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Let us first learn how to form binary numbers.
As the binary number system consists of two digits 0 and 1 hence, its base is 2. Each digit or bit in binary
number system can be either 0 or 1. A combination of binary digits may be used to represent different
quantities like 1001. The positional value of each digit in binary number is twice the place value or face
value of the digit to its right. The weight of each position is a power of 2.
The place value of the digits according to position and weight is as follows:
Position 3 2 1 0 –1 –2
•
Weights 2 3 2 2 2 1 2 0 2 –1 2 –2
Factbot
A single binary digit (like '0' or ‘1’) is called a ‘bit’. For example 11010 is five bits long. The word bit is made up
of the words 'binary digit’.
Octal Number System
Position 7 6 5
The octal number system consists of eight digits from 0 to 7. Weight 8 2 8 1 8 0
Hence, the base of octal number system is 8. In this system, the 2 1 0
position of each digit represents a power of 8. Any digit in this Real Value of 7 × 8 6 × 8 5 × 8
system is always less than 8. Octal number system is used as a each digit
shorthand representation of long binary numbers. The number (841) is not valid in this number system as
8
8 is not a valid digit. The place value of digits according to the position and weight are given in table.
Hexadecimal Number System
The hexadecimal number system consists of 16 digits from 0 to 9 and letters from A to F. The letters A to
F represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position
in hexadecimal number system represents a power of 16. For example, the number (764) is a valid
16
hexadecimal number. It is different from (764) which is seven hundred and sixty four. This number
10
system provides shortcut method to represent long binary numbers. Representation of Hexadecimal
Number System into Decimal Form.
Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F
Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
DECIMAL TO BINARY CONVERSION
To convert a decimal number into a binary number, follow these steps:
Divide the decimal number by 2 (the base of the binary number system).
Note down the quotient and the remainder.
Divide the quotient obtained again by 2 and note down the resulting quotient and remainder.
Repeat the procedure till you reach a quotient less than 2.
Firstly, list the last quotient and all the remainders (moving from bottom to top). You will get your
binary number.
#Number System 13

