Assignment Task: Please design a majority voting machine. The machine can allow three people to vote. Each person can only vote either "Yes", or "No". If the majority vote "Yes", the result is "Yes", otherwise the result is "No". We assume three people are A, B, and C respectively, and the result is X.
1) Please design the truth table.
2) Derive the Boolean Expression for x (hint: please use "1" in x to get the expression, do not simplify it at this step);
3) Simplify the expression using DeMorgan's law attached to have XOR operation for b and c. (hints: B xor C = B'C+ BC')