Suppose we want to design a synchronous circuit that processes a string of 0’s…

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 $b$?