Octal of binary 111 – UGC NET Question

To convert binary 111 into octal, we group the binary digits into sets of three from the right. The group 111₂ corresponds directly to a single octal digit. Evaluating 111₂ gives 4 + 2 + 1 = 7. Therefore, the octal equivalent is 7 (base 8).

Option A:
Option A is correct because 111₂ evaluates to three ones in the 4, 2 and 1 positions, giving 7. Octal 7 exactly matches this binary pattern. Thus 7 (base 8) is the accurate conversion.

Option B:
Option B suggests 5, which in binary would be 101₂, not 111₂. The pattern 101 has a zero in the 2's place, unlike 111. Hence 5 does not correspond to the given binary number.

Option C:
Option C proposes 6, which is 110₂ in binary. Here the 1's place is zero, which does not match the original pattern 111. Therefore, 6 cannot be the correct octal equivalent.

Option D:
Option D gives 8, but a single octal digit ranges only from 0 to 7. The value 8 would require multiple binary digits or multiple octal digits and does not match the direct conversion of 111₂.