Digital Logic Chapter 5
Presented by Prof Tim Johnson
Wentworth Institute of Technology
Department of Electrical Engineering
and Tech.
Boston, MA
Text: Digital Systems by Ronald Tocci
Introduction to Chapter 5
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Logic circuits studied so far have outputs that respond
immediately to inputs at some instant in time.
We now introduce the concept of memory. The flip-flop,
abbreviated FF, is a key memory element.
The outputs of a flip flop are Q and Q
Q is understood to be the normal output, Q is always the
opposite.
When the normal output (Q) is placed in the high or 1
state we say the FF has been set.
When the normal output (Q) is placed in the low or 0 state
we say the FF has been cleared or reset.
NAND Latch: Info
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The NAND gate latch or simply latch is a basic FF.
Two NAND gates are cross-coupled so that the
output of NAND-1 is connected to one of the inputs
of NAND-2, and vice versa.
The gate outputs, Q and Q , are the latch outputs.
Under normal conditions, these two outputs will
always be the inverse of each other.
There are two inputs:
SET  0
 Q  1 (Q  0)
RESET  0  Q  0 (Q  1)
NAND Latch: Function Table
The SET and RESET inputs are active low.
 The output will change when the input is pulsed low.
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NAND Latch: Waveform
Determine the waveform for Q for the inputs given
below. Assume that initially Q = 0.
NAND Latch: Block Symbol
Alternate Representation
Simplified Block Symbol
NOR Latch: Info
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The NOR latch is also a basic FF.
Two NOR gates are cross-coupled so that the output
of NOR-1 is connected to one of the inputs of NOR2, and vice versa.
The arrangement of a NOR latch, as shown below, is
similar to a NAND latch except that the Q and Q
outputs have reversed positions.
SET  1
 Q  1 (Q  0)
RESET  1  Q  0 (Q  1)
NOR Latch: Function Table
NOR Latch
Function Table
Simplified
Block Symbol
The SET and RESET inputs are active high.
 The output will change when the input is pulsed high.
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NOR Latch: Waveform
Determine the Q waveform for the NOR latch.
Assume that initially Q = 0.
Digital Pulses
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Signals that switch between active and inactive
states are called pulse waveforms.
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The transition from low to high on a positive pulse is
called rise time (tr).
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A positive pulse has an active high level.
A negative pulse has an active low level.
Rise time is measured between the 10% and 90% points
on the leading edge of the voltage waveform.
The transition from high to low on a positive pulse is
called fall time (tf).
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Fall time is measured between the 90% and 10% points on
the trailing edge of the voltage waveform.
Digital Pulses: Rise and Fall Times
Clock Signals and Clocked FFs
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Asynchronous system – outputs can change state at any
time the input(s) change.
Synchronous system – output can change state only at
a specific time in the clock cycle.
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The clock signal is a rectangular pulse train or square wave.
Positive going transition (PGT) – when clock pulse 0  1
Negative going transition (NGT) – when clock pulse 1  0.
Transitions are also called edges.
Clock Signals and Clocked FFs
Clock Signals and Clocked FFs
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Clocked FFs change state on one or the other clock
transitions. Some common characteristics:
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Clock inputs are labeled CLK, CK, or CP.
A small triangle at the CLK input indicates that the
input is activated with a PGT (see next page)
A bubble and a triangle indicates that the CLK input
is activated with a NGT (see next page)
Control inputs have an effect on the output only at the
active clock transition (NGT or PGT). These are also
called synchronous control inputs.
The control inputs get the FF outputs ready to change, but
the change is not triggered until the CLK edge.
Clock Signals and Clocked FFs
Clock Signals and Clocked FFs
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Setup time (tS) is the minimum time interval before
the active CLK transition that the control input must
be kept at the proper level.
Hold time (tH) is the time following the active
transition of the CLK during which the control input
must kept at the proper level.
Clocked S-R Flip-Flop: Function
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The SET-RESET FF will change states at the
positive going or negative going clock edge.
Clocked S-R Flip-Flop: Waveform
Clocked S-R Flip-Flop: Internal Circuitry
See Next Page for the Edge Detector
Clocked S-R Flip-Flop: Internal Circuitry
Edge Detectors for (a) PGT and (b) NGT
Clocked J-K Flip-Flop: Info
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Operates like the S-R FF. J is SET, K is RESET.
