UGC NET Questions (Paper – 1)

To convert 7F₁₆ to decimal, we use positional weights of base 16. The digit 7 is in the 16¹ place and F represents 15 in the 16⁰ place. So the decimal value is 7×16 + 15×1 = 112 + 15 = 127. Therefore, the correct decimal equivalent of 7F₁₆ is 127.

Option A:
Option A, 119, would correspond to a different combination of hex digits because 119 is not 7×16 + 15. It implies an incorrect evaluation of the place values or the value of F. Thus, it underestimates the contribution of the least significant digit.

Option B:
Option B, 125, is close to the correct value but still results from a miscalculation of 7×16 + 15. It might arise from incorrectly adding 112 + 13 instead of 15, showing an error in interpreting F. Hence 125 does not match the precise conversion.

Option C:
Option C correctly applies the base-16 positional rule: 7×16 = 112 and F = 15, giving a total of 127. This option not only uses the right weights but also interprets F as 15, which is crucial in hexadecimal arithmetic. Therefore it is the accurate decimal representation of 7F₁₆.

Option D:
Option D, 129, overshoots the correct value and would imply the least significant digit contributed 17 instead of 15. That is not possible because a single hex digit ranges from 0 to 15. Therefore, 129 cannot be the correct conversion of 7F₁₆.

The hex number 16D₁₆ has digits 1, 6, and D. Using positional weights, we compute 1×16² + 6×16¹ + 13×16⁰ = 1×256 + 6×16 + 13×1 = 256 + 96 + 13 = 365. Therefore, 16D₁₆ equals 365 in decimal.

Option A:
Option A correctly interprets D as 13 and applies the weights 256, 16, and 1. The sum 256 + 96 + 13 yields 365, matching the result of a proper base-16 to base-10 conversion.

Option B:
Option B, 349, represents a different combination of digit values and weights and does not equal the computed sum of 1×256 + 6×16 + 13. It indicates an arithmetic or mapping error.

Option C:
Option C, 269, underestimates the value and would imply lower contributions from the hex digits than they actually have. It does not correspond to the given pattern.

Option D:
Option D, 285, neither matches the correct total nor any plausible misinterpretation that preserves digit order while using appropriate weights.