HW 10 Solutions
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Nov 24, 2024
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EE2420 Digital Logic -
Homework Set 10
SOLUTIONS
9 pts total
Problems 1 a), b), and c), 2 a), b), and c), and 3 a), b), and c) are worth 1 point each.
1)
Consider a sequential network with one input (X) and one output (Z).
The circuit accepts one
input value of X per clock cycle.
The circuit outputs Z = 0 unless the total number of X = 1
inputs is nonzero and divisible by three.
Below is an example of inputs and desired outputs:
X
1
0
1
1
0
1
0
0
0
1
0
1
0
1
Z
0
0
0
1
1
0
0
0
0
0
0
1
1
0
a)
Draw the state diagram for the network, including a reset.
b)
How many flip-flops will the circuit need?
c)
Determine the state table for the network.
-2-
2)
A sequential network has one input and one output.
The output is zero until the input sequence
110 occurs, at which time the output becomes 1.
The output remains 1 until the circuit receives
another 1 as an input.
Below is an example of inputs and desired outputs:
X
1
0
0
1
1
0
0
1
1
0
1
0
1
Z
0
0
0
0
0
1
1
0
0
1
0
0
0
a)
Draw the state diagram for the network, including a reset.
b)
How many flip-flops will the circuit need?
c)
Determine the state table for the network.
-3-
3)
A sequential network has one input and one output.
The output is zero until the input sequence
011 occurs, at which time the output becomes 1.
The output remains 1 until the sequence 011
occurs again, at which time the output returns to 0.
The output then remains 0 until 011 occurs
a third time, etc.
a)
Draw the state diagram for the network, including a reset.
b)
How many flip-flops will the circuit need?
c)
Determine the state table for the network.
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-4-
Present State
Q
3
Q
2
Q
1
Input
X
Next State
Q
3
+
Q
2
+
Q
1
+
Output
Z
000
0
001
0
000
1
000
0
001
0
001
0
001
1
010
0
010
0
001
0
010
1
011
0
011
0
100
1
011
1
011
1
100
0
100
1
100
1
101
1
101
0
100
1
101
1
000
1
110
0
XXX
XXX
110
1
XXX
XXX
111
0
XXX
XXX
111
1
XXX
XXX
Problems 1 is derived from Charles H. Roth, Jr., Fundamentals of Logic Design, 2
nd
Ed.
Problem 3 is directly
from Roth, 2
nd
ed.
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