04.01.13

As we know there are three logic gates to define various logics and on the basis of same Boolean Algebra have some basic postulates (fundamental laws) as follows:

1. OR relations (which is also known as logical addition, as it has four cases: 0+0=0, 0+1=1, 1+0=1, 1+1=1)

2. AND relations (which is also known as logical multiplication, as it has four cases: 0.0=0, 0.1=0, 1.0=0, 1.1=1)

3. NOT relations (which is also known as complement rule, as it has two cases: 0=1, 1=0)

Before we start, lets have a look on Principle of Duality in boolean expressions:

Principle of Duality means, that by making changes into the given boolean expression, another boolean expression can be derived. Following changes can be made to the given boolean expression:

0 + 0 = 0, will become, 1 . 1 = 1, after principle of duality is applied to it. And the boolean expression derived is known as DUAL OF ORIGINAL EXPRESSION. And if we see closely, 1 . 1 = 1, is also Postulate II of Boolean Algebra.

This tutorial is based on: "Computer Science - Seventh Edition" book by 'Sumita Arora' Pages: 659-660.

**Postulates of Boolean Algebra**As we know there are three logic gates to define various logics and on the basis of same Boolean Algebra have some basic postulates (fundamental laws) as follows:

1. OR relations (which is also known as logical addition, as it has four cases: 0+0=0, 0+1=1, 1+0=1, 1+1=1)

2. AND relations (which is also known as logical multiplication, as it has four cases: 0.0=0, 0.1=0, 1.0=0, 1.1=1)

3. NOT relations (which is also known as complement rule, as it has two cases: 0=1, 1=0)

Before we start, lets have a look on Principle of Duality in boolean expressions:

Principle of Duality means, that by making changes into the given boolean expression, another boolean expression can be derived. Following changes can be made to the given boolean expression:

- Changing each OR with AND (+ with .) and its reverse (changing . with +)
- Replacing each 0 bit with 1 bit and its reverse, replacing 1 bit with 0 bit.

0 + 0 = 0, will become, 1 . 1 = 1, after principle of duality is applied to it. And the boolean expression derived is known as DUAL OF ORIGINAL EXPRESSION. And if we see closely, 1 . 1 = 1, is also Postulate II of Boolean Algebra.

This tutorial is based on: "Computer Science - Seventh Edition" book by 'Sumita Arora' Pages: 659-660.

*Next topic: 07.01.13: Lecture 9: Theorems of Boolean Algebra*

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