How to write a formula to identify even and odd numbers from two cells (A1 & B1) into one cell (C1)?

[arthurz11]

In Cell A1, can be any numbers from 0 to 3.
In Cell B1, can be any numbers from 0 to 3.
In Cell C1, the answer should be any four options. Depending on the numbers entered in A1 and B1:
EE, or OO, or EO, or OE.
E for Even and O for Odd number.
Example:
If A1 = 1 and B1 = 1. C1 the answer is "OO"
If A1 = 2 and B1 = 2. C1 the answer is "EE"
If A1 = 2 and B1 = 3. C1 the answer is "EO"
If A1 = 1 and B1 = 2. C1 the answer is "OE"
If A1 = 0 and B1 = 2. C1 the answer is "EE" (Note: zero is considered an even number)

In Cell C1, I have used =IF(AND(MOD(A1,2)=1,MOD(B1,2)=1),"OO","EE") but this "ONLY" works if both numbers or even or odd.
How do I combine the formula to include EO or OE? So if it's not EE or OO, it can be EO. or vice versa, OE?

 

[Fluff]

Glad we could help & thanks for the feedback.