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2015-12-15T21:30:20+05:30

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In simple English, binary means ‘two’. Hence binary numeral system is a way to represent numbers using only two digits – 0 and 1. This system is widely used in computers to do all the tasks like calculations, taking logical decisions etc. Each successive digit represents a power of 2.

  Coversion from binary to decimal:
1.    Write down the binary number and list the powers of 2 from right to left.       
2^6      2^5    2^4    2^3    2^2    2^1     2^0  
   1          0        1       1        0        0        1
   

2.    Write the digits of the binary number below their corresponding powers of two.
64      32    16    8     4     2     1 (Power of two)  
1        0      1     1     0     0     1 (binary number)
   

3.    Multiply the digits in the binary number with their corresponding powers of two and add them.
(64*1) + (32*0) + (16*1) + (8*1) + (4*0) + (2*0) + (1*1) =  89

4.    Write the answer along with its base subscript.          
    (89)base 10
       =        
(1011001) base2

Coversion from decimal to binary:
1.    Take the decimal number you want to convert.
(89)base10  

2.    Divide the number by 2 and keep track of the remainder.
89 / 2  = 49; Remainder = 1  

3.    If dividend is odd, remainder = 1 and if dividend = odd, remainder = 0.  

4.    Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 0.       
89 / 2  = 44; Remainder = 1

44 / 2  = 22; Remainder =  0
22 / 2  = 11; Remainder =  0
11 / 2  =  5;  Remainder =  1
5 / 2  =   2;  Remainder =   1
2 / 2  = 1; Remainder =      0
1 / 2  = .5; Remainder =     1
 
5.     Starting with the bottom remainder, read the sequence of remainders upwards to the top
(1011001) base2  = (89) base10      
 
 
1 5 1