Q28

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.

$$\begin{array}{ll} \text{Input sequence:} & 00100011000011100 \\ \text{Output sequence:} & 00000001000001100 \end{array}$$

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 $b$?