Question 91

Computer Awareness Number representations Easy

The decimal equivalent of the binary number \( (1011.01)_2 \)

(A) \( (11.25)_{10} \)
(B) \( (10.123)_{10} \)
(C) \( (11.175)_{10} \)
(D) \( (9.23)_{10} \)
View Dynamic Solution & Explanation
Correct Solution: Option A

Step-by-step Solution:

Convert the binary number \( (1011.01)_2 \) into its decimal equivalent by splitting the integer and fractional parts. \[\] 1. Integer Part: \( 1011_2 \) Using the positional values for binary numbers: \(1011_2 = 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 = 8 + 0 + 2 + 1 = 11\) \[\] 2. Fractional Part: \( 0.01_2 \) Using the positional values for binary fractions: \( 0.01_2 = 0 \cdot 2^-1 + 1 \cdot 2^-2 = 0 + 0.25 = 0.25\) \[\] 3. Combining both: Adding the integer and fractional parts: 11 + 0.25 = 11.25 \[\] So, the decimal equivalent is ( 11.25 ). \[\] Correct Option: (a)