By using this site, you agree to the Privacy Policy and Terms of Use.
Accept
Neet Chennai
Saturday, Jun 14, 2025
  • Call Us Now:
  • +91 7449000979 , +91 7449000989
  • NEET-Syllabus
  • Difference Between
  • NEET Question Answers
  • NEET-Notes
Reading: Draw Logic Diagram of EXOR and EXNOR Gate (NEET Physics)
NEET Crash Course
Font ResizerAa
Neet ChennaiNeet Chennai
Search

Trending →

How Many Zeros in a Trillion? Understanding Millions, Billions, and Beyond

By NeetChennai
March 14, 2025

Shape Names: 10 Common Geometric Shapes You Should Know

By NeetChennai
March 13, 2025

The Mughal Empire in India: 7 Fascinating Facts About Its Rulers, Achievements, and Decline

By NeetChennai
March 13, 2025

Transverse Wave vs Longitudinal Wave: 5 Shocking Differences You Must Know!

By NeetChennai
March 12, 2025

When was Television Invented? 5 Brilliant Minds That Transformed the World

By NeetChennai
March 12, 2025
Follow US
© Foxiz News Network. Ruby Design Company. All Rights Reserved.
NEET Question Answers

Draw Logic Diagram of EXOR and EXNOR Gate (NEET Physics)

NeetChennai
Last updated: November 19, 2024 9:58 am
By NeetChennai
Share
7 Min Read
SHARE

(a)Draw logic diagram of EX-OR and EX-NOR gate using NAND gate and proof it using Boolean equation and truth table.
(b)Draw a logic diagram of EX-OR and EX-NOR gate using NOR gate and proof it using Boolean equation and truth table.

Hint:An Exclusive-OR (EX-OR) gate is a digital logic gate that produces a high output (true) when the number of high inputs is odd. Conversely, an Exclusive-NOR (EX-NOR) gate, which is essentially an EX-OR gate followed by a NOT gate, generates a high output (true) only when the number of high inputs is even. In simpler terms, the EX-NOR gate provides the complementary output of the EX-OR gate for identical input conditions.

Complete answer:
(a)
The logic diagram of EX-OR gate using NAND gate only is given as:

To prove it using the Boolean equation, we know Exclusive-OR gate is “ A or B but not BOTH”.

Let us prove the above expression.
In the first case consider,

A = 0 and B = 0

∴A⊕B=0⊕0=0.\(\overline{0}\)+\(\overline{0}\).0=0.1+1.0=0

In the second case consider,

A = 0 and B= 1

∴A⊕B=0⊕1=0.\(\overline{1}\)+\(\overline{0}\).1=0.0+1.1=1

In third case consider,

∴A⊕B=1⊕0=1.\(\overline{0}\)+\(\overline{1}\).0=1.1+0.0=1

In fourth case consider,

A = 1 and B = 1

∴A⊕B=1⊕1=1.\(\overline{1}\)+\(\overline{1}\).1=1.0+0.1=0

So, it is proved that the Boolean expression for A ⊕ B is

AB¯+A¯B  as  this Boolean expression satisfied all output states with respect to an XOR gate’s inputs conditions.

Proof using truth table:

Input A Input B Output Q
0 0 0
0 1 1
1 0 1
1 1 0

Thus, it is proved using the Truth Table that EX-OR gate gives true output when the number of inputs is odd.
The logic diagram of EX-NOR gate using NAND gate is given as:

To prove it using the Boolean equation, we know the Exclusive-NOR gate is represented as:

A ⊙ BConsider the following cases:

In the first case consider,

A = 0 and B = 0

∴ A ⊙ B = AB + ĀB̄ = (0 · 0) + (1 · 1) = 0 + 1 = 1

In the second case consider,

A = 0 and B = 1

∴ A ⊙ B = AB + ĀB̄ = (0 · 1) + (1 · 0) = 0 + 0 = 0

In third case consider,

A = 1 and B = 0

∴ A ⊙ B = AB + ĀB̄ = (1 · 0) + (0 · 1) = 0 + 0 = 0

In fourth case consider,

A = 1 and B = 1

∴ A ⊙ B = AB + ĀB̄ = (1 · 1) + (0 · 0) = 1 + 0 = 1

Thus, the Exclusive-NOR gate satisfies the Boolean equation A ⊙ B.

