Binary from octal 745 – UGC NET Question

To convert an octal number to binary, each octal digit is replaced by its 3-bit binary equivalent. For 745₈, the digit 7 becomes 111₂, 4 becomes 100₂, and 5 becomes 101₂. Concatenating these gives 111100101₂. Therefore, 111100101₂ is the correct binary representation of 745₈.

Option A:
Option A correctly maps 7→111, 4→100, and 5→101, giving 111100101₂. This approach uses the standard direct mapping rule between octal and binary based on 3-bit groups. Thus, this option faithfully represents the value of 745₈ in base 2.

Option B:
Option B, 111010101₂, corresponds to different 3-bit groups in the middle, implying a digit of 2 or 3 somewhere instead of 4. This does not match the correct octal digit-to-binary mapping for 745₈. Hence, B does not represent 745₈ accurately.

Option C:
Option C, 110111101₂, has a different sequence of bits, especially in the leading and central region, and would correspond to another octal value entirely. Since each octal digit must map exactly to a fixed 3-bit pattern, this pattern cannot correspond to 745₈. Therefore, it is incorrect.

Option D:
Option D, 111001101₂, similarly represents a different binary pattern and thus a different octal number. Its middle bits do not match the required mapping for the digit 4 (100₂), so it cannot be the correct conversion. Thus, this option is also incorrect.