Suppose we want to design a synchronous circuit that processes a string of 0’s and 1’s. Given a string, it produces another string by replacing the first 1 in any subsequence of consecutive 1’s by a 0. Consider the following example.

Input sequence : 00100011000011100

Output sequence : 00000001000001100

A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input.

The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables s, t, b and y respectively.

Assume the initial state of the Mealy machine is 0.

What are the Boolean expressions corresponding to t and y in terms of s and b ?

Consider a Boolean function f(w, x, y, z) such that 

f(w, 0, 0, z) = 1

f(1, x, 1, z) = x + z

f(w, 1, y, z) = wz + y

The number of literals in the minimal sum-of-products expression of f is ______

Consider the following sets, where n > 2:
S1: Set of all n x n matrices with entries from the set {a, b, c}

S2: Set of all functions from the set {0,1, 2, ..., n2 — 1} to the set {0, 1, 2}

Which of the following choice(s) is/are correct?

Choose the correct choice(s) regarding the following propositional logic assertion S:

S : ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))