# 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: You can avail of BYJU’S Exam Prep Online classroom program for all AE & JE Exams:

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