MCQ
Q.
The octal equivalent of the number 11010.1011 is
Correct Answer: A
The correct answer is The octal equivalent of the number 11010.1011 is 32.54.
🔑 Key Points
- First, we need to convert the binary number 11010.1011 into decimal to better understand its value in base 10.
- The binary number 11010 in decimal is calculated as (1*2^4) + (1*2^3) + (0*2^2) + (1*2^1) + (0*2^0) = 16 + 8 + 0 + 2 + 0 = 26.
🧮 Step-by-Step Solution
To find the octal equivalent, we first convert the whole number part 26 to octal. 26 in octal is 32. For the fractional part 0.6875, we find its octal equivalent. Since 0.6875 is $\frac{11}{16}$, and $\frac{11}{16}$ in octal is $\frac{13}{20}$ (because 11 in octal is 13 and 16 in octal is 20), the fractional part .6875 in octal is .54 when converted properly using **octal** fractions, thus making the octal equivalent of 11010.1011 as 32.54.
📄 Additional Information
- To convert a binary number to octal, it's often easier to first convert it to decimal and then to octal. The fractional part .1011 in binary is calculated as (1*2^-1) + (0*2^-2) + (1*2^-3) + (1*2^-4) = 0.5 + 0 + 0.125 + 0.0625 = 0.6875 in decimal.