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The given table shows positional weight of decimal number (724) .
10
Hundreds Tens Units
Weights 10 10 10
2
0
1
0
1
2
Real Value of each digit 7 × 10 2 × 10 4 × 10
Result 700 20 4
Binary Number System

A computer is a machine made up of transistors, switches, and other components. All these electronic
components are in two mutually exclusive states, either ON or OFF. These two states are represented
by two binary digits. A computer converts every instruction into 0's and 1's for understanding and
implementation. Therefore, binary language is referred to as machine language.

The word 'binary' comes from 'Bi', which means two. We see 'bi' in words such as ‘bicycle’ (two wheels)
or ‘binocular’ (two eyes). A binary number is made up of only 0s and 1s.
Example of Binary Number: 110100

There is no 2, 3, 4, 5, 6, 7, 8 or 9 in Binary.

Name Size (bits) Examples
Bit 1 Single digit either 0 or 1

Nibble 4 Group of 4 digits
Byte 8 Group of 8 digits

Word 16 Group of 16 digits

For example: If a document is compost of 256 bits, how many bytes does the document contain?
Number of bytes = 256 bits 8 bits per byte = 32 bytes

So, this is how we calculate the number of bytes.

Let us first learn how to form binary numbers.
As the binary number system consists of two digits 0 and 1, its base is 2. Each digit or bit in a binary
number system can be 0 or 1. A combination of binary digits may be used to represent different
quantities, like 1001. The positional value of each digit in a binary number is twice the place value or
face value of the digit to its right. Each position's weight is a power of 2.

Position 3 2 1 0 -1 -2
•
Weights 2 3 2 2 2 1 2 0 2 -1 2 -2

DIFFERENCES BETWEEN BINARY AND DECIMAL NUMBER SYSTEMS

The table below shows the key differences between the decimal number system and the binary number
system:

#Binary Language 95