# Magnitude Comparator

In this article you will learn about magnitude comparator. 1 Bit & 2 Bit comparators with truth table and circuit diagram.

## Magnitude Comparator

A combinational circuit that compares two digital or binary numbers and compare them in the form of A < B, A = B & A > B is known as magnitude comparator. A Magnitude comparator is also known as digital comparator.

## 1 Bit Magnitude Comparator

A magnitude comparator that compares two bits is known as 1 bit comparator. It consist of two inputs ( A & B ) each of 1 bit and has three outputs. The three outputs are A is less than B ( A < B ) , A is equal to B ( A = B ) and A is greater than B ( A > B ).

### 1 Bit Comparator Truth Table

 A B AB 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0

#### Output Expression

The output expression is written in SOP form ( A = 1 & A’ = 0 ), similarly ( B = 1 & B’ = 0 ).

The output is written only when logic 1 is obtained in the output.

Expression for A < B

Y = A’B

Expression for A = B

Y = A’B’ + AB

Expression for A > B

Y = AB’

## 2 bit Magnitude Comparator

A magnitude comparator that compares two bits, each of two bit is known as two bit comparator. It consist of four inputs ( A1, A0 & B1, B0 ) each of 1 bit and has three outputs. The three outputs are A is less than B ( A < B ) , A is equal to B ( A = B ) and A is greater than B ( A > B ).

### 2 Bit Comparator Truth Table

 A B AB A1 A0 B1 B0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0

The above comparison is done on the basis of weight. Here, A1 & B1 has weight 2 and A2 & B2 has weight 1.

Lets take example of 6 and 9 and compare them

 A1 A0 B1 B0 0 1 1 0 1 0 0 1

In BCD, 6 A0 has weight 1 and B1 has weight 2. So, B will be greater than A.

In BCD, 9 A1 has weight 2 and B0 has weight 1. So, A will be greater than B.

#### Output Expression

The output expression is written in SOP form ( A = 1 & A’ = 0 ), similarly ( B = 1 & B’ = 0 ).

The output is written only when logic 1 is obtained in the output.

K Map for A < B Expression for A < B

Y = A1’B1 + A1’A0’B0 + A0’B1B0

K Map for A = B Expression for A = B

Y = A1’A0’B1’B0’ + A1’A0B1’B0 + A1A0B1B0 + A1A0’B1B0

K Map for A > B Expression for A > B

Y = A1B1’ + A0B1’B0’ + A1A0B0

### Application of Magnitude Comparator

1. Magnitude comparators are used in CPU’s ( Central Processing Unit ) and MCU’s ( Microcontrollers ).
2. It is used in servo motor control.
3. Used in biometric applications and password verifications.

Author

Akash Sharma

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