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 \(b\)?