Let a4a3a2a1a0 be an 5-bit binary number. Write a boolean formula in propositional logic (not boolean algebra) that evaluates to true if either an odd number of bits of this number is 1 or it is a non-zero even number but not both, and false otherwise.

Requirement: Your final answer should only use OR, AND, inverters () or XOR (). Any other answers should be reduced to the requested format. You may not need to use all of the allowed operators in your answer.