Page 11 - Computer Genius Class 07
P. 11
The alue o a num er is determined y multiplying the digits ith the eight o their position and
adding the results. This method is no n as expansion method. The right most digit o the num er
has the lo est eight. This digit is called Least Significant Digit LSD . The le t most digit o a
num er has the highest eight. This digit is called Most Significant Digit MSD . The digit in the
num er 2 is the most significant digit and is the least significant digit.
The gi en ta le sho s positional eight o decimal num er 2 .
1
Hundereds Tens Units
Weights 1 2 1 1 1
Real Value of each digit 1 2 2 1 1 1
Result 2
Binary Number System
The ord inary comes rom i meaning t o. e see i in ords such as icycle t o heels
or inocular t o eyes . The inary num ers ha e the ase o 2.
A computer is a machine made up o transistors s itches and other components. All these electronic
components are in t o mutually e clusi e states either O or OFF. The t o inary digits represent
these t o states. ery instruction gi en to a computer is con erted into s and 1 s so that it can e
understood and implemented y the computer. inary language is there ore no n as the machine
language.
A inary num er is made up o only 0s and 1s. Name Size (bits) Examples
ample o inary um er 110100
it 1 Single digit either or 1
There is no 2 or in inary
i le roup o digits
et us first learn ho to orm inary num ers.
yte roup o digits
As the inary num er system consists o t o
ord 1 roup o 1 digits
digits and 1 hence its ase is 2. ach digit or
it in inary num er system can e or 1. A com ination o inary digits may e used to represent
different uantities li e 1 1. The positional alue o each digit in inary num er is t ice the place
alue or ace alue o the digit o its right side. The eight o each position is a po er o 2.
The place alue o the digits according to position and eight is as ollo s
Position 2 1 1 2
Weights 2 2 2 2 1 2 2 1 2 2
A single inary digit li e or 1 is called a it . For e ample 11 1 is fi e its long. The ord
it is made up rom the ords inary digit .
Number System 9

