Design of Digital Systems II
Introduction
Moslem Amiri, V´aclav Pˇrenosil
Embedded Systems Laboratory
Faculty of Informatics, Masaryk University
Brno, Czech Republic
amiri@mail.muni.cz
prenosil@fi.muni.cz
September, 2012
Analog vs. Digital
Analog systems process time-varying signals that can take on any
value across a continuous range of voltage, current, ...
So do digital systems; the difference is a digital signal is modeled as
taking on only one of two discrete values, 0 and 1
Reasons to favor digital circuits over analog ones
Reproducibility of results
Given the same inputs, a digital circuit always produces the same results
Outputs of an analog circuit vary with temperature, power supply
voltage, component aging, ...
Ease of design
Digital design is logical; no math skills and no insights about operation
of capacitors, transistors, ... are needed
Flexibility and functionality
E.g., using a digital circuit that scrambles recorded voice so that anyone
with key can decipher and hear it undistorted
Programmability
Much of digital design is carried out today by writing programs in
hardware description languages (HDLs)
HDLs allow both structure and function of a digital circuit to be modeled
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Analog vs. Digital
Reasons to favor digital circuits over analog ones (continued)
Speed
Today, transistors can switch in less than 10 picoseconds
A device can examine its inputs and produce an output in less than a
nanosecond
Economy
Digital circuits provide a lot of functionality in a small space
Circuits that are used repetitively can be integrated into a single chip
and mass-produced at a very low cost
Steadily advancing technology
Technology for a digital system always gets faster, cheaper, or otherwise
better
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Digital Devices
Section 1.4 Electronic Aspects of Digital D
ing outputs. A gate is called a combinational circuit because its output depends
only on the current input combination.
A 2-input OR gate, shown in (b), produces a 1 output if one or both of its
inputs are 1; it produces a 0 output only if both inputs are 0. Once again, there are
four possible input combinations, resulting in the outputs shown in the figure.
A NOT gate, more commonly called an inverter, produces an output value
that is the opposite of the input value, as shown in (c).
We called these three gates the most important for good reason. Any digital
function can be realized using just these three kinds of gates. In Chapter 3 we’ll
show how gates are realized using transistor circuits. You should know, however,
(c) 1
(a) 0
0
0
(b) 0
0
0
0 0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
Figure 1-1 Digital devices: (a) AND gate; (b) OR gate; (c) NOT gate or inverter.
combinatio
OR gate
NOT gate
inverter
Figure 1: Digital devices: (a) AND gate; (b) OR gate; (c) NOT gate or inverter.
Any digital function can be realized using just three kinds of gates
shown in Fig. 1
A gate is a combinational circuit because its output depends only on
current combination of input values
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Digital Devices
A flip-flop is a device that stores either a 0 or 1
State of a flip-flop is the value that it currently stores
Stored value can be changed only at certain times determined by a clock
input
New value may depend on flip-flop’s current state and its control inputs
A digital circuit that contains flip-flops is a sequential circuit because
its output at any time depends not only on its current input but also
on past sequence of inputs
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Electronic Aspects of Digital Design
Digital circuits deal with analog voltages and currents and are built
with analog components
Digital abstraction allows analog behavior to be ignored in most cases,
so circuits can be modeled as if they really did process 0s and 1s
Digital abstraction
To associate a range of analog values with 0 or 1
Noise margin
A gate’s output can be corrupted by this much noise and still be
correctly interpreted at inputs of other gates
One important aspect of the digital abstraction is to associate a range of
logic 0
Outputs Inputs
Noise
Margin
Voltage
logic 1
logic 0
logic 1
invalid
gure 1-2
ogic values and noise
argins.
Figure 2: Logic values and noise margins.
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Software Aspects of Digital Design
In computer-aided design, various software tools improve designer’s
productivity and help to improve correctness and quality of designs
Important examples of software tools for digital design
Schematic entry
Allows schematic diagrams to be drawn on-line instead of with paper
and pencil
Checks for common, easy-to-spot errors, e.g., shorted outputs, signals
that don’t go anywhere, ...
