Hex equivalent of 1234 decimal – UGC NET Question

Converting 1234 to hexadecimal involves dividing repeatedly by 16 or expressing it as a sum of powers of 16. We can write 1234 as 4×16² + 13×16¹ + 2×16⁰, where 13 is represented by D in hexadecimal. This gives the compact form 4D2₁₆. Since this exactly reproduces 1234 when converted back to decimal, option C is correct.

Option A:
Option A has the middle digit B, which represents 11 in hexadecimal, and its expansion gives a smaller decimal value than 1234. The difference in the middle digit means the 16¹ place contributes less to the total. Hence, 4B2₁₆ does not correspond to 1234.

Option B:
Option B uses C (12) as the middle digit and therefore produces a decimal value different from 1234. Its place value expansion does not match the decomposition of 1234 into powers of 16. It is therefore not the correct hexadecimal representation.

Option C:
Option C uses D (13) as the middle digit and 2 in the units place, which precisely fits the decomposition of 1234 into 4×256 + 13×16 + 2. This structure makes it the only option that converts back to 1234. Thus, 4D2₁₆ is the correct hexadecimal form.

Option D:
Option D has E (14) in the middle position, increasing the value beyond 1234. Its decimal equivalent is larger and therefore cannot represent 1234. Hence, 4E2₁₆ is an incorrect choice.