Octal of binary 101110 – UGC NET Question

To convert 101110₂ to octal, we group bits into sets of three from the right, giving 101 110. The group 101₂ equals 5 and the group 110₂ equals 6. Combining these yields octal 56₈. Thus, the correct octal equivalent is 56.

Option A:
Option A, 54₈, would correspond to binary 101100₂, where the last group is 100 instead of 110. This does not match the original binary pattern.

Option B:
Option B, 55₈, converts to 101101₂ and differs in the last bit. The original binary ends with 110, not 101, so 55₈ is incorrect.

Option C:
Option C is correct because grouping 101110₂ as 101 and 110 gives octal digits 5 and 6. The combined octal number 56 precisely represents the original binary number.

Option D:
Option D, 57₈, would correspond to binary 101111₂, which has an extra 1 at the end. This changes the original value and makes the option invalid.