Page 11 - Computer_Genius_v2.1_C7_flipbook
P. 11
The value of a number is determined by multiplying the digits with the weight of their position and
adding the results. This method is known as expansion method. The right-most digit of the number
has the lowest weight. This digit is called Least Significant Digit (LSD). The left-most digit of a
number has the highest weight. This digit is called Most Significant Digit (MSD). The digit 7 in the
number 724 is the most significant digit and 4 is the least significant digit.
The given table shows positional weight of decimal number (724) .
10
Hundereds Tens Units
Weights 10 2 10 1 10 0
Real Value of each digit 7 × 10 2 2 × 10 1 4 × 10 0
Result 700 20 4
Binary Number System
The word 'binary' comes from 'Bi' meaning two. We see 'bi' in words such as ‘bicycle‘ (two wheels)
or ‘binocular’ (two eyes). The binary numbers have the base of 2.
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. The two binary digits represent
these two states. Every instruction given to a computer is converted into 0’s and 1’s so that it can be
understood and implemented by the computer. Binary language is therefore known as the machine
language.
A binary number is made up of only 0s and 1s. Name Size (bits) Examples
Example of Binary Number: 110100
Bit 1 Single digit either 0 or 1
There is no 2, 3, 4, 5, 6, 7, 8 or 9 in Binary!
Nibble 4 Group of 4 digits
Let us first learn how to form binary numbers.
Byte 8 Group of 8 digits
As the binary number system consists of two
Word 16 Group of 16 digits
digits 0 and 1 hence, its base is 2. Each digit or
bit in 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 binary number is twice the place
value or face value of the digit of its right side. 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
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 from the words 'binary digit’.
Number System 9

