convert 11110011110100.000v2 into a decimal number 

To convert the binary number \(11110011110100.000_2\) into a decimal number, we’ll break it down as follows:

1. **Separate the Integer and Fractional Parts**  
   The binary number is \(11110011110100.000_2\), which can be divided into:
   - Integer part: \(11110011110100_2\)
   - Fractional part: \(000_2\)

2. **Convert the Integer Part**  
   We convert \(11110011110100_2\) by expanding it as:
   \[
   1 \cdot 2^{13} + 1 \cdot 2^{12} + 1 \cdot 2^{11} + 1 \cdot 2^{10} + 0 \cdot 2^9 + 0 \cdot 2^8 + 1 \cdot 2^7 + 1 \cdot 2^6 + 1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 0 \cdot 2^0
   \]
   Calculating each term:
   \[
   = 8192 + 4096 + 2048 + 1024 + 0 + 0 + 128 + 64 + 32 + 0 + 8 + 0 + 4 + 0 = 17556
   \]

3. **Convert the Fractional Part**  
   The fractional part \(000_2\) simply represents 0 in decimal.

4. **Combine the Integer and Fractional Parts**  
   Therefore, the decimal value is:
   \[
   17556.0
   \]

### Final Answer
\[
11110011110100.000_2 = 17556_{10}
\]

Would you like details on the calculation steps? Here are some further questions to explore:

1. How is binary-to-decimal conversion performed for numbers with non-zero fractional parts?


Convert 11110011110100.000_2 into a decimal number

Learn how to convert the binary number 11110011110100.000 into a decimal. This solution provides a step-by-step guide on handling integer and fractional binary parts, covering essential concepts in number system conversions for students in Grades 9-12.

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