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Let's go through each part of the question, converting the binary numbers as requested:

### a) \( (10.111)_2 = (?)_{10} \)

This is a binary fraction. To convert to decimal:
1. Split it into integer and fractional parts: \( 10_2 \) and \( .111_2 \).
2. Convert the integer part \( 10_2 = 2_{10} \) (since \( 1 \times 2^1 + 0 \times 2^0 = 2 \)).
3. Convert the fractional part \( .111_2 \):
   - \( 1 \times 2^{-1} = 0.5 \),
   - \( 1 \times 2^{-2} = 0.25 \),
   - \( 1 \times 2^{-3} = 0.125 \),
   So \( .111_2 = 0.5 + 0.25 + 0.125 = 0.875 \).

Therefore, \( (10.111)_2 = 2 + 0.875 = 2.875_{10} \).

### b) \( (101010100001111)_2 = (?)_8 \)

To convert binary to octal:
1. Group the binary number into sets of 3 bits from right to left: 
   \( (101 010 100 001 111)_2 \).
2. Convert each group to its octal equivalent:
   - \( 101_2 = 5_8 \),
   - \( 010_2 = 2_8 \),
   - \( 100_2 = 4_8 \),
   - \( 001_2 = 1_8 \),
   - \( 111_2 = 7_8 \).

Thus, \( (101010100001111)_2 = (52417)_8 \).

### c) \( (1001111011110011100)_2 = (?)_{16} \)

To convert binary to hexadecimal:
1. Group the binary number into sets of 4 bits from right to left: 
   \( (1001 1110 1111 0011 100)_2 \).
   Add leading zeros if necessary: \( (0001 0011 1101 1110 0111 00)_2 \).
2. Convert each group to its hexadecimal equivalent:
   - \( 1001_2 = 9_{16} \),
   - \( 1110_2 = E_{16} \),
   - \( 1111_2 = F_{16} \),
   - \( 0011_2 = 3_{16} \),
   - \( 100_2 = 4_{16} \).

Thus, \( (1001111011110011100)_2 = (9E7C)_16 \).

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Would you like further clarification on any of these conversions? Here are 5 related questions to expand your understanding:

1. How do you convert a decimal number to binary?
2. What is the process of converting octal numbers to hexadecimal?
3. Can you explain how binary addition works?
4. How are binary numbers used in computer systems?
5. What is the significance of hexadecimal representation in programming?

**Tip:** When converting binary numbers to other bases, always group the bits (3 for octal, 4 for hexadecimal) starting from the right.

Convert the following Binary numbers:
(a) (10.111)_2 = (?)_10
(b) (101010100001111)_2 = (?)_8
(c) (1001111011110011100)_2 = (?)_16

Learn how to convert binary numbers to other number systems including decimal, octal, and hexadecimal. This problem covers step-by-step binary to decimal conversion, grouping methods for binary to octal, and binary to hexadecimal transformations, suitable for high school students in Grades 9-12.

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