Convert the following binary numbers to their hexadecimal equivalents: A. 1001.1111 B. 110101.011001 C. 10100111.111011

To convert binary numbers to their hexadecimal equivalents, we'll follow these steps:

1. Group the binary digits into sets of four (starting from the binary point or right to left for the integer part, and left to right for the fractional part).
2. Convert each group of four binary digits into their corresponding hexadecimal digit.

Let's do this for each binary number.

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### A. \( 1001.1111_2 \)

1. Split into groups of four:
   - Integer part: \( 1001 \)
   - Fractional part: \( 1111 \)
   
2. Convert each group to hexadecimal:
   - \( 1001_2 = 9_{16} \)
   - \( 1111_2 = F_{16} \)

So, \( 1001.1111_2 = 9.F_{16} \).

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### B. \( 110101.011001_2 \)

1. Split into groups of four:
   - Integer part: \( 110101 \) becomes \( 0011\ 0101 \)
   - Fractional part: \( 011001 \) becomes \( 0110\ 0100 \)
   
2. Convert each group to hexadecimal:
   - \( 0011_2 = 3_{16} \)
   - \( 0101_2 = 5_{16} \)
   - \( 0110_2 = 6_{16} \)
   - \( 0100_2 = 4_{16} \)

So, \( 110101.011001_2 = 35.64_{16} \).

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### C. \( 10100111.111011_2 \)

1. Split into groups of four:
   - Integer part: \( 10100111 \) becomes \( 1010\ 0111 \)
   - Fractional part: \( 111011 \) becomes \( 1110\ 1100 \)
   
2. Convert each group to hexadecimal:
   - \( 1010_2 = A_{16} \)
   - \( 0111_2 = 7_{16} \)
   - \( 1110_2 = E_{16} \)
   - \( 1100_2 = C_{16} \)

So, \( 10100111.111011_2 = A7.EC_{16} \).

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### Final Answers:
A. \( 1001.1111_2 = 9.F_{16} \)  
B. \( 110101.011001_2 = 35.64_{16} \)  
C. \( 10100111.111011_2 = A7.EC_{16} \)

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Would you like any further details or clarifications?  

Here are 5 related questions to expand on this topic:
1. How would you convert a hexadecimal number back to binary?
2. How do you handle binary numbers with more than four digits in each group during conversion?
3. What are the common uses of hexadecimal numbers in computing?
4. How would you convert a fractional decimal number to hexadecimal?
5. What is the relationship between octal and hexadecimal systems?

**Tip:** When converting binary to hexadecimal, always ensure that each group has exactly four bits, padding with zeros if necessary!

Learn how to convert binary numbers 1001.1111, 110101.011001, and 10100111.111011 to hexadecimal equivalents. This problem covers key concepts in number systems, including binary-to-hexadecimal conversion. Suitable for students in Grades 9-12.

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