Proof using truth table:

Input A Input B Output Q
0 0 1
0 1 0
1 0 0
1 1 1

Thus, it is proved using the Truth Table that EX-NOR gate gives true output when the number of inputs is even.

(b)
The logic diagram of EX-OR gate using NOR gate only is given as:

To prove it using the Boolean equation, we know Exclusive-OR gate is “ A or B but not BOTH”.

Let us prove the above expression.
In the first case consider,

A = 0 and B = 0

∴A⊕B=0⊕0=0.1+1.0 = 0

In the second case consider,

A =0 and B = 1,

∴A⊕B = 0⊕1 =0.0+1.1=1

In third case consider,

A =1 and B =0,

∴A⊕B=1⊕0=1.1+0.0=1

In fourth case consider,

A=1 and B=1,

∴A⊕B=1⊕1=1.0+0.1=0

So, it is proved that the Boolean expression for A ⊕ B is  AB¯+A¯B , as this Boolean expression satisfied all output states with respect to an XOR gate’s inputs conditions.

Proof using truth table:

Input A Input B Output Q
0 0 0
0 1 1
1 0 1
1 1 0

Thus, it is proved using the Truth Table that EX-OR gate gives true output when the number of inputs is odd.
The logic diagram of EX-NOR gate using NOR gate is given as:

To proof it using Boolean equation, we know Exclusive-NOR gate is “A⊙B”

In the first case consider,

A = 0 and B = 0
∴A⊙B=AB+ĀB̄=0.0+1.1=1

In the second case consider,

A =o and B=1

∴A⊙B=AB+ĀB̄=0.1+1.0=0

In third case consider,

A=1 and B=0

∴A⊙B=AB+ĀB̄=1.0+0.1=0

In fourth case consider,

A=1 and B=1

∴A⊙B=AB+ĀB̄=1.1+0.0=1

Hence, it is proved that EX-NOR gate is A ⊙ B .
Proof using truth table:

Input A Input B Output Q
0 0 1
0 1 0
1 0 0
1 1 1

Thus, it is proved using the Truth Table that EX-NOR gate gives true output when the number of inputs is even.

Note:
All advanced logic gates can be derived using fundamental logic gates. Therefore, it is essential to have a clear understanding of the basic logic gates and their operations. Referring to their truth tables and Boolean expressions can be highly beneficial in resolving any challenges encountered during the process of building complex logic gates from basic ones.

TAGGED:and gate circuit diagramboolean logiccircuit diagram of nand logic gatelogiclogic gatelogic gate truth table and circuit diagramlogic gateslogic gates and truth tablelogic gates and truth tableslogic gates in hindilogic gates using transistors and diodeslogin gates circuit diagramnand logic gate truth table and circuit diagramtypes of logic gatesxnor logic gate circuit diagramxnor logic gate truth table and circuit diagram
Share This Article
Facebook Copy Link
Leave a Comment

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

You Might Also Like ↷

Relationship Between the Peak and RMS (NEET Physics)

November 19, 2024

Information about Solar Light and Solar Water Heaters (NEET Biology)

October 28, 2024

Differences Between Chasmogamous and Cleistogamous Flowers (NEET Biology)

November 7, 2024

Increasing Order of EMF of the Given Pairs (NEET Chemistry)

November 12, 2024

Best Neet Coaching in Chennai – Maduravoyal 

Neet Chennai
393.9kFollowersLike
34.3kFollowersFollow
4.42MSubscribersSubscribe
30.4kFollowersFollow
&copy NeetChennai – Maduravoyal
Our Newsletter
Subscribe now for a front-row seat to the latest in technology, marketing strategies, and market trends – Your Gateway to Innovation
[mc4wp_form]
Zero spam, Unsubscribe at any time.