HDLs
Are used to design anything from individual function modules to large,
multichip digital systems
HDL text editors, compilers, and synthesizers
Text editor is used to write an HDL program
HDL compiler checks it for syntax and related errors
Synthesizer creates a corresponding circuit realization that is targeted to
a particular hardware technology
Before synthesis, designer runs HDL program on a simulator to verify
behavior of design
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Software Aspects of Digital Design
Important examples of software tools for digital design (continued)
Simulators
Once first chip is built, it’s very difficult to debug it by probing internal
connections, or to change gates and interconnections
Simulators help predict electrical and functional behavior of a chip,
allowing most bugs to be found before chip is fabricated
Simulators
Used in overall design of systems with many individual components
However, it’s easier to make changes in components and
interconnections on a printed-circuit board
Test benches
Environments to simulate and test HDL-based digital designs
A set of programs are built around HDL programs to automatically
exercise them, checking both their functional and timing behavior
Timing analyzers and verifiers
Automate task of drawing timing diagrams and specifying and verifying
timing relationships between different signals in a complex system
Word processors
HDL-specific text editors are useful for writing source code, but word
processors can be used to create documentation
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Integrated Circuits
Integrated circuit (IC)
A collection of one or more gates fabricated on a single silicon chip
An IC is initially part of a larger, circular wafer, containing dozens to
hundreds of replicas of same IC
All of IC chips on wafer are fabricated at the same time
Each piece (IC chip) is called a die
Each die has pads around its periphery, i.e., electrical contact points, so
wires can be connected later
After wafer is fabricated, dice are tested in place on wafer using tiny,
probing pins that contact pads, and defective dice are marked
Then wafer is sliced up to produce individual dice, and marked ones are
discarded
Each good die is mounted in a package, its pads are wired to package
pins, packaged IC is subjected to a final test, and shipped to a customer
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Integrated Circuits
Small-scale integration (SSI) ICs
Contain equivalent of 1 to 20 gates
Are largely supplanted by programmable logic devices (PLDs)
Are still sometimes used as glue to tie together larger-scale elements in
complex systems
Section 1.6 Integrated Circuits
In the early days of integrated circuits, ICs were classified by size—small,
medium, or large—according to how many gates they contained. The simplest
type of commercially available ICs are still called small-scale integration (SSI),
and contain the equivalent of 1 to 20 gates. SSI ICs typically contain a handful of
small-scale integr
(SSI)
(b) (c)(a) 0.3"
0.1"
pin 1 pin 14
pin 8
0.1"
pin 1 pin 20
0.3"
pin 11
0.6"
0.1"
pin 1 pin 28
pin 15
Figure 3: Dual inline pin (DIP) packages: (a) 14-pin; (b) 20-pin; (c) 28-pin.
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Integrated Circuits
Copyright © 1999 by John F. Wakerly Copying Prohibited
determine the pin numbers for a particular IC. In the schematic diagram for a
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7400
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7402
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7404
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7410
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7411
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7420
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7421
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7430
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7432
1
2
3
4
5
6
7
14
13
12
11
10
9
8GND
VCC
7408
Figure 1-5 Pin diagrams for a few 7400-series SSI ICs.
Figure 4: Pin diagrams for a few 7400-series SSI ICs.