Difference from the S-R FF: When J and K are
both high, the output is toggled from whatever
state it is into the opposite state – the toggle
mode.
May be PGT or NGT.
Has the ability to do everything the S-R FF does,
plus operating in the toggle mode.
Clocked J-K Flip-Flop: Function Table
PGT
NGT
Clocked J-K Flip-Flop: Internal Circuitry
Clocked J-K Flip-Flop: Waveform
Exercises (Clocked J-K FF)
Exercises (Clocked NOR FF)
Clocked D Flip-Flop: Info
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One data input.
The output changes to the value of the input at either
the positive going or negative going clock trigger.
May be implemented with a J-K FF by tying the J input
to the K input through an inverter.
Useful for parallel data transfer.
Clocked D Flip-Flop: Function
Clocked D Flip-Flop: Parallel Data Transfer
D Latch (Transparent Latch): Info
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One data input.
The clock has been replaced by an enable line.
The device is NOT edge triggered.
The output follows the input only when EN is
high.
D Latch: Function
D Latch: Waveform
Asynchronous (Override) Inputs
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Inputs that depend on the clock are synchronous.
Most clocked FFs have asynchronous inputs that do
not depend on the clock.
The labels PRE and CLR are used for asynchronous
inputs.
Active low asynchronous inputs will have a bar over
the labels and inversion bubbles.
If the asynchronous inputs are not used they will be
tied to their inactive state.
Note: We didn’t talk about this. The materials are included here for your information.
Asynchronous Inputs: Function
Note: We didn’t talk about this. The materials are included here for your information.
IEEE/ANSI Symbols
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Note the differences in the representations below.
PRE
CLR
Note: We didn’t talk about this. The materials are included here for your information.
Flip-Flop Timing Considerations
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Important timing parameters:
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Setup and hold times
Propagation delay – the time for a signal at the input
to be shown at the output.
Maximum clocking frequency – highest clock
frequency that will give a reliable output.
Clock pulse high and low times – minimum time that
clock must high before going low, and low before
gong high.
Propagation delay may cause unpredictable outputs.
Note: We didn’t talk about this. The materials are included here for your information.
Flip-Flop Applications
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Examples of applications:
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Synchronization
Synchronous Data Transfer
Frequency Division
Many FF applications are categorized as
sequential, which means that the output
follows a predetermined sequence of states.
Application: Synchronization (1)
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Most systems are primarily synchronous in
operation, where changes depend on the clock.
Asynchronous and synchronous operations are often
combined.
The random nature of asynchronous inputs can result
in unpredictable results.
Example shown on the next page describes the
problem and a solution using FF.
Application: Synchronization (2)
A Synchronization Problem:
The synchronization problem solved by FF:
Application: Detecting an Input Sequence
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FFs provide features that pure combinational logic
gates do not.
If an output is desired only when inputs change state
in sequence, an arrangement similar to the following
figure can be used.
How about three inputs in sequence?
Application: Synchronous Data Transfer (1)
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FFs are commonly used for storage and transfer of
data in binary form.
Groups of FFs used for storage are registers.
Data transfers take place when data is moved
between registers or FFs.
Synchronous transfers take place at either PGT or
NGT of the clock.
Transferring the bits of a register simultaneously is
a parallel transfer.
Transferring the bits of a register one bit at a time is
a serial transfer.
Application: Parallel Data Transfer
Parallel Transfer:
Register contents
are transferred
simultaneously with
a single clock cycle.
Faster, the circuit is
more complex.
Application: Serial Data Transfer
Serial Transfer:
Register contents are
transferred one bit at
a time, with a clock
pulse for each bit.
Slower, the circuit is
simpler.
Application: Frequency Division & Counting (1)
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FFs are often used
to divide a
frequency.
Application: Frequency Division & Counting (2)
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The same circuit
is also acting as a
binary counter.
Application: Frequency Division & Counting (3)
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The counter has 23 = 8 different
states.
It is referred to as a MOD-8
counter, where the MOD
number indicates the number
of states in the counting
sequence.
In general, if N flip-flops are
connected in a similar
arrangement, the counter has 2N
different states and so it is a
MOD-2N counter. It can count
up to 2N-1 before returning to its
0 state.
State Transition Diagram
Microcomputer Application