# Decimal to binary conversion

Decimal to binary

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:

Divide 26 by 2,
quotient obtained from this division will become dividend in next step,

dividend =13 ( rem=0 )
again, divide it with 2.( Keeping track of remainders),

dividend = 6 ( rem=1)

repeat the same process until dividend become less than the divisor.

dividend =3 ( rem=0)

dividend =1 ( rem=1)
now, dividend =1 is less than 2

Stop dividing when dividend become less than the divisor.

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

(last dividend is 1 & remainders in reverse order)

This will be the final answer i. e. (  11010  )2
answer is ( 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.

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