	0