# DIGITAL ELECTRONICS : Logic Gates

By Yash Bansal|Updated : September 6th, 2021

Logic Gate is a very important topic from an exam point of view. In this article, we will discuss the important concepts, Formulas, and notes regarding the Logic Gate.

### Logic Gates

A logic gate is an idealised or physical device implementing a Boolean function, that is, it performs a logical operation in one or more logical inputs and produces a single logical output.

The logic gates can be classified as

• NOT, AND, OR are basic gates.
• NAND, NOR are universal gates.
• EXOR, EXNOR are an arithmetic circuit or code converter or comparators.

NOT Gate (Inverter)

Truth Table for NOT Gate:

Circuit Symbol for NOT Gate:

AND Gate:

Truth Table for AND Gate:

Circuit Symbol for AND Gate:

Properties of AND logic:

1. Commutative Law: AB = BA
2. Associative Law: ABC = (AB) C = (AC)B = A(BC)

OR Gate:

Truth Table:

Circuit Symbol for OR Gate:

Properties of OR logic:

1. Commutative Law: A + B = B + A
2. Associative Law: (A + B + C) = (A + B) + C = A + (B+ C)

NAND Gate:

Truth Table:

Circuit Symbol for NAND Gate:

NOR Gate:

Truth Table:

Circuit Symbol for NOR Gate:

• NOR gate follows commutative law but not follow associative law

EXOR Gate:

Truth Table:

Circuit Symbol for EXOR Gate:

Properties of EXOR Logic:

• Enable input = 0
• Disable input = 1
• It is also called stair case switch.
• It is widely used in parity generation and detection.
• When both the inputs are different, then output becomes high or logic 1.
• When both the inputs are same, then output becomes low or logic 0.

Note:

EX-NOR Gate:

Truth Table:

Circuit Symbol for EX-NOR Gate:

Properties of EXNOR Gate:

• Enable input = 1
• Disable input = 0
• When both the inputs are same, then output .becomes high or logic 1.
• When both the inputs are different, then output becomes low or logic 0.

### Logic Gate Conversions

• OR Gate using NAND Gate:

• AND Gate using NOR Gate:

• NAND Gate using NOR Gate

• NOR Gate using AND Gate

NAND and NOR Gate as Universal Gate

Designing different gates using NAND Gate as Universal Gate:

(i) NOT Gate:

(ii) AND Gate:

(iii) OR Gate:

h

(iv) EXOR Gate:

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