Experiments- 11

 Verify the truth table of one bit and two-bit comparator using logic gates.

Introduction

A magnitude digital comparator is a combinational circuit that compares two digital or binary numbers in order to find out whether one binary number is equal, less than or greater than the other binary number. We logically design a circuit for which we will have two inputs one for A and other for B and have three output terminals, one for A > B condition, one for A = B condition and one for A < B condition.

Figure-1: Block Diagram of Comparator


1) 1-Bit Magnitude Comparator :

A comparator used to compare two bits is called a single bit comparator. It consists of two inputs each for two single bit numbers and three outputs to generate less than, equal to and greater than between two binary numbers. The truth table for a 1-bit comparator is given below :


Figure-2: Truth Table of 1-Bit Comparator

From the above truth table logical expressions for each output can be expressed as follows:
A > B: AB'
A < B: A'B
A = B : A'B' + AB

By using these Boolean expressions, we can implement a logic circuit for this comparator as given below :


Figure-3: Logic Circuit of 1-Bit Comparator

Simulator 1:

  • Step-1) Switch ON the power supply button to supply 5V to the circuit.
  • Step-2) Press Switch 1 for input A and Switch 2 for input B. The switch in ON state is  and the switch in OFF state is 
  • Step-3) i)When the input A is greater than the input B,LED 1 lits up.
  • ii)When the input A is lesser than the input B, LED 2 lits up.
  • iii)When the input A is equal to the input B, LED 3 lits up.

  • The LED in OFF state is  and the LED in ON state is  .
  • Step-4) Click on "Add" Button to add data to the Truth Table.
  • Step-5) Repeat Steps 2 to 4 for another set of data.
  • Step-6) Click "Print" to get the printout of the Truth Table.

Simulator 2:

  • Step-1) Enter the Boolean input "A" and "B".
  • Step-2) Enter the Boolean output for your corresponding inputs.
  • Step-3) Click on "Check" Button to verify your output.
  • Step-4) Click "Print" if you want to get print out of Truth Table.

LAB Simulation

1-Bit Comparator     

2) 2-Bit Magnitude Comparator :

A comparator used to compare two binary numbers each of two bits is called a 2-bit magnitude comparator. It consists of four inputs and three outputs to generate less than, equal to and greater than between two binary numbers.

The truth table for a 2-bit comparator is given below:


Figure-4: Truth Table of 2-Bit Comparator


From the above truth table logical expressions for each output can be expressed as follows:
A > B : A1B1’ + A0B1’B0’ + A1A0B0’
A = B : A1’A0’B1’B0’ + A1’A0B1’B0 + A1A0B1B0 + A1A0’B1B0’
           : A1’B1’ (A0’B0’ + A0B0) + A1B1 (A0B0 + A0’B0’)
           : (A0B0 + A0’B0’) (A1B1 + A1’B1’)
           : (A0 Ex-Nor B0) (A1 Ex-Nor B1)
A < B : A1’B1 + A0’B1B0 + A1’A0’B0

By using these Boolean expressions, we can implement a logic circuit for this comparator as given below :


Figure-5: Logic Circuit of 2-Bit Comparator


Applications of Comparators: 

  1. Comparators are used in central processing units (CPUs) and microcontrollers (MCUs).
  2. These are used in control applications in which the binary numbers representing physical variables such as temperature, position, etc. are compared with a reference value.
  3. Comparators are also used as process controllers and for Servo motor control.
  4. Used in password verification and biometric applications.

Simulator 1:

  • Step-1) Switch ON the power supply button to supply 5V to the circuit.
  • Step-2) Press Switch 1 for input A1,Switch 2 for input A0,Switch 3 for input B1and Switch 4 for input B0. The switch in ON state is  and the switch in OFF state is 
  • Step-3) i)When the input A1A0 is greater than the input B1B0,LED 1 lits up.
  • ii)When the input A1A0 is lesser than the input B1B0,LED 2 lits up.
  • iii)When the input XA1A0 is equal to the input B1B0,LED 3 lits up.

  • The LED in OFF state is  and the LED in ON state is  .
  • Step-4) Click on "Add" Button to add data to the Truth Table.
  • Step-5) Repeat Steps 2 to 4 for another set of data.
  • Step-6) Click "Print" to get the print out of the Truth Table.

Simulator 2:

  • Step-1) Enter the two bit Boolean input "A" and "B".
  • Step-2) Inputs should be written such that for 'A'="A1A0" and for 'B'="B1B0"
  • Step-3) Enter the Boolean output for your corresponding inputs.
  • Step-4) Click on "Check" Button to verify your output.
  • Step-5) Click "Print" if you want to get print out of Truth Table.


