The document describes an experiment where a student constructed a synchronous counter circuit based on a given state diagram and state table. The circuit was built using Karnaugh maps to determine the inputs for each flip-flop. The circuit was tested and debugged after it was found one flip-flop was not working properly due to an incorrect connection. Methods for determining the next states for unused states in the state table are also discussed.

1. Ha, Stephanie
December 1, 2008
EXPERIMENT 20: DESIGN OF SYNCHRONOUS COUNTERS POST-LAB
Summary
In this experiment, a synchronous counter was constructed based on the state diagram
presented in the Figure 20-1 in the data section. From Table 20-1, the Karnaugh maps (Figure
20-2) for each flip-flop were obtained after determining the inputs of each flip-flop.
From Figure 20-2, the circuit was constructed based on these equations. Figure 20-3
illustrates a schematic of the circuit where flip-flop C is the most significant. In constructing the
circuit, it was determined that ‘011’ went to the next state of ‘000’ instead of ‘010’.
From the previous experiment, the circuit was then debugged to find that QB was not
working properly. Each flip-flop was tested with a logic indicator to verify its output. It was
found that KB was not working properly: it was connected to QC’ (pin14) instead of QC (pin15).
Making the appropriate change, the circuit worked properly.
The next state for unused states 5 and 7 can be determined through various methods. One
method is from the previous experiment where the sequence can be determined to set and reset
the value to state 5 and state 7 and then use a pushbutton switch to reset these values. Another is
to use Table 20-2, Table 20-3, and Figure 20-3 to determine the input of each flip from its K-
map.
Data
Figure 20-1: Required Sequence for Circuit
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2. Table 20-2: State Table and Flip-Flop for Circuit
Present State Next State Flip-Flops
qC qB qA QC QB QA JC KC JB KB JA KA
0 0 0 0 0 1 0 x 0 x 1 x
0 0 1 0 1 1 0 x 1 x x 0
0 1 1 0 1 0 0 x x 0 x 1
0 1 0 1 1 0 1 x x 0 0 x
1 1 0 1 0 0 x 0 x 1 0 x
1 0 0 0 0 0 x 1 x 0 0 x
1 0 1 x x x x x x x x x
1 1 1 x x x x x x x x x
*Note: Highlighted areas indicate unused state
Figure 20-2: Karnaugh Maps for JK Flip-Flops
Figure 20-3: Schematic for Circuit from equations in Figure 20-2
Review Questions
1. Complete the design for the sequential counter in Figure 20-3 by constructing Karnaugh
maps for the B and A flip-flops. Read the maps. As a check, you can compare your result
with the circuit drawn in Figure 19-1.
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3. State Diagram for Fig. 20-3
State Table and Excitation Table for Flip-Flops
Present State Next State Flip-Flops
qD qC qB qA QD QC QB QA JD KD JC KC JB KB JA KA
0 0 0 1 0 0 1 1 0 x 0 x 1 x x 0
0 0 1 1 0 0 1 0 0 x 0 x x 0 x 1
0 0 1 0 0 1 1 0 0 x 1 x x 0 0 x
0 1 1 0 0 1 0 0 0 x x 0 x 1 0 x
0 1 0 0 1 1 0 0 1 x x 0 0 x 0 x
1 1 0 0 1 0 0 0 x 0 x 1 0 x 0 x
1 0 0 0 1 0 0 1 x 0 0 x 0 x 1 x
1 0 0 1 0 0 0 1 x 1 0 x 0 x 0 x
Karnaugh Maps for Fig. 20-3 (D + C Flip-Flops)
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4. 2. Describe the logic necessary to add a seven-segment display to the circuit you designed in
this experiment to enable the display to show the state of the counter.
a. Connect seven-segment display, MAN72 to seven-segment to BCD decoder or 7447A
(from previous experiment). Connect flip-flops to inputs of 7447A (DCBA) with C being
the most significant.
3. Assume you wanted to make the sequential circuit you designed in this experiment start in
state 5 if a reset pushbutton is pressed. Describe how you would modify the circuit to
incorporate this feature.
a. Derive the K-map for state 5Connect clocks C and A together to push button switch,
leaving B grounded to obtain a clock of ‘101’. Leave all other connections as it is.
4. Assume you wanted to change the circuit from this experiment to be able to reverse the
sequence. How would you go about this?
a. Start all over again (repeat process) by reversing the state diagram for the circuit in the
experiment.
i. State Diagram
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5. ii. State table
Present State Next State Flip-Flops
qC qB qA QC QB QA JC KC JB KB JA KA
0 0 0 1 0 0 1 x 0 x 0 x
1 0 0 1 1 0 x 0 1 x 0 x
1 1 0 0 1 0 x 1 x 0 0 x
0 1 0 0 1 1 0 x x 0 1 x
0 1 1 0 0 1 0 x x 1 x 0
0 0 1 0 0 0 0 x 0 x x 1
iii. K-Maps
iv. Construct circuit based on K-map (not shown)
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6. ii. State table
Present State Next State Flip-Flops
qC qB qA QC QB QA JC KC JB KB JA KA
0 0 0 1 0 0 1 x 0 x 0 x
1 0 0 1 1 0 x 0 1 x 0 x
1 1 0 0 1 0 x 1 x 0 0 x
0 1 0 0 1 1 0 x x 0 1 x
0 1 1 0 0 1 0 x x 1 x 0
0 0 1 0 0 0 0 x 0 x x 1
iii. K-Maps
iv. Construct circuit based on K-map (not shown)
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