Decimal to binary conversion

 Any decimal number can be converted to its binary equivalent.

  •  For integers ,conversion is obtained just by dividing number continuously by 2 and keeping track of remainders obtained .

Example:

(  26  )10 = (   ?   )2

Solution:

Firstly you should know,Now, Divide 26 by 2,
we get,Now ,quotient obtained from this division will become dividend in next step,
again, divide it with 2.( Keeping track of remainder)
again, same processagain,Now, at last  stop dividing when dividend become less than the divisor.

Now write in following sequence,
First write the last dividend left and then write remainders obtained in reverse order .
As shown below,

This will be the final answer i. e. (  11010  )2
You can write this in simple manner also, shown below,
answer will be ( 1 1 0 1 0 )2

  • While for fractional part ,the conversion is done by continuous multiplication by 2 and keeping track of the integers generated.See in given example,

Example:

(  0.625  )10 = (   ?   )

Solution:

0.625 ×  2  = 1.25  , integer obtained is 1

now,multiply the fractional part obtained  with 2

0.25  × 2 = 0.5 ,integer obtained  0

again, same process,

0.5  × 2 = 1  ,integer obtained  1 

now, we don’t have any fractional part left .So stop multiplying here.
Next step is , write down the integer obtained  in the sequence they obtained after radix point ,as follows:

 =  (  0.101  )2

This is the way we can convert a decimal number into its binary equivalent.

Examples of decimal to binary conversion

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