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Integrated Circuits
Medium-scale integration (MSI) ICs
Contain equivalent of about 20 to 200 gates
Typically contain a functional building block, such as a decoder,
register, or counter
Even though use of discrete MSI ICs has declined, equivalent building
blocks are used extensively in design of larger ICs
Large-scale integration (LSI) ICs
Contain equivalent of 200 to 1,000,000 gates or more
LSI parts include small memories, microprocessors, programmable logic
devices, and customized devices
Very large-scale integration (VLSI) ICs
Contain over a few million transistors
E.g., today’s most microprocessors, memories, larger programmable
logic devices and customized devices
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Programmable Logic Devices
There are a wide variety of ICs that can have their logic function
programmed into them after they are manufactured
Most of them can be reprogrammed (for fixing bugs)
Programmable logic arrays (PLAs)
Historically, first programmable logic devices
Contained a two-level structure of AND and OR gates with
user-programmable connections
Programmable array logic (PAL) devices
PLA structure was enhanced and PLA costs were reduced with
introduction of PAL devices
Today, such devices are generically called programmable logic devices
(PLDs)
PLDs are MSI of programmable logic industry
Complex PLD (CPLD)
To design larger PLDs for larger applications, for technical reasons, basic
two-level AND-OR structure of PLDs could not be scaled to larger sizes
IC manufacturers devised CPLD architectures to achieve required scale
CPLD is a collection of multiple PLDs and a programmable
interconnection structure, all on the same chip
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Programmable Logic Devices
Field-programmable gate array (FPGA)
While CPLDs were being invented, other IC manufacturers took a
different approach to scaling size of PLDs
Compared to a CPLD, an FPGA contains a much larger number of
smaller individual logic blocks
FPGA provides a large, distributed interconnection structureChapter 1 Introduction
PLD PLD PLD PLD
PLD PLD PLD PLD
Programmable Interconnect
(a) (b) = logic block
Figure 1-6 Large programmable-logic-device scaling approaches: (a) CPLD; (b) FPGA.Figure 5: Large PLD scaling approaches: (a) CPLD; (b) FPGA.
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Application-Specific ICs (ASICs)
ASICs or semicustom ICs
Chips designed for a particular, limited product or application
Reduce total component and manufacturing cost of a product by
reducing chip count, physical size, and power consumption
Provide higher performance
Nonrecurring engineering (NRE) cost for an ASIC design can
exceed cost of a discrete design by $10,000 to $500,000 or more
NRE charges are paid to IC manufacturer and others responsible for
designing internal structure of chip, creating tools such as metal masks,
developing tests, and making first few sample chips
An ASIC design makes sense if NRE cost is offset by per-unit savings
Custom LSI chip
A chip whose functions, internal architecture, and detailed
transistor-level design is tailored for a specific customer
Its NRE cost is very high, $500,000 or more
I.e., chips that have general commercial application like microprocessors,
or high sales volume in a specific application like a digital watch chip
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Application-Specific ICs (ASICs)
Standard cells
Developed to reduce NRE charges
Libraries of standard cells include commonly used MSI and LSI functions
In a standard-cell design, designer interconnects functions like as in a
multichip MSI/LSI design
Custom cells are created only if absolutely necessary
All of cells are then laid out on chip, optimizing layout to reduce
propagation delays and minimize chip size
NRE cost for a standard-cell design is $250,000 or more
Gate array
Developed to reduce NRE charges even further
Is an IC whose internal structure is an array of gates whose
interconnections are initially unspecified
Designer specifies gate types and interconnections
Even though chip design is ultimately specified at this very low level,
designer works with macrocells, the same high-level functions used in
multichip MSI/LSI and standard-cell design
Software expands high-level design into a low-level one
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Application-Specific ICs (ASICs)
Standard-cell vs. gate-array design
Macrocells and chip layout of a gate array are not as highly optimized as
those in a standard-cell design, so chip may be 25% or more larger and
therefore may cost more
Not possible to create custom cells in gate-array approach
A gate-array design can be finished faster and at lower NRE cost,
ranging from $10,000 to $100,000
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Printed-Circuit Boards (PCBs)
An IC is mounted on a PCB that connects it to other ICs in a system
Multilayer PCBs have copper wiring etched on multiple, thin layers of
fiberglass that are laminated into a single board
PCB traces
Individual wire connections
Are 10 to 25 mils (1 mil = 1/1000 inch) wide in typical PCBs
In fine-line PCB technology, traces are 3 mils wide with 3-mil spacing
between adjacent traces
If higher connection density is needed, more layers are used
Surface-mount technology (SMT)
Instead of having long pins of DIP packages that poke through board
and are soldered to underside, leads of SMT IC packages are bent to
make flat contact with top surface of PCB
First, a solder paste is applied to contact pads on PCB using a stencil
Then, SMT components are placed on pads
Finally, entire assembly is passed through an oven to melt solder paste,
which then solidifies when cooled
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Printed-Circuit Boards (PCBs)
Surface-mount tech. coupled with fine-line PCB tech.
