Hex of binary 101011 – UGC NET Question

To convert 101011₂ to hexadecimal, we group bits in sets of four from the right, padding with zeros on the left if needed. This gives 0010 1011. The left group 0010₂ is 2 and the right group 1011₂ is 11, represented by B in hexadecimal. Thus, the hexadecimal equivalent is 2B₁₆.

Option A:
Option A, 2A₁₆, would correspond to 0010 1010₂, where the right group is 1010₂ = 10. This differs from the given binary number, whose last four bits are 1011₂.

Option B:
Option B is correct because the grouping 0010 1011₂ maps directly to the hex digits 2 and B. This representation preserves the value of 101011₂ accurately.

Option C:
Option C, 1B₁₆, would correspond to 0001 1011₂, which has a different leading group and thus a smaller value.

Option D:
Option D, 1D₁₆, translates to 0001 1101₂, where the right group 1101₂ differs from the original 1011₂. This makes it an incorrect conversion.