Writing “Either Or” formula in Excel [Formula Howtos]

We all know the AND, OR & NOT formulas in Excel using which you can perform simple logical operations And, Or & Negate. But what if you are the chief of HR at ACME Company, where they have a strange rule on extra allowance like this:

Now, to calculate the dates in a month that meet this clause, we need an “exclusive OR” formula or what geeks call as “XOR” operation.

Wikipedia defines XOR as,

The logical operation … exclusive or (symbolized XOR, EOR), … results in a value of true if exactly one of the operands has a value of true. A simple way to state this is “one or the other but not both.”

Now, XOR or exclusive Or is a fairly common logical test, but there is no straight forward formula to test this. Instead we have to use a lengthy combination or AND, OR and NOT formulas to arrive at XOR.

For eg. assuming you want TRUE only when one of the two logical conditions A or B is TRUE,

you have to write,

=OR(AND(NOT(A),B),AND(A,NOT(B))) [Afterall, that is how XOR operation is defined to begin with]

Now, that seems like an awful formula. May be there is a better formula after all?!? One that is less crazier than the HR clause of ACME Co.

Well, there is.

If you observe closely, XOR is nothing but <> (not equal to sign). So, instead of going nuts writing the lengthy ANDORNOT combination, you can simplify the formula to,

=A<>B and it gives the same outcome.

So, the formula to find whether a given date (in cell A1) qualifies for bonus allowance,

=IF((WEEKDAY(A1)=6)<>(MOD(DAY(A1),5)=0),"Pay Bonus","Pay Regular")

More about logical formulas in Excel

AND Formula | OR Formula | NOT Formula | 51 common excel formulas

Do you XOR in real life?

There have been few occasions when I had to XOR in my worksheets. I found that writing the correct formula can be a bit tricky depending on how crazy the rule is. But almost always a combination of <>, NOT, AND and OR worked for me well.

What about you? Do you write formulas that involve complex IF clauses?