Question

The decimal equivalent of the binary number 110.101 is ................

Hint:

To convert a binary number to decimal, convert both the integer and fractional parts separately, then combine them.

Answer 1

Correct Answer: 6.625

Step 1: Break the binary number into integer and fractional parts.
The binary number is \( 110.101 \). Split it into: \[ 110 \text{ (integer part)} \quad \text{and} \quad 0.101 \text{ (fractional part)}. \]
Step 2: Convert the integer part to decimal.
The binary number \( 110_2 \) can be converted to decimal by expanding it as: \[ 110_2 = 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 4 + 2 + 0 = 6. \]
Step 3: Convert the fractional part to decimal.
For the fractional part \( 0.101_2 \), convert it as follows: \[ 0.101_2 = 1 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} = \frac{1}{2} + 0 + \frac{1}{8} = 0.5 + 0.125 = 0.625. \]
Step 4: Combine the integer and fractional parts.
Adding the integer and fractional parts together: \[ 6 + 0.625 = 6.625. \]
Step 5: Conclusion.
Thus, the decimal equivalent of the binary number \( 110.101 \) is 6.625.