Convert the following hexadecimal numbers to their decimal equivalents: A. C B. 9F C. D52 D. 67E E. ABCD

Let's convert each hexadecimal number to its decimal equivalent:

### A. \( \text{C} \)
- Hexadecimal: \( \text{C} = 12 \) (decimal).

So, \( \text{C}_{16} = 12_{10} \).

### B. \( \text{9F} \)
- Hexadecimal \( \text{9F} \) can be broken down as:
  - \( 9 \times 16^1 = 9 \times 16 = 144 \)
  - \( F \times 16^0 = 15 \times 1 = 15 \)

Total: \( 144 + 15 = 159 \).

So, \( 9F_{16} = 159_{10} \).

### C. \( \text{D52} \)
- Hexadecimal \( \text{D52} \) can be broken down as:
  - \( D \times 16^2 = 13 \times 256 = 3328 \)
  - \( 5 \times 16^1 = 5 \times 16 = 80 \)
  - \( 2 \times 16^0 = 2 \times 1 = 2 \)

Total: \( 3328 + 80 + 2 = 3410 \).

So, \( D52_{16} = 3410_{10} \).

### D. \( \text{67E} \)
- Hexadecimal \( \text{67E} \) can be broken down as:
  - \( 6 \times 16^2 = 6 \times 256 = 1536 \)
  - \( 7 \times 16^1 = 7 \times 16 = 112 \)
  - \( E \times 16^0 = 14 \times 1 = 14 \)

Total: \( 1536 + 112 + 14 = 1662 \).

So, \( 67E_{16} = 1662_{10} \).

### E. \( \text{ABCD} \)
- Hexadecimal \( \text{ABCD} \) can be broken down as:
  - \( A \times 16^3 = 10 \times 4096 = 40960 \)
  - \( B \times 16^2 = 11 \times 256 = 2816 \)
  - \( C \times 16^1 = 12 \times 16 = 192 \)
  - \( D \times 16^0 = 13 \times 1 = 13 \)

Total: \( 40960 + 2816 + 192 + 13 = 43981 \).

So, \( ABCD_{16} = 43981_{10} \).

### Summary:
- A. \( C_{16} = 12_{10} \)
- B. \( 9F_{16} = 159_{10} \)
- C. \( D52_{16} = 3410_{10} \)
- D. \( 67E_{16} = 1662_{10} \)
- E. \( ABCD_{16} = 43981_{10} \)

Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you convert a decimal number to hexadecimal?
2. What is the hexadecimal representation of \( 255 \) in decimal?
3. Why is hexadecimal often used in computing instead of decimal?
4. How do you add two hexadecimal numbers?
5. What is the largest digit in the hexadecimal number system?

**Tip:** In hexadecimal, digits go from \( 0 \) to \( F \), where \( F \) represents \( 15 \) in decimal.

Convert hexadecimal numbers C, 9F, D52, 67E, and ABCD to their decimal equivalents. This step-by-step solution covers key concepts in number systems and powers of 16, ideal for students in Grades 9-12.

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