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	A<B	A=B	A>B
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		A<B	A=B	A>B
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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