LAB Simulation


2-Bit Comparator     

TEST

All the comparisons made by comparator is done using _____________ .
One that is not the outcome of magnitude comparator is ____________ .
If two numbers are not equal then binary variable will be ____________ .
Which one is a basic comparator?
Comparators are used in ____________ .

References

  1. William Gothmann H, Digital Electronics : An Introduction To Theory And Practice , Prentice Hall, 2nd ed. 1982
  2. M. Morris Mano, Michael D Ciletti, "Digital Design", Pearson, 4th ed. 2008
  3. Thomas L. Floyd, R. P. Jain, "Digital Fundamentals", Pearson, 11th ed. 2017
  4. S Salivahanan, S Arivazhagan, "Digital Circuits and Design", Vikas Publishing House Pvt Ltd., 3rd ed. 2009
  5. Ronald J. Tocci, Neal S. Widmer, Gregory L. Moss, "Digital Systems", Pearson, 10th ed. 2009
  6. Anil K. Maini, "Digital Electronics: Principles, Devices and Applications", Wiley-Blackwell, 2007
  7. 1 Bit comparator: https://www.youtube.com/watch?v=UO-K0Jx2Hs0
  8. Magnitude Comparator: https://www.geeksforgeeks.org/magnitude-comparator/
  9. Digital Comparator and Magnitude Comparator: https://www.electronicshub.org/digital-comparator-and-magnitude-comparator/

Comments

Post a Comment

Popular posts from this blog

BCA Syllabus Topics

SEMESTER-2 nd Course: BCA SUBJECT: DIGITAL COMPUTER ORGANIZATION Syllabus : Unit-I : Digital computer and digital system; Binary number system: number base conversion. Compliments: one's, two's, 9's and 10's complements code: Gray BCD, ASCII, and error detection code. Logic Gates: AND, OR, NOT, EX-OR, Universal gate. Logic Circuit. Boolean function: Rules and simplification, simplification of Boolean function using map method, don't care condition. Unit-II: Combinational Circuits: Adders, Subtractors, Multiplexer, Demultiplexer Decoder, Encoder) Sequential Circuit: Flip-Flop: RS, Clocked RS, JK, D flip-flop, and Master board, Case studies to understand organization of laptop like Dell, Lenovo etc. slave flip-flop. Register- Introduction, Shift register, serial Transfer & parlor Load. Counters- Ripple Counter (Asynchronous), Synchronous Counters. Unit-III: 8086 internal architecture, register organization of 8086, addressing modes, instruction set and assembler ...
Read more

Quine-Mccluskey Method

Image
 Quine-Mccluskey Method It also known as Tabular method. It is more systematic method of minimizing expressions of even larger number of variables. It is suitable for hand computation as well as computation by machines i.e., programmable. . The procedure is based on repeated application of the combining theorem.  PA+P =P (P is set of literals) on all adjacent pairs of terms, yields the set of all PI‘s from which a minimal sum may be selected.  Consider expression ∑m(0,1,4,5)= + C+A +A C First,  second terms & third, fourth terms can be combined ( + ) + (C+ )= + A Reduced to (      +    ) = The same result can be obtained by combining m 0 & m 4 & m 1 &m 5 in first step & resulting terms in the second step. Procedure: Decimal Representation Don‘t cares PI chart EPI Dominating Rows & Columns Determination of Minimal expressions in c...
Read more

Alternate Logic-Gate Representations

Image
Alternate Logic-Gate Representations We have discussed the five basic logic gates (AND, OR, INVERTER, NAND, and NOR) and the standard symbols used to represent them in a logic circuit diagram. Most of the logic networks use standard symbols. But in some networks an alternative set of symbols is used in addition to the standard symbols. The table shows the alternate set of symbols for the five basic gates. Table: Alternate Logic Gate Representations To convert any normal symbol to its corresponding alternate symbol, the following steps are used: METHODOLOGY: TO CONVERT STANDARD SYMBOL TO ALTERNATE SYMBOL Step 1: Add bubbles (indication of inversion) at those input or output points where it is not present. Step 2: Remove all pre-existing bubbles of the normal symbol, if there is any at the point (only NOT, NAND and NOR gates) Step 3: If the existing normal logic symbol is AND, change it to OR, Similarly, if it is OR, then change it to AND. There is no change for the triangular symbol of ...
Read more