EGR 277

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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Reading Assignment - Chapter 5 in Logic and
Computer Design Fundamentals, 4th Edition by
Mano - Online supplement to text Design and
Analysis using JK and T Flip-Flops (www.prenhall.
com/mano)

• Sequential Counters
• Counters are an important class of sequential
  circuits.
• Counters follow a predetermined sequence of
  states.
• A counter changes state upon application of an
  input pulse. The input pulse is not necessarily
  a periodic clock. For example, a traffic counter
  is clocked each time a car passes.
• Key uses of counters
• Count occurrences of an event
• Example Traffic counter
• Example Line counter on ASEE autonomous vehicle
  (illustrate in class)
• Generate timing sequences to control operations
• Frequency division

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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example Show that a JK flip-flop in the toggle
mode acts as a modulo-2 counter or a divide-by-2
circuit.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example Show that a 3-bit counter can serve as
a modulo-8 counter or a divide-by-8 circuit.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example Show how a circuit with a 1MHz master
clock might use counters (as frequency dividers)
to provide synchronized lower frequencies.
Note This same technique can be used in
software. In Lab 7 we will use a VHDL program
that implements a divide-by-50 million circuit
to produce a 1 Hz clock from the 50 MHz internal
clock on an FPGA board. We will need the 1 Hz
clock to display a designed counting sequence on
a 7-segment display.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Simplified Counter Design using T flip-flops A
full circuit excitation table may not be
necessary in some cases with T flip-flops,
especially when the states are in counting order.
It is easy to see which bits need to be toggled
to produce the next state.
Example Design a mod-6 counter using T
flip-flops.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Counters with multiple counting
sequences Switches can be easily used to control
counting direction or counting sequences.
Example Design a mod-6 UP/DOWN counter using T
flip-flops.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example Design a counter with 2 input
switches, x and y, that can count in 4 possible
sequences based on the switch positions. Use JK
flip-flops.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Flip-flop Excitation Tables
Q(t) Q(t1) J K S R D T
0 0 0 X 0 X 0 0
0 1 1 X 1 0 1 1
1 0 X 1 0 1 0 1
1 1 X 0 X 0 1 0
Circuit Excitation Table
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Flip-flop Input Functions and Circuit Output
Functions
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Self-starting counters Counters are considered
to be self-starting if all unused counts
eventually lead to the correct counting sequence.
Since the initial state for a flip-flop is
unpredictable upon powering up the IC, a counter
that is not self-starting could possibly power up
into an unused state that would not eventually go
into the correct counting sequence (so the
counter might lock up in an incorrect count or
counting pattern. Recall that the next states
for unused counts were sometimes treated as
dont cares. With this method it is difficult
to predict what will happen if the counter powers
up into an unused count (although it can be later
determined by analyzing the circuit). A safer
technique it to let all unused counts have a
valid count for their next state.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example Consider the state diagrams for two
modulo-5 counters below. Are they self-starting?
Case 1 Counter is NOT self-starting. Next
states for unused counts 5, 6, and 7 were perhaps
treated as dont cares.
Case 2 Counter is self-starting. Next states
for unused counts 5, 6, and 7 were all set to
count 0.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example Determine the counting sequence for the
counter shown (begin with count 0). Use a timing
diagram to display the values of Clock, JA, KA,
JB, KB, JC, KC, A, B, and C. Is the counter
self-starting?
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Sequence Detector An example of a circuit whose
output sequence is critical and the numeric value
of the states is unimportant is a sequence
detector. Such a circuit might be used to
detect a certain bit pattern (such as in
synchronizing two signals) or for a digital lock
where the lock is unlocked when a correct
combination (sequence) is entered.
Example Detect the sequence 101, including
overlapping sequences. Define the output, Y, as
follows
Fill out the values for Y in the table below
X 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 1
Y
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example Design a sequence detector to detect
the sequence 1010. The sequence detector should
also detect overlapping sequences. The circuit
should output a binary 1 when a valid sequence is
detected. Show designs using both Moore and
Mealy models.
Moore Model
Mealy Model
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example (continued) Test the state diagram
from the previous page with the input sequence
0101011001010100 to see if they produce the same
output sequence.
Moore Model
Mealy Model
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example (continued) Draw the logic diagram for
the design based on the Mealy model.
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Lecture 13 EGR 270 Fundamentals of
Computer Engineering
Example Serial 2s Complementer Circuit Design
a one input, one output serial 2s complementer
using a Mealy Model. The circuit accepts a
string of bits from the input and generates the
2s complement at the output. The circuit can be
reset asynchronously to start and stop the
operation. Implement the circuit using JK
flip-flop(s).