Octal of binary thousand – UGC NET Question

To convert 1000₂ to octal, we group the binary digits into sets of three from the right. Padding on the left gives 001 000. The group 001₂ equals 1 and 000₂ equals 0, so the octal number is 10₈. This means binary 1000 corresponds to octal 10.

Option A:
Option A, 7₈, corresponds to binary 111₂, not 1000₂. It represents a different decimal value and fails to match the binary input.

Option B:
Option B is correct because 1000₂ is 8 in decimal and 8 is written as 10₈ in octal. Grouping 001 000 demonstrates this equivalence clearly.

Option C:
Option C, 11₈, represents decimal 9 because it equals 1×8 + 1. Binary 1000₂ represents 8, so 11₈ is too large and does not match.

Option D:
Option D, 8, is not a valid single octal digit since octal digits range only from 0 to 7. Therefore, 8 cannot be the correct octal representation for any value.