UGC NET Questions (Paper – 1)

To convert a decimal integer into another base, we repeatedly divide the number by the target base and track the remainders. These remainders form the digits of the new base when read in reverse order. This procedure is known as the repeated division method and works for any positional base. Hence, repeated division is the correct operation.

Option A:
Option A is correct because dividing by the base successively shrinks the number while yielding remainders that directly correspond to the new base digits. This algorithm is a standard topic in number system conversions.

Option B:
Option B, multiplication, is used mainly when converting fractional parts to another base by repeated multiplication, not for integer parts. Using repeated multiplication on integers would not directly yield their digits in another base.

Option C:
Option C, subtraction, can help conceptually but is not the usual systematic algorithm for base conversion. It would be cumbersome and error-prone compared to repeated division.

Option D:
Option D, rounding, is a numerical approximation technique and not a structural method for finding exact digits in a new base. Rounding might introduce errors rather than produce precise conversions.