xor equivalent with AND OR logic

Which of the following expressions is equivalent to the following function? xor(A,B)

(A & B) & (A | B)

(A | B) | ~(A & B)

(A | B) & ~(A & B)

(A | B) | (A & B)

I don't understand exactly what these options are doing. I know xor gives a 0 if both statements are true or false, and gives a 1 if one statement is true and one statement is false. But how does that translate to one of these options symbolically?

Answer 1

[Star Strider]

Actually, the correct expression is much simpler:

TF = A ~= B

The ‘XOR’ operation is best described as ‘one or the other but not both’. This holds if, in this instance, A is not equal to B. The tilde ‘~’ in MATLAB is the logical negative operator, so prefacing the equal sign with it turns the expression into ‘not equal’.

Using the ‘ne’ (not equal) function has the same effect:

TF = ne(A,B)

[Rick]

Yes, but of those options, which one is correct?

[Roger Stafford]

The third one.

[Star Strider]

I created this code snippet to test them:

A = 0;
B = 1;

C1 = (A & B) & (A | B);
C2 = (A | B) | ~(A & B);
C3 = (A | B) & ~(A & B);
C4 = (A | B) | (A & B);

TF1 = A ~= B;
TF2 = ne(A,B);

fprintf(1,'\n\tA = %d \tB = %d \n\t\t\tC1 = %d  \tC2 = %d  \tC3 = %d  \tC4 = %d  \tTF = %d\n', A, B, C1, C2, C3, C4, TF1)

I varied A and B between runs:

  A = 0 B = 0 
      C1 = 0  C2 = 1  C3 = 0  C4 = 0  TF = 0

  A = 1 B = 0 
      C1 = 0  C2 = 1  C3 = 1  C4 = 1  TF = 1

  A = 1 B = 1 
      C1 = 1  C2 = 1  C3 = 0  C4 = 1  TF = 0

  A = 0 B = 1 
      C1 = 0  C2 = 1  C3 = 1  C4 = 1  TF = 1

The only condition that exactly matches my ‘TF’ condition is ‘C3’, so it is equivalent to ‘XOR’

Answer 2

[per isakson]

See

• Logical Operations
• Venn diagram