Combinational Circuits Study Notes for GATE Exams

Introduction to Combinational Circuit

Logic Circuits can be divided into two types.

• Combinational Logic Circuit, and
• Sequential Logic Circuit.

1. Combinational Logic Circuit

The combinational logic circuit contains the logic gates whose output is determined by the combination of current inputs.

• It comprises logic gates, input variables, and output variables.
• No feedback is required.
• No memory is required.

• Examples of combinational circuits are Encoder, Parallel Adders, Multiplexer, Decoder, , etc.

2. Sequential Logic Circuit

It contains the logic gates which are arranged in parallel and its output is determined by the combination of the current input and the prior output. The sequential circuit also consists of memory elements that are capable to store the information of the prior output.

• Examples of sequential circuits are Counters, Flip-flops, Shift Registers, etc.

Logic Gates

A logic gate is a physical device implementing the Boolean function i.e. it is used to perform the logical operation for 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 is an arithmetic circuit which is also called 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 is expressed as AB = BA
2. Associative Law is expressed as ABC = (AB) C = (AC)B = A(BC)

OR Gate

Truth Table:

Circuit Symbol for OR Gate:

Properties of OR logic:

1. Commutative Law is expressed as A + B = B + A
2. Associative Law is expressed as (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 gates tries to follow commutative law whereas it doesn't 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 mostly used in detection and parity generation.
• If both the inputs are different, then output comes out to be high or logic 1.
• If both the inputs are same, then output comes out to be 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
• If both the inputs are the same, then output comes out to be high or logic 1.
• If both the inputs are different, then output comes out to be 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:

(iv) EXOR Gate:

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