Hex of decimal forty five – UGC NET Question

To convert 45 to hexadecimal, we divide by 16. The quotient is 2 and the remainder is 13. In hexadecimal, 13 is represented by the digit D, so the number becomes 2D₁₆. Therefore, 2D is the correct hexadecimal representation of decimal 45.

Option A:
Option A, 2B₁₆, corresponds to 2×16 + 11 = 43 in decimal, which is less than 45. It has a smaller remainder than needed.

Option B:
Option B, 2C₁₆, equals 2×16 + 12 = 44, still one less than 45. The remainder of 12 does not match the required 13.

Option C:
Option C, 1D₁₆, represents 1×16 + 13 = 29, which is far from 45. It uses too small a multiple of 16.

Option D:
Option D is correct because 2×16 + 13 = 45. The mapping of 13 to D ensures that 2D₁₆ exactly matches the decimal value.