The logic XOR operation of (4AC0)₁₆ and (B53F)₁₆ results________

The correct answer is FFFF

Explanation:

• Here we have to perform an XOR operation on two Hexadecimal numbers.
• The boolean expression for XOR is A \(\bigoplus\) B = \(A\bar B\) + \(\bar AB\)
• The truth table for XOR is:

• Symbol	Truth Table
  2-input Ex-OR Gate	B	A	Q
  	0	0	0
  	0	1	1
  	1	0	1
  	1	1	0
  Boolean Expression Q = A ⊕ B	A OR B but NOT BOTH gives Q

• Means A and B are the expressions given to us in Hex code. So, we need to find the binary equivalent of the Hexadecimal numbers. This is because these codes will be executed in 1 and 0 in the CPU.
• The following table is to be memorized in order to convert Hexadecimal to Binary:

• Hex	Binary
  0	0000
  1	0001
  2	0010
  3	0011
  4	0100
  5	0101
  6	0110
  7	0111
  8	1000
  9	1001
  A	1010
  B	1011
  C	1100
  D	1101
  E	1110
  F	1111

• Therefore, (4AC0)₁₆ = 0100101011000000
• And (B53F)16 = 1011010100111111
• Now follow the Truth Table to perform the operation on every bit in XOR gate:
  • (4AC0)16   \(\bigoplus\)  (B53F)16  = 0100101011000000   \(\bigoplus\)   1011010100111111
  • 0100101011000000   \(\bigoplus\)   1011010100111111   =  1111111111111111
• So the result obtained is (1111111111111111)₂ which is the Binary Equivalent of (FFFF)₁₆ (using the table given above).
• Hence the correct answer is FFFF.