Digital Comparator and Magnitude Comparator Guide

In today's world, electronics have become an integral part of human life, with the global community witnessing significant advancements in the use of electronic devices. The advantages of electronics are so numerous that it is now easier to list the devices that don’t incorporate them than those that do. The ongoing trend in electronic technology today has brought to the forefront widely used devices like digital comparators and magnitude comparators. Following the extensive performance of operational amplifiers, comparators have become the most widely accepted simple electronic devices. Let's delve deeper into the topics of what a digital comparator is, its operation, performance, and applications.

 

Digital Comparator and Magnitude Comparator

 

A detailed discussion of digital comparator and magnitude comparator mainly includes the following:

 

What is a Digital Comparator?

 

In many digital systems, data comparison is essential during logical or arithmetic operations. Digital comparators are the optimal choice for comparing data. They are combinational logic circuits designed to compare the relative magnitudes of two binary numbers.

The device accepts two binary numbers (A and B) as input and generates an output based on the magnitude of the given inputs (e.g., A=B, A>B, or A<B). Digital comparators are developed using logic gates such as AND, NOT, or NOR gates. They are available as identity comparators and magnitude comparators.

 

What is Magnitude Comparator?

 

Magnitude comparators are predominantly used in microcontrollers and CPUs for data comparison, register functions, and other arithmetic operations. They are implemented in many devices, and every auto-turn-off device is designed using a comparator.

 

A comparator is a decision-making tool and can be executed in numerous control devices. By accepting two binary numbers as input (A and B), magnitude comparators perform data comparison and produce an output to indicate equality (A=B) or logic 1 when (A>B or A<B).

 

Types of Magnitude Comparators

 

There are different kinds of magnitude comparators, including the following:

 

1-bit Magnitude Comparator

 

A comparator that compares two binary bits and produces three outputs based on the relative magnitudes of the given binary bits is called a 1-bit magnitude comparator.

 

Truth Table

 

A	B	A<B	A>B	A=B
0	0	0	0	1
0	1	1	0	0
1	0	0	1	0
1	1	0	0	1

 

The truth table derives the expressions for A<B, A>B, and A=B as follows:

 

A<B – A’B

A>B – AB’

A=B – A’B’+AB

With these expressions, the circuit diagram can be as follows:

2-bit Magnitude Comparator

 

 

A comparator that compares two binary numbers (each number having 2 bits) and produces three outputs based on the relative magnitudes of the given binary bits is called a 2-bit magnitude comparator.

Truth Table

 

A1	A0	B1	B0	A<B	A=B	A>B
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 truth table derives the expressions for A<B, A>B, and A=B as below.

A<B – A1’B1’+ A0’B1B0 + A1’A0’B0

A>B – A1B1’ + A0B1’B0’ + A1A0B0’

A=B – (A0 Ex-Nor B0) (A1 Ex-Nor B1)

 

 

With these expressions, the circuit diagram can be as follows:

3-bit Magnitude Comparator

 

 

A comparator that compares two binary numbers (each number having 3 bits) and produces three outputs based on the relative magnitudes of the given binary bits is called a 3-bit magnitude comparator.

The equal functions are A0 = B0, A1 = B1, A2 = B2.

 

Then A=B = (A0’B0’ + A0B0)(A1’B1’ + A1B1)(A2’B2’ + A2B2).

 

The output is A < B in the following cases:

 

A2 < B2

A2 = B2 and A1 < B1

A2 = B2, A1 = B1, and A0 < B0

A<B = A2’B2 + [(A2’B2’ + A2B2) * A1’B1] + [(A2’B2’ + A2B2) * [(A1’B’ + A1B1) * A0’B0]].

 

The output is A > B in the following cases:

 

A2 > B2

A2 = B2 and A1 > B1

A2 = B2, A1 = B1, and A0 > B0

A>B = A2B2’ + [(A2’B2’ + A2B2) * A1B1’] + [(A2’B2’ + A2B2) * [(A1’B’ + A1B1) * A0B0’]].

 

4-bit Magnitude Comparator

 

A comparator that compares two binary numbers (each number having 4 bits) and produces three outputs based on the relative magnitudes of given binary bits is called a 4-bit magnitude comparator.

 

The input bits can be termed as A = A3 A2 A1 A0 and B = B3 B2 B1 B0.

 

The output is A > B in the following cases:

 

A3 = 1 and B3 = 0

A3 = B3 and A2 = 1, B2 = 0

A3 = B3 and A2 = B2 and A1 = 1 and B1 = 0

A3 = B3 and A2 = B2 and A1 = B1 and A0 = 1 and B0 = 0

A>B can be expressed as:

 

A>B = A3B3’ + (A3 ⊙ B3) A2B2’ + (A3 ⊙ B3) (A2 ⊙ B2) A1B1’ + (A3 ⊙ B3) (A2 ⊙ B2) (A1 ⊙ B1) A0B0’

 

While

 

A<B can be expressed as:

 

A<B = A3’B3 + (A3 ⊙ B3) A2’B2 + (A3 ⊙ B3) (A2 ⊙ B2) A1’B1 + (A3 ⊙ B3) (A2 ⊙ B2) (A1 ⊙ B1) A0’B0

 

And similarly, A=B can be expressed as:

 

A=B = (A3 ⊙ B3) (A2 ⊙ B2) (A1 ⊙ B1) (A0 ⊙ B0).

 

With these expressions, the circuit diagram can be as follows:

 

Mostly, 4-bit comparators are in the form of ICs, with the IC 7485 being widely used. Data comparison can be performed by grounding A>B, A<B, and A=B inputs to the Vcc terminal. Furthermore, this integrated circuit supports cascading operations, enabling the cascading of multiple comparators.

 

8-bit Magnitude Comparator

 

Here, data comparison is achieved by cascading two 4-bit comparators. The circuit is connected as follows:

The outputs of the lower-order comparator are connected to the corresponding cascading inputs of the higher-order comparator.

 

In the lower-order comparator, the cascading input (A=B) needs to be connected HIGH, and A, B need to be connected to LOW. The result of the 8-bit comparator is the output of the higher-order comparator.

 

Applications of Comparators

 

Digital comparators and magnitude comparators are used in various applications where data comparison is crucial. These applications offer numerous benefits as well.

 

Now, let's explore a few applications of comparators:

 

• Used for authorization purposes (such as password management) and biometric applications.
• Implemented in process controllers and servo motor controls.
• Used for comparing variables such as temperature and pressure with reference values.
• Utilized in address decoding circuitry in computers.

Thus, this concludes the discussion on digital comparator and magnitude comparator. The enhanced performance of comparators has significantly increased their prominence in the electronics industry and enabled their implementation in various applications.

 

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