Build a circuit that takes a 3-bit number x2x1x0 as an input, and provides one output indicating whether the number of bits equal to 1 in the input is even (0) or odd (1). For example, if the input is 110, there are 2 bits set to 1; since 2 is an even number, the output should be 0. If the input is 111, there are 3 bits set to 1; since 3 is an odd number, the output should be 1. a) Write a truth table that represents the behavior of this circuit.

b) Obtain a Boolean function F for the output of the circuit. Infer this Boolean function from the truth table in a canonical form based on a sum of minterms. Then simplify the Boolean function using Boolean algebra.

c) Draw a gate diagram for this circuit, clearly labeling its inputs and outputs.

So I did the truth table for the circuit and I got a boolean function

The function is F= ab'c' + a'bc' + a'b'c + abc

Please help me in simplifying the function and generating a gate diagram for the circuit