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 ? Correct Answer t = b y = sb Answer: Option 1 Concept: Mealy Machine: In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs i.e. inputs and output mentioned on transition edges. Explanation: Given: Mealy Machine which replaces the first 1 in any subsequence of consecutive 1’s by a 0. s = current state t = next state b = next incoming bit t = output bit consider the following Mealy Machine for the given scenario. [ alt="F1 Raju.S 27-03-21 savita D9" src="//storage.googleapis.com/tb-img/production/21/03/F1_Raju.S_27-03-21_savita_D9.png" style="width: 180px; height: 127px;"> we need to find expression for t and y t is next state, at state '0' in Mealy Machine t = b at state '1' in Mealy Machine t = b now we left with two options Option 1 and Option 4. y is output bit at state '0' in Mealy Machine both the output bit is 0, we can not be sure which is true sb or sb̅. at state '1' in Mealy Machine one output which loops to itself s=1 and b=1 then sb=1 and output bit is also 1. Hence t = b and y = sb