Allows extremely dense packing of ICs and other components on a PCB
Saves space
Minimizes transmission-line effects
Minimizes speed-of-light limitations
Multichip modules (MCMs)
Developed to satisfy the most stringent requirements for speed and
density
IC dice are not mounted in individual plastic or ceramic packages
IC dice for a high-speed subsystem (e.g., a processor and its cache
memory) are bonded directly to a substrate that contains required
interconnections on multiple layers
MCM is sealed and has its own external pins for power, ground, and just
those signals that are required by system that contains it
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Digital-Design Levels
Digital design can be carried out at several different levels of
representation and abstraction
Sometimes it is needed to go up or down a level or two to get the job
done
Industry and most designers are moving to higher levels as circuit
density and functionality increase
Lowest level = device physics and IC manufacturing processes
Won’t be discussed in this course
Transistor level design =⇒ logic design using HDLs
Will be discussed in this course
Level of functional building blocks is center of our discussion
Highest level = computer design and overall system design
Won’t be discussed in this course
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Digital-Design Levels: Example
Multiplexer
t the transistor level and go all
DLs. We stop short of the next
ll system design. The “center”
ding blocks.
we’ll cover, consider a simple
ultiplexer” with two data input
bit Z. Depending on the value
ther A or B to the output Z. This
1-7. Let us consider the design
at higher level, for some funcning
at the transistor level. The
s how the multiplexer can be
zed transistor circuit structures
A
B
Z
S
Figure 1-7
Switch model for
multiplexer function.
Figure 1-8
Multiplexer design using
CMOS transmission gates.
Figure 6: Switch model for multiplexer function.
For some functions it is advantageous to optimize them by designing
at transistor level
Multiplexer is such a function
Multiplexer can be designed in CMOS technology using specialized
transistor circuit structures called transmission gates
Using this approach, mux can be built with just six transistors
Any other approach requires at least 14 transistors
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Digital-Design Levels: Example
Copyright © 1999 by John F. Wakerly Copying P
multiplexer is such a function. Figure 1-8 shows how the multiplexe
designed in “CMOS” technology using specialized transistor circuit s
A
B
S
VCC
Z
Figure 1-8
Multiplexer design u
CMOS transmission
Figure 7: Multiplexer design using CMOS transmission gates.
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Digital-Design Levels: Example
Truth table
Is used to describe logic function
Traditional logic design methods use Boolean algebra and minimization
algorithms to derive an optimal two-level AND-OR equation from truth
table
For Tab. 1
Z = S .A + S.B (1)
to
u-
C
of
nd
ly
in
all
xt
r”
le
ut
ue
is
gn
c-
he
be
es
A
B
Z
S
Figure 1-7
Switch model for
multiplexer function.
Table 1: Truth table for the multiplexer function.
S A B Z
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
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Digital-Design Levels: Example
Going one step further, (1) can be converted into a set of logic gates,
as shown in Fig. 8
This circuit requires 14 transistors
1999 by John F. Wakerly Copying Prohibited
iplexer is a very commonly used function, and most digital logic
provide predefined multiplexer building blocks. For example, the
n MSI chip that performs multiplexing on two 4-bit inputs simultaure
1-10 is a logic diagram that shows how we can hook up just one
-bit building block to solve the problem at hand. The numbers in
numbers of a 16-pin DIP package containing the device.
