Binary to octal 947 relation – UGC NET Question

To convert binary to octal, we group the binary digits into triples from the right and convert each group to its octal digit. The binary 1110110011₂ can be written as 001 110 110 011, giving octal digits 1, 6, 6 and 3. This results in the octal number 1663₈. Since this corresponds to the same value as the original binary, option D is correct.

Option A:
Option A corresponds to a different octal pattern whose binary form is not 1110110011₂. When regrouped into binary, it yields a distinct set of bits and therefore a different decimal value. Thus, it does not match the given binary number.

Option B:
Option B produces a larger octal number which, when converted back to binary and then decimal, exceeds the value of 1110110011₂. It involves a higher octal digit in one position, making it inconsistent with the required binary pattern. Hence, it is not correct.

Option C:
Option C differs from the correct option in one of its octal digits, which changes the underlying three-bit group. This leads to a binary value that is not 1110110011₂ and therefore not equal to the given binary number. Thus, it is an incorrect octal equivalent.

Option D:
Option D correctly groups the binary digits and converts each group to its octal counterpart, yielding 1663₈. Its reverse conversion reproduces the original binary number exactly. Therefore, this option represents the accurate octal equivalent of 1110110011₂.