Find the binary equivalent of the decimal number 0.3125 ?

CONCEPT:

Conversion of Fractional Decimal Numbers into Binary Numbers:

Fractional numbers can be converted to binary form by successive multiplication by 2. In each step, the digit before the decimal point is being transferred binary record and the process is repeated with the remaining fraction.

The last step is reached, if the fraction part is zero or it is terminated, when the desire accuracy is attained.

Note:

The first bit obtained is the most significant and the last is the least significant.

CALCULATION:

Here, we have to find the binary equivalent of 0.3125

So, let's start multiplying the given decimal number by 2 until the fraction part is zero or it is terminated, when the desire accuracy is attained.

0.3125 × 2 = 0.625 [0]

0.625 × 2 = 1.25 [1]

0.25 × 2 = 0.5 [0]

0.5 × 2 = 1.00 [1]

So, the binary equivalent of 0.3125 is (0.0101)₂

Hence, option B is the correct answer.