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The numbers 725 and 1629 can be expressed as:
(725) = 7 × 10 + 2 × 10 + 5 × 10 0
1
2
10
(1629) = 1 × 10 + 6 × 10 + 2 × 10 + 9 × 10 0
1
2
3
10
Binary Number System (Base 2)
The Binary number system consists of only two digits ‘0’ and ‘1’. So, the
base of the binary number system is 2. The digits ‘0’ and ‘1’ are known
as Binary Digits, or Bits.
A digital computer represents data and information using the binary
number system. It is based on electronic circuits, which have two
states – ON and OFF. The ON state is assigned the value ‘1’, while the
OFF state is assigned the value ‘0’.
In the Binary number system, each place represents a power of 2, just as each place represents a
power of 10 in the decimal number system.
Powers of Two

6 Position 5 Position 4 Position 3 Position 2 Position 1 Position
st
nd
th
th
rd
th
32 16 8 4 2 1
2 5 2 4 2 3 2 2 2 1 2 0
Two to the Two to the Two to the Two to the Two to the Two to the
power five power four power three power two power one power zero

The numbers 1001 and 10110 can be expressed as :
(1001) = 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 0
2
3
1
2
(10110) = 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 0 × 2 0
1
3
2
4
2
A Bit is the smallest unit of data in a computer. A sequence of 8 bits, such as 10110001 constitute a
Byte. A byte can represent a letter, a number, or a symbol.
Octal Number System (Base 8)
The Octal number system consists of 8 digits, 0 to 7. So, the base of the Octal number system is 8.
Hexadecimal Number System (Base 16)
The Hexadecimal number system consists of 16 symbols. So, the base of the Hexadecimal number
system is 16. It uses 10 digits (0 to 9) and 6 letters (A to F). Letters A to F represent the numbers 10 to 15.
Let us learn to convert numbers from one number system into another.

CONVERSION OF DECIMAL NUMBER INTO BINARY NUMBER
To convert a decimal number into a binary number:

• Divide the decimal number constantly by two.
• Write the remainder on the right hand side.
• Continue the process till you reach a zero quotient.
• Write the remainders from bottom to top to form the binary equivalent of the decimal number.
The first remainder becomes the last binary digit, and the final remainder becomes the first
binary digit.

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