Question

What is the equivalent decimal value of the unsigned binary number 10101.10101?

• A. 51.125
• B. 125.25
• C. 25.375
• D. 21.65625

Hint:

To convert binary to decimal, separately convert the integer part and fractional part, then sum them.

Answer 1

The Correct Option is D

The given binary number is \( 10101.10101_2 \). We will convert this into decimal by handling the integer and fractional parts separately. 

1. Integer part: \[ 10101_2 = 1 \cdot 2^4 + 0 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 = 16 + 4 + 1 = 21 \] 2. Fractional part: \[ .10101_2 = 1 \cdot 2^{-1} + 0 \cdot 2^{-2} + 1 \cdot 2^{-3} + 0 \cdot 2^{-4} + 1 \cdot 2^{-5} = 0.5 + 0.125 + 0.03125 = 0.65625 \] Thus, the decimal value is: \[ 21 + 0.65625 = 21.65625 \] The equivalent decimal value is \( \boxed{21.65625} \).