What is the binary representation of 0xCA? (0x refers to hexadecimal)
- 10111010
- 11010101
- 11001010
- 11011010
The correct answer and explanation is:
The correct binary representation of 0xCA (which is a hexadecimal number) is:
11001010
Explanation
1. Understanding Hexadecimal (0x)
Hexadecimal (base 16) is a number system that uses 16 symbols:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Each digit represents values from 0 to 15. In this system:
- A = 10, B = 11, C = 12, D = 13, E = 14, F = 15
2. Converting Hexadecimal (0xCA) to Binary
Each hexadecimal digit corresponds to 4 binary bits (a nibble).
- Convert C (12 in decimal) to binary:
- 12 in binary is 1100
- Convert A (10 in decimal) to binary:
- 10 in binary is 1010
Now, combining both:
C = 1100 and A = 1010, so 0xCA = 11001010 (binary)
3. Verifying the Answer
To ensure accuracy, convert 11001010 (binary) back to decimal: (1×27)+(1×26)+(0×25)+(0×24)+(1×23)+(0×22)+(1×21)+(0×20)(1 \times 2^7) + (1 \times 2^6) + (0 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (0 \times 2^0) =128+64+8+2=202= 128 + 64 + 8 + 2 = 202
202 in decimal is CA in hexadecimal, confirming our result.
Thus, the binary representation of 0xCA is 11001010.
Generated Image
Now, I’ll generate an image representing this conversion.
Here is the generated infographic explaining the conversion of 0xCA to binary 11001010. Let me know if you need any modifications!
