Class 10 > Unit # 17:Introductory Electronics > Logic gates (AND,OR,NOT,NAND,NOR)

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Basic Logic Gates: Definitions, Symbols, and Truth Tables

Introduction to Logic Gates

"Logic gates are fundamental building blocks of digital electronic circuits that make logical decisions based on the combination of digital inputs (0 and 1)."

Below are the definitions, mathematical operations, symbols, and truth tables for the five standard logic gates: AND, OR, NOT, NAND, and NOR.

1. AND Gate

An AND gate is a digital circuit with two or more inputs and a single output. It operates on the rules of logical multiplication. The output is high ($1$) only when all inputs are high ($1$).

Boolean Expression: $Y = A \cdot B$ (for two inputs)

Fig: Standard logic symbol of an AND gate.

Truth Tables

Two-Input AND Operation

A	B	Y = A · B
0	0	0
0	1	0
1	0	0
1	1	1

Three-Input AND Operation

A	B	C	Y = A · B · C
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	0
1	0	0	0
1	0	1	0
1	1	0	0
1	1	1	1

2. OR Gate

An OR gate is a digital circuit with two or more inputs and a single output. It operates on the rules of logical addition. The output is high ($1$) if at least one input is high ($1$).

Boolean Expression: $Y = A + B$ (for two inputs)

Fig: Standard logic symbol of an OR gate.

Truth Tables

Two-Input OR Operation

A	B	Y = A + B
0	0	0
0	1	1
1	0	1
1	1	1

Three-Input OR Operation

A	B	C	Y = A + B + C
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	1
1	0	0	1
1	0	1	1
1	1	0	1
1	1	1	1

3. NOT Gate (Inverter)

A NOT gate is a digital circuit with a single input and a single output. It operates on the rules of logical complement (inversion), reversing the input state.

Boolean Expression: $Y = \overline{A}$

Fig: Standard logic symbol of a NOT gate.

Truth Table

A	Y = $\overline{A}$
0	1
1	0

4. NAND Gate

A NAND gate (Not-AND) is a digital circuit with two or more inputs and a single output. It is constructed by connecting a NOT gate at the output of an AND gate. The output is low ($0$) only when all inputs are high ($1$).

Boolean Expression: $Y = \overline{A \cdot B}$

Fig: Standard logic symbol of a NAND gate.

Truth Table

A	B	Y = $\overline{A \cdot B}$
0	0	1
0	1	1
1	0	1
1	1	0

5. NOR Gate

A NOR gate (Not-OR) is a digital circuit with two or more inputs and a single output. It is constructed by connecting a NOT gate at the output of an OR gate. The output is high ($1$) only when all inputs are low ($0$).

Boolean Expression: $Y = \overline{A + B}$

Fig: Standard logic symbol of a NOR gate.

Truth Table

A	B	Y = $\overline{A + B}$
0	0	1
0	1	0
1	0	0
1	1	0

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