To convert the binary number $1111111010.1001_2$ to decimal:

Step 1: Convert the integer part $1111111010_2$ to decimal

Each binary digit represents a power of 2:

$(1 \times 2^9) + (1 \times 2^8) + (1 \times 2^7) + (1 \times 2^6) + (1 \times 2^5) + (1 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (0 \times 2^0)$

$= 512 + 256 + 128 + 64 + 32 + 16 + 8 + 0 + 2 + 0 = 1018$

Step 2: Convert the fractional part $.1001_2$ to decimal

Each digit represents a negative power of 2:

$(1 \times 2^{-1}) + (0 \times 2^{-2}) + (0 \times 2^{-3}) + (1 \times 2^{-4})$

$= 0.5 + 0 + 0 + 0.0625 = 0.5625$

Step 3: Combine integer and fractional parts

$1018 + 0.5625 = 1018.5625$

Final Answer:

$\mathbf{1018.5625_{10}}$

Would you like a step-by-step breakdown of any part?

Related Questions:

1. Convert $110101.011_2$ to decimal.
2. Convert $111.1011_2$ to decimal.
3. Convert $1001101.1101_2$ to decimal.
4. Convert $10101010.1010_2$ to decimal.
5. Convert $1111111111.1111_2$ to decimal.

Tip:

When converting binary fractions to decimal, each digit after the point represents decreasing powers of 2 (e.g., $2^{-1}, 2^{-2}, 2^{-3}$, etc.).