Page 173 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes In the previous example of machine with 5 states, we need three flip-flops. Let us choose assignment
1, which is binary assignment for our sequential machine example (shown in the Table 10.6).
The unspecified states can be used as do not-cares and will therefore help in simplifying the logic.
The excitation table of previous example is shown. There are three states, 000, 110, and 111 that
are not listed in the Table 10.7 under present state and input.

Table 10.7: Excitation Table

Present state Input Next state Flip-flop inputs Output

A B C x A B C SA RA SB RB SC RC y
0 0 1 0 0 0 1 0 X 0 X X 0 1
0 0 1 1 0 0 1 0 X 1 0 0 1 1
0 1 0 0 0 1 0 0 X X 0 1 0 1
0 1 0 1 0 1 0 1 0 0 1 0 X 1
0 1 1 0 0 1 1 0 X 0 1 X 0 1
0 1 1 1 0 1 1 1 0 0 1 0 1 1
1 0 0 0 1 0 0 X 0 0 X 1 0 1
1 0 0 1 1 0 0 X 0 0 X 0 X 0
1 0 1 0 1 0 1 0 1 0 X X 0 1
1 0 1 1 1 0 1 X 0 0 X 0 1 0

With the inclusion of input 1 or 0, we obtain six do-not-care minterms: 0, 1, 12, 13, 14, and 15.

Figure 10.7: K-maps

Cx c
00 01 11 10
AB
00 X X X X X X X X 1
01 1 1 X X X
B X X X X
11 X X X X X X X X
A
10 X X X 1

x
SA =Bx RA = Cx’ SB =A’B’x
X X X X X X X X X 1
1 1 1 1 X X X

X X X X X X X X X X X X
X X X X 1 X X 1
RB=BC+Bx SC=x° RC=x

X X 1 1
1 1 1 1

X X X X
1 1
y= A’+x’= (Ax)’

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