Multiplication method for fraction conversion – UGC NET Question

For fractional parts less than 1, the standard procedure to convert from decimal to binary is repeated multiplication by 2. At each step, the integer part produced becomes the next binary fractional bit, and the fractional remainder is multiplied again. This process is continued until the fraction terminates or a desired precision is reached. Thus, repeated multiplication by 2 is the correct method.

Option A:
Option A, addition, does not systematically reveal binary fractional bits. Simply adding values does not give the correct positional representation of a fraction in base 2.

Option B:
Option B is correct because multiplying by 2 repeatedly shifts fractional bits left and exposes them as integer parts. This aligns with the structure of binary fractions based on powers of 2.

Option C:
Option C, division, is more suitable for converting integer parts when dividing by the target base. For fractional parts, division by 2 would move us away from the needed pattern.

Option D:
Option D, subtraction, could theoretically be used in an iterative approximation but is not the standard, efficient method taught for binary fraction conversion.