A
S
B
Z
SN
ASN
SB
9
gic diagram
er function.
Figure 8: Gate-level logic diagram for multiplexer function.
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Digital-Design Levels: Example
Multiplexer is a very commonly used function
Most digital logic technologies provide predefined multiplexer building
blocks
E.g., 74x157 is an MSI chip that performs multiplexing on two 4-bit
inputs simultaneously Section 1.10
We can also realize the multiplexer function as part of a programm
logic device. Languages like ABEL allow us to specify outputs using Boo
equations similar to the one on the previous page, but it’s usually more co
74x157
1A
1B
2A
2B
3A
3B
4A
4B
G
2
4
1Y
7
2Y
9
3Y
12
4Y
3
5
6
11
10
14
13
S
1
15
S
B
A
Z
Figure 1-10
Logic diagram for a
multiplexer using an
MSI building block.
Figure 9: Logic diagram for a multiplexer using an MSI building block.
25 / 30
Digital-Design Levels: Example
We can also realize multiplexer function as part of a PLD
HDLs allow us to specify logic functions using Boolean equations like (1)
An HDL’s higher-level language elements can create a more readable
program
Table 2: ABEL program for the multiplexer.
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Digital-Design Levels: Example
VHDL and Verilog are even higher-level languages than ABEL
They can be used to specify multiplexer function in a way that is very
flexible and hierarchical
Table 3: VHDL program for the multiplexer.
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Digital-Design Levels: Example
Input/output definitions (entity) and internal realization (architecture)
are separate in VHDL
Easy to define alternate realizations of functions
An alternate, structural architecture for multiplexer is shown in Tab. 4
Table 4: ”Structural” VHDL program for the multiplexer.
called “transmission gates,” discussed in Section 3.7.1. Using this approach, the
multiplexer can be built with just six transistors. Any of the other approaches
that we describe require at least 14 transistors.
In the traditional study of logic design, we would use a “truth table” to
describe the multiplexer’s logic function. A truth table list all possible combinations
of input values and the corresponding output values for the function. Since
the multiplexer has three inputs, it has 23 or 8 possible input combinations, as
shown in the truth table in Table 1-1.
Once we have a truth table, traditional logic design methods, described in
Section 4.3, use Boolean algebra and well understood minimization algorithms
to derive an “optimal” two-level AND-OR equation from the truth table. For the
multiplexer truth table, we would derive the following equation:
This equation is read “Z equals not S and A or S and B.” Going one step further,
we can convert the equation into a corresponding set of logic gates that perform
the specified logic function, as shown in Figure 1-9. This circuit requires 14
transistors if we use standard CMOS technology for the four gates shown.
A multiplexer is a very commonly used function, and most digital logic
technologies provide predefined multiplexer building blocks. For example, the
74x157 is an MSI chip that performs multiplexing on two 4-bit inputs simultaneously.
Figure 1-10 is a logic diagram that shows how we can hook up just one
bit of this 4-bit building block to solve the problem at hand. The numbers in
color are pin numbers of a 16-pin DIP package containing the device.
Z = S′ ⋅ A + S ⋅ B
A
S
B
Z
SN
ASN
SB
Figure 1-9
Gate-level logic diagram
for multiplexer function.
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Digital-Design Levels: Example
VHDL is powerful enough to define operations that model functional
behavior at transistor level
Won’t be explored in this course
Verilog syntax is somewhat C-like
Like C, Verilog is less picky about variable and type definition
E.g., in Tab. 5 all of variables default to being 1-bit wires
Unlike VHDL, Verilog does not require separate definitions of entity and
architecture
Verilog provides a means for defining functions structurally as in VHDL
example of Tab. 4
Table 5: Verilog program for the multiplexer.
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References
John F. Wakerly, Digital Design: Principles and Practices (4th
Edition), Prentice Hall, 2005.
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