Question

The binary equivalent of the octal number 13.54 is:

• A. 1011.1011
• B. 1001.1110
• C. 1101.1110
• D. None of these

Hint:

Convert each octal digit to exactly 3 binary bits. For fractions, keep the order and precision as per the original octal digits.

Answer 1

The Correct Option is A

We are given the octal number $13.54$ and must convert it to binary.
Recall: Each octal digit can be directly converted to 3 binary bits because $8 = 2^3$.
Step 1: Separate the integer and fractional parts.
Integer part: $13_(8)$ Fractional part: $54_(8)$
Step 2: Convert integer part:
$1_(8) = 001_(2)$
$3_(8) = 011_(2)$
So $13_(8) = 001\ 011_(2)$ (we can remove leading zeros): $1011_(2)$
Step 3: Convert fractional part:
$5_(8) = 101_(2)$
$4_(8) = 100_(2)$
So $54_(8) = 101\ 100_(2)$
Step 4: Combine:
$13.54_(8) = 1011.101100_(2)$
If we are keeping the same number of octal fractional digits represented in binary (each exact conversion), we can stop here.
Rounding to match options: $1011.1011_(2)$ is the closest correct representation.