Written Hwk #9 (due 3/30/2011)
ECE 290
Problem Set #9
Due: March 30, 2011
Problem 9.1
Consider a 3bit twisted ring counter consisting of 3 D flipflops (labelled C, B, A from lefttoright) and an inverter, connected such that DB = QC, DA = QB, and DC = QA'.
Starting with state QCQBQA = 111, give the counting sequence in binary.
a.
Which states are illegal? Verify that the circuit is not selfcorrecting by showing the count sequence(s) for these illegal states.
b.
Modify the DC input to be DC = QCQB' + QA'. Verify that this modified circuit is selfcorrecting.
c.
Problem 9.2
Implement a mod 6 counter which counts in the following CBA sequence and repeats: 111, 010, 100, 001, 101, 000. I.e., the counter proceeds through its 6 states in the (nonstandard) order 7, 2, 4, 1, 5, 0.
Draw the state diagram for this counter.
Note:
There are no "input/output" labels on the edges, because there is no input (other than the clock) and the output is just the state.
a.
You will implement the counter using 3 T flipflops. Draw the next state/excitation table, showing the current state CBA, the next state C
+
B
+
A
+
, and the flipflop excitation inputs T
C
T
B
T
A
.
b.
Give the Kmaps and provide minimal SOP expressions for T
C
, T
B
, T
A
.
c.
Draw the augmented state diagram; i.e., include the don't care states. Is this counter selfstarting? Explain.
d.
Modify your circuit so that, from any don't care state, the next state will be 000. Show your work.
Hint:
Go back to part (c) to make the necessary changes.
e.
Problem 9.3
Design a 4bit register, whose inputs and outputs are as shown in the diagram below. The mode operation table is also given under the diagram.
M
0
M
1
M
2
Operation
0
0
0
No Change
0
0
1
Logical Shift Right
0
1
0
Logical Shift Left
0
1
1
Increment value by 1
1
0
0
Clear all bits
1
0
1
Complement all bits
1
1
0
Arithmetic Shift Right
1
1
1
Parallel Load
Use D flipflops to implement the PISO (Parallelin SerialOut) shift register. You can use this as a block N in your final design.
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 Spring '08
 Staff
 2k, Digital circuits, Arithmetic shift, Logical shift, Donna J. Brown

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