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Introduction to Number Systems - Binary to Decimal Conversion

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Binary to Decimal Conversion

To convert a binary numbers Into decimal number, following are the steps: 
Step 1: Write the given binary Number
Step 2: Write the binary weightage below each number 
Step 3: Cancel the weightage, which is placed below zero because any number multiplied by zero is zero. 
Step 4: Add the remaining numbers. 

Examples Of Binary to Decimal Conversion 

1)  Convert (110011)2  into decimal 

     1         1        0        0          1         1

=  25  +   24  +   23 +   22   +   21   +  20

= 32  +   16   + `\cancel(8)`  +  `\cancel(4)`   +   2     +  1

=(51)10                

 ∴ (110011)2   =   (51)10

2)  If  (100001)2   =  (x)10  find X

         1          0            0         0         0       1

        32    + `\cancel(16)`+      `\cancel(8)`+     `\cancel(4)`+    `\cancel(2)`+    1

         X    =      33              

 ∴(100001)2   =    (33)10

Fractional binary numbers:
To convert the mixed binary numbers containing integers and fractions, we can follow the same steps

1) Convert (1100 . 1011)into decimal  

(1100 . 1011)2 = (1 x 23) + ( 1 x 22) + (0 x 21) + (0 x 20) + (1 x 2-1)  + (0 x  2-2) + (1 x 2-3) + (1 x 2-4)
                         =   8 + 4 + 0 + 0 +  0.5  + 0 + 0.125 + 0.0625 
                         =  (12.6875) 10
.

 

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