The binary number $101.1101_2$ can be converted to a base 10 number by considering the place values of each digit.

Steps for Conversion:

Integer Part:

The integer part is $101_2$, which represents: $1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5$

Fractional Part:

The fractional part is $0.1101_2$, where each digit corresponds to negative powers of 2: $1 \times 2^{-1} + 1 \times 2^{-2} + 0 \times 2^{-3} + 1 \times 2^{-4}$ $= \frac{1}{2} + \frac{1}{4} + 0 + \frac{1}{16}$ $= 0.5 + 0.25 + 0 + 0.0625 = 0.8125$

Combining Both Parts:

$101.1101_2 = 5 + 0.8125 = 5.8125_{10}$

Thus, the binary number $101.1101_2$ is equal to $5.8125_{10}$ in decimal.

Would you like further clarification on any step?

Related Questions:

1. How do you convert a binary number with more fractional digits to decimal?
2. What is the base-10 representation of $1101.101_2$?
3. How does binary representation work in computer systems?
4. What is the significance of base-2 (binary) in computing?
5. Can you explain the conversion process for octal and hexadecimal numbers to base 10?

Tip:

When converting from binary to decimal, remember that the integer part uses positive powers of 2, while the fractional part uses negative powers of 2.