Consider a Moore-type state machine corresponding to the state diagram below. Note that the machine has one input variable w. Labelling a transition with "0, 1" means the transition is taken for both w=0 and w=1. Assume the machine has three bits of outputs z2 z1 z0 specified by the output table below: (a) Write the state table for the machine. (b) Write a state-assigned table for the machine. Please use 3 bits to encode the state and use a state assignment which is the same as the output bits. (c) Derive the simplest sum-of-product expressions for the next state logic and the output logic. Show details of your work