This document provides information about different number systems including: - Types of numbers like natural numbers, whole numbers, integers, rational and irrational numbers. - Binary, decimal, octal and hexadecimal number systems. It explains how to convert between these systems using examples. - ASCII is described as a code for representing English characters as numbers to allow transfer of data between computers. - Fractions are explained in the binary system using powers of 2 to determine the value of each place. - Various methods of converting between number systems like decimal to binary, octal or hexadecimal and vice versa are outlined.

1. NUMBER SYSTEM
Made BY : Raman, Quais, Nikhil / Class : IX-A
MATHS PROJECT WORK

2.  Types of Number
 ASCII
 BINARY
 DECIMAL
 OCTAL
 HEXADECIMAL
 FRACTIONAL
 CONVERSIONS

3.  Natural number – 1, 2, 3, 4……..n
 Whole number - It is collection of Natural number along
with 0 (0, 1, 2, 3, 4…….n)
 Integers - It is collection of whole Number along with
negative numbers (-n……-3, -2, -1, 0, 1, 2, 3…….n)
 Rational numbers- Any number which can be expressed
in form of p/q where p and q are intefers and q is not
equal to 0 is known as Rational numbers (3/4, -3/9, 2)
 Irrational numbers - Any number which cannot be
expressed in form of p/q where p and q are intefers and q
is not equal to 0 is known as Irrational numbers ( 2 ,
5 )

4. ASCII
 American Standard Code for Information Interchange
 ASCII is a code for representing English characters as numbers, with each
letter assigned a number from 0 to 127. For example, the ASCII code for
uppercase M is 77. Most computers use ASCII codes to represent text, which
makes it possible to transfer data from one computer to another.
 Text files stored in ASCII format are sometimes called ASCII files. Text editors
and word processors are usually capable of storing data in ASCII format .
 Numeric data files or Executable programs are never stored in ASCII format.

5. BINARY System
 A method of representing numbers in which only the digits 0 and 1 are used.
Successive units are powers of 2 .
 The first ten numbers in binary notation, corresponding to the numbers 0, 1,
2, 3, 4, 5, 6, 7, 8, and 9 in decimal notation, are 0, 1, 10, 11, 100, 101, 110,
111, 1000, and 1001.
 The decimal equivalent of a binary number can be calculated by adding
together each digit multiplied by its power of 2; for example, the
binary number 1011010 corresponds to (1 × 26
) + (0 × 25
) + (1 × 24
) +
(1 × 23
) + (0 × 22
) + (1 × 21
) + (0 × 20
) = 64 + 0 + 16 + 8 + 0 + 2 + 0 = 90 in the
decimal system.

6. DECIMAL System
 Decimal system is a way of writing numbers. Any number, from huge
quantities to tiny fractions, can be written in the decimal system using only
the ten basic symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0.
 The value of any of these symbols dep ends on the place it occupies in the
number.
 Example : 258610 = (2X1000)+(5X100)+(8X10)+(6X1)
or
2X103 + 5X102 + 8X101 + 6X100

7. OCTAL System
 The octal, or base 8, number system is a common system used with
computers. Because of its relationship with the binary system.
 It is useful in programming some types of computers.
 One octal digit is the equivalent value of three binary digits.
 Example : 5628 = 5X82
+ 6X81
+ 2X80
= 320 + 48 + 2
= 37010

8. HEXADECIMAL System
 It is number system having a base 16; the symbols for the numbers 0--9 are
the same as those used in the decimal system, and the numbers 10--15 are
usually represented by the letters A--F.
 The system is used as a convenient way of representing the internal binary
code of a computer.
 Example : 2A3B16 = 2x163
+ A(10)x162
+ 3x161
+ B(11)X160
= 8192 + 2560 + 48+ 11
= 1081110

9. FRACTIONAL System
 The decimal system uses powers of 10 to determine the value of a position.
The binary system uses powers of 2 to determine the value of a position.
 All numbers or values to the left of the radix point are whole numbers, and
all numbers to the right of the radix point are fractional numbers.
 Example : Binary no. 101.12 = 1x22
+ 0x21
+ 1x20
+ 1x2-1
= 4 + 0 + 1 +.5
=5.510

10. CONVERSIONS
 Decimal to Binary Number
We will take the number 29 and divide it by 2 until the answer reaches 0 and where
there is a remainder we write one (1) where there is no remainder we write zero (0).
470610 =1001011000102
2910 = 111012

11. CONVERSIONS
 Decimal to Octal Number
250210 = 47068

12. CONVERSIONS
 Decimal to Hexadecimal Number
42810 = 1AC16

13. CONVERSIONS
 Binary to Decimal Number
110012 = 1x24 + 1x23 + 0x22 + 0x21 + 1x20
= 16 + 8 + 0 + 0 + 1
= 25110
101010102 = 1x27 + 0x26 + 1x25 + 0x24 + 1x23 + 0x22 + 1x21 + 0x20
= 128 + 0 + 32 + 0+ 8 + 0 + 2 + 0
= 17010

14. CONVERSIONS
 Octal and Hexadecimal to Decimal Number
Octal :
5628 = 5x82 + 6x81 + 2x80
= 320 + 48 + 2
= 37010
Hexadecimal :
 2A3B16 = 2x163
+ A(10)x162
+ 3x161
+ B(11)X160
= 8192 + 2560 + 48+ 11
= 1081110

15. CONVERSIONS
 Fractional to Decimal Number
Binary to Decimal:
110.1012 = 1x22 + 1x21 + 0x20 + 1x2-1 + 0x2-2 + 1x2-3
= 4 + 2 + 0 + .5 + 0 + .125
=6.62510
Octal to Decimal:
127.5488 = 1x82 + 2x81 + 7x80 + 5x8-1 + 4x8-2 + 8x8-3
= 64 + 16 + 7 + 5/8 + 4/64
= 87 + 0.625 + 0.0625
= 87.687510
Hexadecimal to Decimal :
2B.C416 = 2x161 + B(11)x160 + C(12)x16-1 + 4x16-2
= 32 + 11 + 12/16 + 4/256
= 43 + 0.75 + 0.015625
= 43.76565210

16. THANK YOU