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 Base-of-10 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
N is a real
N = bn qn… b3 q3 + b2 q2 + b1 q1 + b0 q0 + b-1 q-1 + b-2 q-2… 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