Chapter 1: Chapter 1:

Number System. Number System. BIM BIM

Digital Logic NotesDigital Logic NotesAnil SahaAnil Saha

Introduction Introduction

Number system is the way to representing an entity. Number system is the way to representing an entity.

Types of Number System.Types of Number System.

1.1. Positional Number SystemPositional Number System

A number system where the position of a number A number system where the position of a number changes the value of the number eg: decimal changes the value of the number eg: decimal number system. number system.

2. Non Positional Number System2. Non Positional Number System

A number system in which value of the number A number system in which value of the number doesn’t change according to its position it is nun doesn’t change according to its position it is nun positional number. Eg. Roman Numbers. positional number. Eg. Roman Numbers.

Decimal Number System: The number system Decimal Number System: The number system having 10 digit form 0-10 and having base 10 is having 10 digit form 0-10 and having base 10 is called decimal number system. called decimal number system.

Octal Number System: The number system having Octal Number System: The number system having 8 digit from 0-7 and having base 8 is called octal 8 digit from 0-7 and having base 8 is called octal number system. number system.

Binary Number System: The number system Binary Number System: The number system having 2 digit from 0-1 and having base 2 is having 2 digit from 0-1 and having base 2 is called binary number system. called binary number system.

HexaDecimal Number System: The number HexaDecimal Number System: The number system having 16 digit from 0-F and having base system having 16 digit from 0-F and having base 16 is called hexadecimal number system. 16 is called hexadecimal number system.

Structure of Number System. Structure of Number System.

Positional Number System: Positional Number System:

1.1. Decimal Number SystemDecimal Number System

2.2. Binary Number SystemBinary Number System

3.3. Octal Number SystemOctal Number System

4.4. Hexadecimal Number SystemHexadecimal Number System

5.5. Non-Positional Number SystemNon-Positional Number System

Number System Forms Number System Forms Decimal, Octal, Hexadecimal, BinaryDecimal, Octal, Hexadecimal, Binary00 00 00 0000000011 11 11 0001000122 22 22 0010001033 33 33 0011001144 44 44 0100010055 55 55 0101010166 66 66 0110011077 77 77 0111011188 1010 88 1000100099 1111 99 100110011010 1212 AA 101010101111 1313 BB 101110111212 1414 CC 110011001313 1515 DD 110111011414 1616 EE 111011101515 1717 FF 11111111

Number conversion Number conversion (Decimal to any number system divide)(Decimal to any number system divide)

Decimal to Binary Conversion: Decimal to Binary Conversion:

(65)(65)10 10 = (?)= (?)22

Boolean Algebra: Boolean Algebra:

Boolean Algebra is the mathematics of digital Boolean Algebra is the mathematics of digital system. system.

Variable:Variable:

Variable is the symbol which can be representing Variable is the symbol which can be representing the logical quantity. the logical quantity.

Complement: Complement:

Complement is the inverse of the variables which Complement is the inverse of the variables which can be represented bar over the variables can be represented bar over the variables

Literal: Literal:

Literal is the variable or complement of variable. Literal is the variable or complement of variable.

DE Morgan’s Theorems:DE Morgan’s Theorems:

Law1: The complement of the product of the Law1: The complement of the product of the variable is equal to the sum of complement variable is equal to the sum of complement of variable. of variable.

The complement of two or more variables The complement of two or more variables product is equivalent to the sum of individual product is equivalent to the sum of individual variable. variable.

Law.:2Law.:2The complement of sum of variables is equal The complement of sum of variables is equal to the product of the complement of the to the product of the complement of the variables;variables;

The complement of a sum of variables is equal The complement of a sum of variables is equal to the product of two or more variables OR is to the product of two or more variables OR is equivalent to the AND of the complement of equivalent to the AND of the complement of the individual variable. the individual variable.