Hex equivalent of 947 decimal – UGC NET Question

In hexadecimal, each digit represents a power of 16, so 3B3₁₆ expands as 3×16² + 11×16¹ + 3×16⁰. This evaluates to 3×256 + 11×16 + 3, which is 768 + 176 + 3 = 947. Since this exactly matches the given decimal number, 3B3 is the correct hexadecimal representation of 947. Therefore, option C is the only option that represents 947 in base 16.

Option A:
Option A uses the digits 3, A and 3, but its place value expansion in base 16 gives a decimal value smaller than 947. The middle digit A represents 10, and when multiplied by 16 it does not produce the same sum as 947. Thus, although it looks similar, 3A3₁₆ is not the hexadecimal equivalent of 947.

Option B:
Option B also looks similar but the last digit B represents 11 in base 16, which changes the total decimal value. When expanded, its decimal value differs from 947, so it cannot be the correct conversion. It is therefore an incorrect representation for the given decimal number.

Option C:
Option C correctly matches the decimal number because its hexadecimal digits, when multiplied by the appropriate powers of 16, sum exactly to 947. The presence of B as the middle digit contributes 11×16, which is essential to reaching 947. Any change in these digits would change the decimal value. Hence, 3B3₁₆ is the accurate and unique hexadecimal representation among the options.

Option D:
Option D has the rightmost and leftmost digits the same as the correct option but a different middle digit. This different digit changes the weight at the 16¹ position and leads to a decimal sum that is less than 947. For this reason, 37B₁₆ does not represent 947 and is incorrect.