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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.

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

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 $b$?

  1. $\begin{array}{l} t=s+b \\ y=sb \end{array} \\$
  2. $\begin{array}{l} t=b \\ y=sb \end{array} \\$
  3. $\begin{array}{l} t=b \\ y=s \overline{b} \end{array} \\ $
  4. $\begin{array}{l} t=s+b \\ y=s \overline{b} \end{array}$
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3 Answers

Best answer
14 votes
14 votes

In $(a∕b), ‘a\text{’}$ is input and $‘b\text{’}$ is output

Option B is correct. 

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53 votes
53 votes

         correct option to question is B

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0 votes

We can get Boolean Expressions by following method :-

1.For y:-

Variables(s,b) b=0 b=1
s=0 0 0
s=1 0 1

Y is 1 only when s=1,b=1 Therefore Y=sb

Explanation for y:- As Y is Output bit for this Machine .We can say Y will produce 1 only when previous bit and current bit =1 ,Therefore as the State 1 means previous input bit was 1.The product of s and b gives y.

 

2.For t :-   As t is for next state which depends only on incoming bit nothing else.Therefore t=b.

Answer:

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