Logic XOR of hexadecimal numbers

XOR or exclusive OR is a logical operation that outputs true only when the two binary inputs are different. XOR operation is represented by the symbol ⊕. When used with hexadecimal numbers, the XOR operation is performed on each pair of corresponding bits.

Given hexadecimal numbers (4AC0)16 and (B53F)16, the XOR operation can be performed as follows:

4AC0 = 0100 1010 1100 0000
B53F = 1011 0101 0011 1111
XOR = 1111 1111 1111 1111

The result of the XOR operation is (FFFF)16, which is option C.

Explanation

- XOR operation: The XOR operation is a binary operation that takes two binary inputs and outputs true only if the inputs are different. The XOR operation is represented by the symbol ⊕.
- Conversion to binary: To perform the XOR operation on hexadecimal numbers, we need to convert them to binary. Each hexadecimal digit represents four binary digits or bits. For example, (4AC0)16 is equivalent to (0100 1010 1100 0000)2 in binary.
- Performing XOR: Once the numbers are in binary form, we can perform the XOR operation on each pair of corresponding bits. If both bits are the same, the result is 0. If the bits are different, the result is 1.
- Result: After performing the XOR operation on each pair of bits, we get the binary result of (1111 1111 1111 1111)2, which is equivalent to (FFFF)16 in hexadecimal form.

Conclusion

The logic XOR operation of (4AC0)16 and (B53F)16 results in (FFFF)16. This result is obtained by converting the hexadecimal numbers to binary, performing the XOR operation on each pair of corresponding bits, and converting the binary result back to hexadecimal form.