This document provides an overview of different number systems including decimal, binary, octal, and hexadecimal. It defines each system, their bases, examples of conversions between them, and their uses in computing. Decimal is base 10, binary is base 2, octal is base 8, and hexadecimal is base 16. Conversions between binary, decimal, octal and hexadecimal are demonstrated through examples. Number systems are important in computing because binary is used for electronic circuitry, octal and hexadecimal allow more compact notation than binary, and decimal is used for basic calculations.

2. S.no. Description Slide no.
1. Introduction to Number System 3
2. Basic facts 4
3. Decimal Number System 5-6
4. Binary Number System 7
5. Conversions 8-9
6. Octal Number System 10
7. Hexadecimal Number System 11
8. Table 12
9. Uses in Computer System 13
10. Sources 14

3. A number system defines how a number can be represented
using distinct symbols. A number can be represented differently
in different systems.
Many number systems were introduced with the passage
of time, like:
•Decimal number system
•Binary number system
•Octal number system
•Hexadecimal number system

4. •A unit of information expressed as either a 0 or 1
in binary notation.
•A group of binary digits or bits (usually eight)
operated on as a unit.
•A byte is considered as a unit of memory size.
•The base is the number of digits used in it.
•The larger the base, the more numerals are required.
Decimal- Base 10
Binary- Base 2
Octal- Base 8
Hexadecimal- Base 16

5. The need for counting has paved the path to introduce decimal number system in which
10 digits 0,1,2,3…9 are used to form any number. Most of our arithmetic operations are
performed with decimal numbers.
•The prefix ‘deci’ stands for 10.
•The decimal number system is a base 10 number system.
•Each number can be used individually or they can be grouped to form a numeric value.
•Example- 52, 16.83, -243 etc.
The value of each digit in a number depends upon the following:
The face value of the digits
The base of the number system
The position of the digit in the number

8. Conversion of decimal number into binary system.
The rules are:
1. Divide the given decimal number with the base 2.
2. Write down their remainder and divide the quotient again by 2.
3. Repeat the step 2 till the quotient is 0.
Example-

9. Conversion of binary into decimal number
The rules are:
1. Multiply each binary number with 2 having the power 0 for unitary position,
starting from the extreme right digit.
2. Increase the power one by one keeping the base fixed as 2.
3. Sum up all the products to get the decimal number.
Example-

10. •Octal (base 8) was previously a popular choice for representing
digital circuit numbers in a form that is more compact than
binary.
•The octal number system consists of 8 digits i.e. 0 to 7 with the
base 8.
•1 octal digit is equivalent to 3 bits.
Examples:
278 = 2×81+7×80 = 16+7 = 23
308 = 3×81+0×80 = 24
43078 = 4×83+3×82+0×81+7×80= 2247

11. •The prefix ‘hexa’ stands for 6 and the prefix ‘deci’ stands for
10.
•This number system contains 16 systems and therefore has
the base 16.
•It uses the digits (0-9) and (A-F).
•Numbers are 0, 1, 2…8, 9, A, B, C, D, E, F. B is 11, E is 14.
•1 Hex digit is equal to 4 bits.
•Each place value in a hexadecimal number is a power of 16.
Examples:
2816 = 28H = 2×161+8×160 = 40
2F16 = 2FH = 2×161+15×160 = 47
BC1216 = BC12H = 11×163+12×162+1×161+2×160= 48146

13. 1. A switch is just used to turn ON or turn OFF any desired
device… using the concept binary system.
2. Electronic Circuitry uses the octal system and
hexadecimal system.
3. Decimal number system uses basic calculation and
complex calculation in daily life.

14. •www.easytechtips24.com/
•www.aqua-calc.com/
•www.rapidtables.com/
•I.T. Apps School Book Class 7
•www.wikipedia.org/