Dr Ajay Nagne NUMBER SYSTEM Dr Ajay Nagne

Dr. Ajay Nagne NUMBER SYSTEM Dr. Ajay Nagne 1

Table of Contents 2 What is Number System? Types of Number System Conversion Dr. Ajay Nagne

What is Number System? 3 A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, Multiplication and Dr. Ajay Nagne division.

The value of any digit in a number can be determined by: 4 The digit Its position in the number The base of the number system Dr. Ajay Nagne

Types of Number System 5 There are various types of number system in mathematics. The four most common number system types are: �Decimal number system (Base- 10) �Binary number system (Base- 2) �Octal number system (Base-8) �Hexadecimal number system (Base- 16) Dr. Ajay Nagne

6 Dr. Ajay Nagne

Decimal Number System (Base 10 Number System) 7 Decimal number system has base 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is expressed in decimal numbers. Dr. Ajay Nagne

Decimal Number System (Base 10 Number System) 8 Every position shows a particular power of the base (10). For example, the decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in the hundreds position, and 1 in the thousands place whose value can be written as Dr. Ajay Nagne

Decimal Number System (Base 10 Number System) 9 ( 1 4 5 7 )10 = = (1× 103) + (4× 102)+ (5× 101) + (7× 100) = (1× 1000) + (4× 100) + (5× 10) + (7× 1) = 1000 + 400 + 50 + 7 = 1457 Dr. Ajay Nagne

1) Decimal to Binary No. system 10 Most Significant Digit (MSD ) �The Left Most digit having the Highest weighted Value is Call as MSD. Least Significant Digit (LSD) The right Most digit having the Lowest weighted Value is Call as LSD. Ex. MSD 2789 LSD Dr. Ajay Nagne

Binary Number System (Base 2 Number System) 11 The base 2 number system is also known as the Binary number system wherein, only two binary digits exist, i. e. , 0 and 1. Specifically, the usual base-2 is a radix of 2. This system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number. Dr. Ajay Nagne

Binary Number System 12 bit = 0 or 1 1 Byte = 8 bits 1 Kilobyte = 1024 Byte 1 Megabyte = 1024 Kb 1 Gigabyte= 1024 MB 1 Terabyte = 1024 GB Dr. Ajay Nagne

13 MS B LS B Binary Digit 28 27 26 25 24 23 22 21 20 256 12 8 64 32 16 8 4 2 1 Dr. Ajay Nagne

Binary Number System 14 Ex. 10010 Dr. Ajay Nagne

Binary Number System 15 Most Significant Bit (MSB ) �The Left Most bit having the Highest weighted Value is Call as MSB. Least Significant Bit (LSB) The right Most bit having the Lowest weighted Value is Call as LSB. Ex. MSB 10010 LSB Dr. Ajay Nagne

Octal Number System (Base 8 Number System) 16 In the octal number system, the base is 8 and it uses numbers from 0 to 7 to represent numbers. Octal numbers are commonly used in computer applications. Converting an octal number to decimal is the same as decimal conversion and is explained below using an example. Dr. Ajay Nagne

Hexadecimal Number System (Base 16 Number System) 17 In the hexadecimal system, numbers are written or represented with base 16. In the hex system, the numbers are first represented just like in decimal system, i. e. from 0 to 9. Then, the numbers are represented using the alphabets from A to F. The below-given table shows the representation of numbers in the hexadecimal number system. Dr. Ajay Nagne

Cont. . . 18 Hexa 0 decimal 1 2 3 4 5 6 7 8 9 A B C D E F Decima 0 l 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Dr. Ajay Nagne

Decimal Binary Octal Hexadecimal 0 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Dr. Ajay Nagne

20 Name Decimal Base Symbols Example 0, 1, 2, 3, 4, 5, 6, 7, 10 (279)10 8, 9 Binary 2 0, 1 10010 Octal 8 0, 1, 2, 3, 4, 5, 6, 7 (157)8 Hexadecimal 0, 1, 2, 3, 4, 5, 6, 7, 16 8, 9, A, B, C, D, E, F Dr. Ajay Nagne 3 DB

21 Conversion from One Number System to Another Number system Dr. Ajay Nagne

Decimal to Other Base System 22 Decimal to Binary No. system 2) Decimal to Octal No. system 3) Decimal to Hexadecimal No. system 1) Dr. Ajay Nagne

1) Decimal to Binary No. system 23 Most Significant Bit (MSD ) �The Left Most digit having the Highest weighted Value is Call as MSD. Least Significant Bit (LSD) The right Most digit having the Lowest weighted Value is Call as LSD. Ex. MSD 2789 LSD Dr. Ajay Nagne