How a binary number can be converted into decimal number?Explain with example.
Subject  Introduction to Computer System 

NU Year  Set: 1.(d) Marks: 4 Year: 2013 
The decimal or “denary”
counting system uses the Baseof10 numbering system where each digit in a
number takes on one of ten possible values, called “digits”, from 0 to 9,
eg. 21310 (Two Hundred and Thirteen).
But as well as having
10 digits ( 0 through 9 ), the decimal numbering system also has the
operations of addition ( + ), subtraction ( – ),
multiplication ( × ) and division ( ÷ ).
In a decimal system
each digit has a value ten times greater than its previous number and this
decimal numbering system uses a set of symbols, b, together with a
base, q, to determine the weight of each digit within a number. For
example, the six in sixty has a lower weighting than the six in six hundred.
Then in a binary numbering system we need some way of converting Decimal
to Binary as well as back from Binary to Decimal.
Any numbering system
can be summarised by the following relationship:
N = bi qi 

where: 
N is a real
positive number 
N = bn qn… b3 q3 + b2 q2 + b1 q1 + b0 q0 + b1 q1 + b2 q2… etc.
For
example: N = 616310 (Six Thousand One Hundred and
Sixty Three) in a decimal format is equal to:
6000 + 100 + 60 + 3 = 6163
or it can be written
reflecting the weight of each digit as:
( 6×1000
) + ( 1×100 ) + ( 6×10 ) + ( 3×1
) = 6163
or it can be written in
polynomial form as:
( 6×103 ) + (
1×102 ) + ( 6×101 ) + ( 3×100 ) = 6163