- Chapter 1- C plus plus Revision Tour
- Chapter 2- Object Oriented Programming in C plus plus
- Chapter 3- Implementation of OOP Concepts in C plus plus
- Chapter 4- Constructor and Destructor
- Chapter 5- Inheritance
- Chapter 6- Data File Handling
- Chapter 7- Pointers
- Chapter 8- Arrays
- Chapter 9- Stack
- Chapter 10- Queue
- Chapter 11- Database Concepts
- Chapter 12- Structured Query Language
- Chapter 14- Networking and Open Source Concepts

Chapter 1- C plus plus Revision Tour |
Chapter 2- Object Oriented Programming in C plus plus |
Chapter 3- Implementation of OOP Concepts in C plus plus |
Chapter 4- Constructor and Destructor |
Chapter 5- Inheritance |
Chapter 6- Data File Handling |
Chapter 7- Pointers |
Chapter 8- Arrays |
Chapter 9- Stack |
Chapter 10- Queue |
Chapter 11- Database Concepts |
Chapter 12- Structured Query Language |
Chapter 14- Networking and Open Source Concepts |

Which gates are known as universal gates ? Why?

**Answer
1** :

Universal gates are the ones which can be used for implementing any gate like AND, OR and NOT or any combination of these basic gates. NAND and NOR gates are universal gates.

Draw the equivalent logic circuit for the following Boolean expression :

**Answer
2** :

**Answer
3** :

(A . B)’ = +

( + )’ = A + B

Specify which axioms/theorems are being used in the following Boolean reductions :

(a) (be)’ + be = 1

(b) xyz + zx = xz

**Answer
4** :

(a) x + x’ = 1 & Complementary law

(b) y + x = x & Absorption law.

**Answer
5** :
Associative Law: This law states that:

(A + B) + C = A + (B + C)

(A.B).C = A. (B.C)

Proof:

∴ From above truth table,

(A + B) + C = A + (B + C)

Similarly, we can prove,

A. (B.C) = (A. B).C

(A + B) + C = A + (B + C)

Similarly, we can prove,

A. (B.C) = (A. B).C

Correct the following boolean statements :

1. X+1 = X

2. (A’)’ = A’

3. A+A’ = 0

4. (A+B)’ = A.B

**Answer
6** :

1. X+l=l or X+0=X

2. ((A’)’) = A

3. A + A’ = 1 or A. A’ = 0

4. (A 4- B)’ = A’.B1

**Answer
7** :

(P+Q+R).(P’+Q+R).(P’+Q’+R)

**Answer
8** :

Absorption law states that :

A + AB = A and A. (A + B) = A

Algebraic method :

Taking LHS

A + AB = (A.l) + (A.B) by Identity

= A. (1 + B) by Distribution

= A.l by Null Element

= A

**Answer
9** :

Principle of duality : Duality principle states that from every boolean relation another boolean relation can be derived by :

(i) Changing each OR sign (+) to an AND sign (-).

(ii) Changing each AND sign (-) to an OR sign (+)

ex : Dual of A + A’B = A. (A’ + B)

Importance in Boolean Algebra : The principle of duality is an important concept in Boolean algebra, particularly in proving various theorems. The principle of duality is used extensively in proving Boolean algebra theorem. Once we prove that an expression is valid, by the principle of duality, its dual is also valid. Hence, our effort in proving various theorems is reduced to half.

X+ .Y = X + Y.

**Answer
10** :

This law is called “AbsorptionLaw” also referred as redundance law.

Name:

Email:

Copyright 2017, All Rights Reserved. A Product Design BY CoreNet Web Technology