EXAMPLE 3 Construct the state table for the finite-state machine with the state diagram shown in Figure 3. Solution: The state table for this machine is shown in Table 3. An input string takes the starting state through a sequence of states, as determined by the transition function. As we read the input string symbol by symbol (from left to right), each input symbol takes the machine from one state to another. Because each transition produces an output, an input string also produces an output string. Suppose that the input string is x = x,x..x. Then, reading this input takes the machine from state so to state s1, where s, = f(sSo, x1), then to state s2, where s, = f(s1, x2), and so on, with s; = f(s 1,x;) for j = 1,2, ..., k, ending at state s = f(s-I). This sequence of transitions produces an output string y,y2 ... Y where y, = g(so, x) is the output corresponding to the transition from so to s1, y2 = g(s1, x2) is the output corresponding to the transition from s, to sz. and so on. In general, y; = g(s_1, x;) for j= 1, 2, ...,k. Hence, we can extend the definition of 0.1 TABLE 3 Input Input 0,1 State 1 1 Start. 0,0 1,0 0.0 1,0 So $3 $2 1 1,0 $3 S3 S4 0,0 0. 1,0 S3 So S4 53 S4 FIGURE 3 A finite-state machine.
EXAMPLE 3 Construct the state table for the finite-state machine with the state diagram shown in Figure 3. Solution: The state table for this machine is shown in Table 3. An input string takes the starting state through a sequence of states, as determined by the transition function. As we read the input string symbol by symbol (from left to right), each input symbol takes the machine from one state to another. Because each transition produces an output, an input string also produces an output string. Suppose that the input string is x = x,x..x. Then, reading this input takes the machine from state so to state s1, where s, = f(sSo, x1), then to state s2, where s, = f(s1, x2), and so on, with s; = f(s 1,x;) for j = 1,2, ..., k, ending at state s = f(s-I). This sequence of transitions produces an output string y,y2 ... Y where y, = g(so, x) is the output corresponding to the transition from so to s1, y2 = g(s1, x2) is the output corresponding to the transition from s, to sz. and so on. In general, y; = g(s_1, x;) for j= 1, 2, ...,k. Hence, we can extend the definition of 0.1 TABLE 3 Input Input 0,1 State 1 1 Start. 0,0 1,0 0.0 1,0 So $3 $2 1 1,0 $3 S3 S4 0,0 0. 1,0 S3 So S4 53 S4 FIGURE 3 A finite-state machine.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
100%
Subject:Discrete Mathematics
Topic: Finite State Machines with Output.
Perform Example 3 and use D flip flop for the circuit diagram
Transcribed Image Text:EXAMPLE 3 Construct the state table for the finite-state machine with the state diagram shown in Figure 3.
Solution: The state table for this machine is shown in Table 3.
An input string takes the starting state through a sequence of states, as determined by the
transition function. As we read the input string symbol by symbol (from left to right), each input
symbol takes the machine from one state to another. Because each transition produces an output,
an input string also produces an output string.
Suppose that the input string is x = x,xz...x. Then, reading this input takes the machine
from state s, to state s1, where s, = f(so x1), then to state s2, where s, = f(s1, x2), and so on, with
s; = f(sj-1, x;) for j = 1, 2, ..., k, ending at state s = f(s-1, X). This sequence of transitions
produces an output string y,y2 ... Yk. where y, = g(so, x) is the output corresponding to the
transition from so to s1, y2 = g(s1, x2) is the output corresponding to the transition from s, to s2,
and so on. In general, y; = g(s_1,x;) for j = 1, 2, ...,k. Hence, we can extend the definition of
0.1
TABLE 3
1, 1
f
Input
Input
0,1
State
1
1
Start.
1,0
0,0
1,0
So
3
1
1
1
1,0
s3
S3
S4
0,0
0.
0.
1,0
S3
So
S4
S3
S4
0.
FIGURE 3 Afinite-state machine.
0. 0
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