Conversion of Binary to Decimal

by SmartCareer
Conversion of Binary to Decimal

Conversion of Binary to Decimal:
In the case of Integer numbers, to convert a binary number to a decimal number, the whole digit of the binary must be multiplied by the local value (2x, 2 is the base of binary). In the case of fractions, the digits have to multiply their local value (2x). Here you have to set values ​​like x = -1, -2, -3 from MSB to LSB.
MSB = Most Significant bit
LSB = Least Significant Bit.
Note: x0 = 1 and x1 = x | Here ‘x’ is any number.
Here,

 If  x = 1, 2, 3 ————.
For example, if x = 1 then 2-1 = 1/2
If x = 2 then 2-2 =1/4
If x = 3 then 2-3 = 1/8———- etc.

Example 1:

(11011. 101)2 , to determine the value of the equivalent decimal number:
(11011.101)2 = 1 × 24+ 1 × 23 + 0 x 22 + 1+ 21 + 1 x 20 +1 x 2-1 + 0 x 2-2 + 1 x 2-3
= 16 + 8 + 0 + 2 + 1 + 1/2 + 0 +1/8

= 27 + 0.5 + 0.125

= (27.625)10
So (11011.101)2 = (27.625)10 (Answer)

Example 2:
(1100011.011)2,  to determine the value of the equivalent decimal number: (1100011.011)2 = 1 x 26 + 1 x 25 + 0 x 24 + 0 x 23 + 0 x 22 + 1 + 21 + 1 x 20 + 0 x 2-1 +  1 x 2-2 + 1 x 2-3
 = 64 + 32 + 0 + 0 + 0 + 2 + 1 + 0 +1/4+1/8
 = 99 + 0.25 + 0.125
 = 99.375
 = (1100011.011)2 = (99.375)10 (Answer)

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