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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