How can we implement the function:
F=A'B'C'D+A'B'CD'+A'BC'D'+A'BCD+AB'CD
without simplifying it and using ONLY XOR gates (not using AND/OR gates) ? NOT gates are usable too, since they can be implemented from an XOR and an entry with the value "1".
[Math] Implement using only XOR gates F=A’B’C’D+A’B’CD’+A’BC’D’+A’BCD+AB’CD
boolean-algebra
Best Answer
You can't.
Hint: XOR is associative and commutative, so every function you can implement using XOR (and the constant "1") only is equivalent to one in a particular canonical form.
This leaves very few functions that can be so expressed. Besides the special cases of the constant "0" and "1" functions, each of them is true for exactly half of the $2^4$ possible combinations of truth values for the four inputs. But the function you're trying to express here doesn't have that property.