This document discusses different number systems including decimal, binary, octal, hexadecimal, BCD, and Gray code. It provides the following information: - Decimal uses base 10 with digits 0-9. Binary uses base 2 with digits 0-1. Octal uses base 8 with digits 0-7. Hexadecimal uses base 16 with digits 0-9 and A-F. - BCD represents each decimal digit with a 4-bit binary code, allowing decimal numbers to be written in binary. Gray code is a non-weighted binary code where successive codes differ by one bit. - Each number system defines a set of values or symbols to represent quantities. The base determines how many unique symbols are

1. CLASS – IX
NUMBER SYSTEM
Name: Sandeep Jaiswal
Reg. no.: 11813483
Integrated. B.sc B.Ed.
Lovely Professional University

2. WHAT IS NUMBER SYSTEM ?
•A system for representing number of certain type.
•A number system defines a set of values used to
represent quantity.
• Example:
–There are several systems for representing the counting
numbers.
–These include the usual base “10” or decimal system :
0,1,2,3,…..10,11,12,..99,100,…

3. NUMBER SYSTEM
•Decimal is the number system and is used in our day to day life
•Binary is a number system that is used in computers
•Octal is a number system that represents groups of binary
numbers. It is used in digital displays.
•Hexadecimal (Hex) is a number system that represents groups
of binary numbers. Hex is primarily used in computing.

4. DIFFERENT NUMBER SYSTEM
•Decimal Number System
-Base 10
• Binary Number System
- Base 2
• Octal Number System
-Base 8
• Hexadecimal Number Sys tem
- Base 16

8. DECIMAL NUMBER SYSTEM
• Decimal number system contains ten unique symbols 0,1,2,3,4,5,6,7,8 and 9.
• Since counting in decimal involves ten symbols, we can say that its base or radix is ten.
• In this system, any number (integer, fraction or mixed) of any magnitude can
be represented using these ten symbols only
Each symbols in the number is called a “Digit”
Examples
• 1214
• 1897
• 9875.54

9. BINARY NUMBER SYSTEM
•Binary number system is a positional weighted system.
•It contains two unique symbols 0 and 1.
•Since counting in binary involves two symbols , we can say that its base or
radix is two.
•A binary digit is called a “Bit”
•A binary number consists of a sequence of bits, each of which is either
a 0 or a 1.
•The binary point separates the integer and fraction parts.
•Examples, 1110
0000, 1001, 0101

10. OCTAL NUMBER SYSTEM
•Octal number system is a positional weighted system.
•It contains eight unique symbols 0,1,2,3,4,5,6 and 7.
•Since counting in octal involves eight symbols, we can say that its base or
radix is eight.
•The largest value of a digit in the octal system will be 7.
•That means the octal number higher than 7 will not be 8, instead of that it
will be 10

11. HEXADECIMAL NUMBER SYSTEM
•Binary numbers are long. These numbers are fine for machines but are too
lengthy to be handled by human beings. So there is a need to represent the
binary numbers concisely.
•One number system developed with this objective is the hexadecimal number
system (or Hex)
•It contains sixteen unique symbols
•0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F.
•Since counting in hex involves sixteen symbols, we can say that its base or radix
is sixteen.

12. BCD OR 8421 NUMBERS
•BCD means BinaryCoded Decimal.
•BCD is a system of weiting a numbers that a four-digit binary code to
each digit 0 through 9 in decimal numbers.
•The smallest BCD number is (0000) and the largest is (1001). The next
number to 9 will be 10 which is expressed as (0001 0000) in BCD.
•There are six illegal combinations 1010, 1011,1100, 1101, 1110 and 1111
in this code i.e. they are not part of the 8421 BCD code

13. DECIMAL TO BCD CONVERSION
Sr.No. Decimal Number BCD
1 2 0010
2 11 00010001
3 6 0110
4 213 001000010011
5 10 0001000

14. GRAY CODE(NON WEIGHTED BINARY CODE)
• The gray code is non-weighted code.
• It is not suitable for arithmetic operations.
• It is a cyclic code i.e. unit distance code
• PROPERTIES OF GRAY CODE 1.Unit
Distance Code
successive code words in this code differ in one bit position only.
2.Reflective Code
grey codes for all decimal numbers can be generated through the reflective
property through the table.

15. GRAY CODE(NON WEIGHTED BINARY CODE)