Convert the following numbers as stated (i) Decimal 64.005125 to binary (ii) Decimal 2376 to hexadecimal (iii)  Character A and Z to ASCII and Unicode Hexadecimal CFE9A to binary

Let's go step-by-step to solve each part:

### (i) Convert Decimal 64.005125 to Binary

First, we will convert the integer part and the fractional part separately.

1. **Integer Part (64):**
   - \( 64 \div 2 = 32 \) remainder 0
   - \( 32 \div 2 = 16 \) remainder 0
   - \( 16 \div 2 = 8 \) remainder 0
   - \( 8 \div 2 = 4 \) remainder 0
   - \( 4 \div 2 = 2 \) remainder 0
   - \( 2 \div 2 = 1 \) remainder 0
   - \( 1 \div 2 = 0 \) remainder 1

   So, the binary of \( 64 \) is \( 1000000_2 \).

2. **Fractional Part (0.005125):**
   Multiply by 2 until the fractional part becomes 0 or until we reach sufficient precision:
   - \( 0.005125 \times 2 = 0.01025 \) → Integer part: 0
   - \( 0.01025 \times 2 = 0.0205 \) → Integer part: 0
   - \( 0.0205 \times 2 = 0.041 \) → Integer part: 0
   - \( 0.041 \times 2 = 0.082 \) → Integer part: 0
   - \( 0.082 \times 2 = 0.164 \) → Integer part: 0
   - \( 0.164 \times 2 = 0.328 \) → Integer part: 0
   - \( 0.328 \times 2 = 0.656 \) → Integer part: 0
   - \( 0.656 \times 2 = 1.312 \) → Integer part: 1
   - \( 0.312 \times 2 = 0.624 \) → Integer part: 0
   - \( 0.624 \times 2 = 1.248 \) → Integer part: 1

   The binary of the fractional part \( 0.005125 \) is approximately \( 0.0000001010_2 \).

   **Final answer:** \( 64.005125 \) in binary is approximately \( 1000000.0000001010_2 \).

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### (ii) Convert Decimal 2376 to Hexadecimal

1. \( 2376 \div 16 = 148 \) remainder 8
2. \( 148 \div 16 = 9 \) remainder 4
3. \( 9 \div 16 = 0 \) remainder 9

So, \( 2376 \) in hexadecimal is \( 0x948 \).

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### (iii) Convert Characters 'A' and 'Z' to ASCII and Unicode

- **Character 'A':**
  - ASCII value: 65
  - Unicode: U+0041

- **Character 'Z':**
  - ASCII value: 90
  - Unicode: U+005A

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### (iv) Convert Hexadecimal CFE9A to Binary

Convert each hex digit to its 4-bit binary equivalent:
- C → \( 1100 \)
- F → \( 1111 \)
- E → \( 1110 \)
- 9 → \( 1001 \)
- A → \( 1010 \)

So, \( CFE9A \) in binary is \( 11001111111010011010_2 \).

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### Summary:
1. \( 64.005125_{10} = 1000000.0000001010_2 \)
2. \( 2376_{10} = 948_{16} \)
3. \( 'A' \) → ASCII: 65, Unicode: U+0041  
   \( 'Z' \) → ASCII: 90, Unicode: U+005A
4. \( CFE9A_{16} = 11001111111010011010_2 \)

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Would you like more details on any of these steps or additional clarifications?

Here are some related questions:
1. How do you convert binary to hexadecimal?
2. What is the process for converting decimals with repeating fractions to binary?
3. How are ASCII and Unicode encoding different?
4. What is the method to convert fractional binary to decimal?
5. How are negative decimal numbers converted to binary?

**Tip:** When converting decimals to binary, the integer and fractional parts must be handled separately, as shown.

Convert the following numbers as stated (i) Decimal 64.005125 to binary (ii) Decimal 2376 to hexadecimal (iii) Character A and Z to ASCII and Unicode (iv) Hexadecimal CFE9A to binary

Learn how to convert decimal 64.005125 to binary, decimal 2376 to hexadecimal, and the characters 'A' and 'Z' to their ASCII and Unicode equivalents. Additionally, see how to convert hexadecimal CFE9A to binary with step-by-step solutions. Suitable for students in Grades 9-12.

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