Learning Objectives
- Define the function of XOR, also called EOR.
- Complete the XOR truth table.
- Distinguish XOR from inclusive OR.
- Recognise problem statements requiring exactly one true input.
Key Terms
- XOR gate
- A two-input gate that outputs 1 when the inputs are different.
- EOR
- An alternative name for XOR meaning exclusive OR.
- Exclusive
- Allowing one of two conditions, but excluding the case where both are true.
- Different inputs
- The combinations 0,1 and 1,0.
- Same inputs
- The combinations 0,0 and 1,1.
Function Of XOR
XOR stands for exclusive OR and may also be labelled EOR. It outputs 1 when exactly one input is 1. The input combinations 01 and 10 produce 1. The combinations 00 and 11 produce 0.
Another reliable definition is that XOR outputs 1 when the two inputs are different and 0 when they are the same.
The symbol resembles OR but has an additional curved line on the input side. There is no output bubble.
Truth Table For XOR
| A | B | X = A XOR B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
XOR Compared With OR
| Inputs | OR Output | XOR Output |
|---|---|---|
| 0,0 | 0 | 0 |
| 0,1 | 1 | 1 |
| 1,0 | 1 | 1 |
| 1,1 | 1 | 0 |
Language That Indicates XOR
Phrases such as either A or B but not both, exactly one condition, one and only one, inputs are different, or only one switch is active indicate XOR.
For example, a two-way indicator is lit when exactly one of two switches is on. Let A and B represent the switches. Then X = A XOR B.
If a statement says at least one or one or both, it indicates ordinary OR rather than XOR.
Identifying XOR From A Truth Table
A two-input truth table with outputs 0,1,1,0 in the standard row order is XOR. The two middle rows are 1 because the inputs differ. The first and last rows are 0 because the inputs are equal.
Check that the input row order is 00, 01, 10, 11 before identifying the pattern. A table printed in another order must be interpreted by the actual input values, not by memorised row position.
XOR In A Larger Circuit
For X = (A XOR B) AND C, calculate the XOR result P first. Then AND P with C. The final output is 1 only when A and B are different and C is 1.
For X = A XOR (NOT B), invert B first, then compare A with the inverted value. Intermediate columns are essential for reliable tracing.
XOR remains a two-input gate under the syllabus. A three-condition exclusive rule must be represented in stages if it appears in the given expression.
Avoiding Informal Misinterpretation
The word or in normal conversation can be exclusive or inclusive depending on context. In logic questions, use the precise statement and expected output. If the both-true case should produce 1, use OR. If it should produce 0, use XOR.
A truth table can resolve ambiguity. Always check the 11 row because that is where OR and XOR differ.
Reverse Reasoning
If XOR outputs 1, the inputs must be different, but either 01 or 10 is possible. If XOR outputs 0, the inputs must be the same, either 00 or 11.
This reasoning can help complete missing input or output values in a partially given circuit table.
Worked Examples
XOR With Different Inputs
Question: Find X when A = 1 and B = 0.
- Compare the two inputs.
- They are different.
- XOR outputs 1 for different inputs.
Answer: X = 1.
Selecting OR Or XOR
Question: A lamp should be on when one and only one of two sensors is active. Which gate is required?
- The phrase one and only one excludes the both-active case.
- This is the exclusive OR rule.
Answer: XOR (EOR).
Examination Guidance
- Memorise the definition exactly one input is 1.
- Alternatively, use different gives 1 and same gives 0.
- Inspect the extra curved line when identifying the symbol.
- Check the 1,1 row to distinguish XOR from OR.
- Use intermediate columns when XOR is part of a larger circuit.
Common Mistakes
- Writing 1 for the 1,1 row.
- Drawing the ordinary OR symbol.
- Using XOR when the wording says at least one.
- Assuming every use of the word either means XOR.
- Trying to give XOR more than two inputs.
Knowledge Check
1. What does XOR stand for?
2. What other name may be used?
3. When does XOR output 1?
4. What is XOR for 1,1?
5. How is its symbol distinguished from OR?
