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GATE Computer Science (CS) 2021 Shift 2 Solved Paper
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Question : 38
Total: 65
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 ?
t = b
y = sb
t = s + b
y = sb
t = s + b
y = sb̅
t = b
y = sb̅
Validate
Solution:
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