How to use the XOR function
What is the XOR function?
The XOR function calculates the exclusive OR. It was introduced in Excel 2013.
Table of Contents
1. Introduction
What is XOR an abbreviation of?
XOR stands for the logical exclusive OR.
What is OR?
At least one argument must be TRUE to return TRUE. All arguments must be FALSE in order to return FALSE.
For example,
OR(FALSE, FALSE, TRUE) returns TRUE
but
OR(FALSE, FALSE, FALSE) returns FALSE.
What is XOR (the logical exclusive OR)?
The XOR function returns TRUE if only value1 is TRUE, or only value2 is TRUE.
All arguments must be evaluated to FALSE or all augments are TRUE for the XOR function to return FALSE.
For example using three arguments,
XOR(FALSE, FALSE, TRUE) returns TRUE because only one argument is TRUE
but
XOR(FALSE, TRUE, TRUE) returns FALSE because two arguments are TRUE.
What is a Boolean value?
A Boolean value in Excel is a value that can only be TRUE or FALSE. It represents binary logic and is the result of a logical expression using logical operators or a result of a few Excel functions that I'll discuss below.
Mastering Boolean logic and logical expressions is key to manipulating data and controlling workflow in Excel.
What is binary logic?
Binary logic refers to values having one of two states, TRUE or FALSE. This allows Boolean algebra in Excel using logical operators.
What is a logical expression?
A logical expression is a statement that evaluates to TRUE or FALSE. For example:
=A1<4
These expressions use comparison operators to evaluate a condition and produce a Boolean result.
What are the comparison operators?
= - equal sign
< - less than sign
> - greater than sign
These operators let you build more operators like this:
<> - not equal to
<= - less than or equal to
>= - greater than or equal to
These comparison operators let you create logical expressions like: A2<>5 meaning if the value in cell A2 is not equal to 5, the result is either TRUE or FALSE.
What are the logical operators?
The main logical operators in Excel are:
- AND - Returns TRUE if all conditions are true
- OR - Returns TRUE if any condition is true
- NOT - Negates a logical expression
- XOR - Returns TRUE if only one condition is true
Which functions returns the Boolean value TRUE or FALSE?
| Excel Function and Arguments | Description |
|---|---|
| AND(logical1, logical2, ...) | Returns TRUE if all arguments are TRUE |
| OR(logical1, logical2, ...) | Returns TRUE if any argument is TRUE |
| NOT(logical) | Reverses the logic of its argument |
| XOR(logical1, logical2, ...) | Returns TRUE if an odd number of arguments are TRUE |
| ISEVEN(number) | Returns TRUE if number is even |
| ISFORMULA(value) | Returns TRUE if value is a formula |
| ISLOGICAL(value) | Returns TRUE if value is logical value |
| ISNA(value) | Returns TRUE if value is #N/A error |
| ISNONTEXT(value) | Returns TRUE if value is not text |
| ISNUMBER(value) | Returns TRUE if value is number |
| ISODD(number) | Returns TRUE if number is odd |
| ISREF(value) | Returns TRUE if value is reference |
| ISTEXT(value) | Returns TRUE if value is text |
| ISBLANK(value) | Returns TRUE if value is blank |
| ISERR(value) | Returns TRUE if value is error except #N/A |
| ISERROR(value) | Returns TRUE if value is any error |
What are the numerical equivalents of Boolean values?
Boolean values are automatically converted into their numerical equivalents when you perform arithmetic operations.
TRUE is 1
FALSE is 0 (zero)
For example,
TRUE + 0 = 0
FALSE + 0 = 0
TRUE * 1 = 1
FALSE * 1 = 0
What is the difference between the XOR function and the BITXOR function?
XOR performs logical exclusion on Boolean (TRUE/FALSE) values whereas the BITXOR function performs a bitwise XOR operation on the binary representations.
The binary positions are important in the BITXOR function, this is not the case with the XOR function.
2. Syntax
XOR(logical1, [logical2],…)
The XOR function has one argument and up to 253 optional arguments.
| logical1 | Required. A condition that evaluates to either TRUE or FALSE or their numerical equivalents 1 or 0 (zero). An argument may also be a reference or array. |
| [logical2] | Optional. Up to 253 additional conditions. |
Can you use more than 254 Boolean values in the XOR function?
Yes, use a cell reference that points to all the Boolean values instead of single cell references separated by a comma. This allows you to use more than 254 arguments.
3. Example
The XOR function in Excel performs an "exclusive OR" operation. It returns TRUE if an odd number of its arguments are TRUE, and FALSE if an even number (including zero) of its arguments are TRUE. In this case, with two inputs, it effectively returns TRUE only when the inputs are different. The function can take two or more logical values or expressions as arguments.
Cells B3 and C3 contain FALSE and FALSE respectively.
Formula in cell D3:
The formula in cell D3 returns FALSE because the XOR function returns TRUE only when exactly one of its arguments is TRUE. Since both inputs are FALSE, it returns FALSE.
Cells B4 and C4 contain FALSE and TRUE respectively.
Formula in cell D4:
The formula in cell D4 returns TRUE because exactly one of its arguments (C4) is TRUE, while the other (B4) is FALSE.
Cells B5 and C5 contain TRUE and FALSE respectively.
Formula in cell D5:
The formula in cell D5 returns TRUE because exactly one of its arguments (B5) is TRUE, while the other (C5) is FALSE.
Cells B6 and C6 contain TRUE and TRUE respectively.
Formula in cell D6:
The formula in cell D6 returns FALSE because the XOR function returns FALSE when both of its arguments are TRUE. It only returns TRUE when exactly one argument is TRUE.
4. Function not working
The XOR function returns #VALUE! error value if no logical values can be found in the arguments.
5. XOR function tips
You don't need to type a comma between each cell reference. Simply type a cell reference to the entire range of Boolean values.
For example,
The XOR function ignores empty and text values, 0 (zero) is evaluated to FALSE and any other numerical value is evaluated to TRUE.
Functions in 'Logical' category
The XOR function function is one of 16 functions in the 'Logical' category.
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