Binary of octal 27 – UGC NET Question

Each octal digit is converted to a 3-bit binary group. For octal 27₈, the digit 2 becomes 010₂ and the digit 7 becomes 111₂. Combining these groups gives 010111₂. This pattern represents the correct binary equivalent of 27₈.

Option A:
Option A, 001111₂, corresponds to octal 17₈ and not 27₈. Its first group 001₂ represents 1 rather than 2.

Option B:
Option B, 011111₂, would map to octal 37₈, since 011₂ equals 3 and 111₂ equals 7. This is different from the given octal number.

Option C:
Option C, 011011₂, converts back to octal 33₈, as both groups 011₂ equal 3. It clearly does not match 27₈.

Option D:
Option D is correct because 2 maps to 010₂ and 7 maps to 111₂. Concatenating those groups produces the binary representation 010111₂ for 27₈.