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The numbers 725 and 1629 can be expressed as:
(725) = 7 × 10 + 2 × 10 + 5 × 10 0
2
1
10
(1629) = 1 × 10 + 6 × 10 + 2 × 10 + 9 × 10 0
3
2
1
10
Knowledge Discovery Subject Enrichment
The powers of the base of a number system are counted from right to left, starting with zero (0). The value
of a number is equal to the sum of the place values of all its digits.

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
th
nd
st
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
3
2
1
2
(10110) = 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 0 × 2 0
4
3
1
2
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.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

The Hexadecimal number system is also called Alphanumeric number system as it uses both alphabet
and numbers to represent the digits.
Let us learn to convert numbers from one number system into another.

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