What Is the Correct Truth Table for This Xor Equation?

In summary, the truth table shows the output of ((X xor Y) xor Z) xor T, assuming T is always True. The output is 0 when X and Z are both 1 or both 0, and 1 when one of them is 1 and the other is 0. The value of T does not affect the output, as it is always True.
  • #1
XodoX
203
0
(( X xor Y ) xor Z ) xor T

I hope the truth table is correct. I'm not sure, because of the T. T is always 1, right?

X Y Z - (( X xor Y ) xor Z ) xor T

111 - 0
110 - 1
101 - 1
100 - 0
011 - 1
010 - 0
001 - 0
000 - 1
 
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  • #2
I cannot fathom what T is or why you say it is always 1. Given the assumption that it is, then your solution is correct but you need to explain why T is always 1. You do not show it in your work.

And by the way, you are supposed to show your work, not just your final answer, else if you have something wrong how would we have any idea where you made a mistake?
 
  • #3
T is always T (True), so: yes -- provided 1 is True in your 'system'.
I don't think I can improve on your table :wink:
 
  • #4
BvU said:
T is always T (True), so: yes -- provided 1 is True in your 'system'.
I don't think I can improve on your table :wink:
Ah. "T" for "True". I thought it was just another variable. Good catch. It's early. I'm still asleep. That's my story and I'm sticking with it. :smile:
 

1. What is a truth table?

A truth table is a table used in logic to determine the truth or falsity of a statement or proposition. It lists all possible combinations of truth values for the variables in a statement and shows the resulting truth value for the entire statement.

2. What is the XOR operator?

The XOR (exclusive OR) operator is a logical operator that compares two statements and returns a true value only if one of the statements is true and the other is false. If both statements are true or both are false, the XOR operator returns a false value.

3. How is XOR represented in a truth table?

In a truth table, XOR is typically represented by the symbol ⊕ or by the letters XOR. It is commonly used in computer programming and digital electronics to compare binary values.

4. What is the significance of XOR in logic and computer science?

XOR has several important applications in logic and computer science, such as in cryptography, error detection and correction, and Boolean algebra. It is also used in combination with other logical operators to create more complex expressions and statements.

5. Can XOR be used with more than two statements?

Yes, XOR can be used with any number of statements. For example, in a truth table with three variables, the XOR operator will return a true value only if one of the variables is true and the other two are false. This can be extended to any number of variables, with the XOR operator returning a true value if an odd number of variables are true and the rest are false.

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