3. Introduction
3
Logic design is one of the disciplines that has enabled digital revolution,
which has dramatically altered our economics, communication, and life
in general!
Cars are growingly more computers!
5. What is Design?
• Design is the process of coming up with a solution to a problem:
– Need to understand the problem
– Need to understand the constraints
We desire an ‘efficient’ design!
• Consider, the problem of building an university:
– Create an xyz sq ft of floor area, where say 10,000 people can work
efficiently.
– Constraints:
• Dimensions
• Aesthetics
• Departments, rooms
• Other services
• Lifts
• Parking Space
• Emergency Exits…
• Money and Time 5
6. Divide and Conquer
• A very efficient methodology which humans have developed
because of their inability of handling too many details!
• Divide the problem into sub-problems:
– Associate sub-contractors (Split/Divide)
• Each have their own design problems
• Continues in a recursive fashion
– Merge the solutions (Conquer)
• The chief-architect is responsible for integrating
• Toughest job!
• Good communication and team work is a key!
– It is difficult for the stair-case contractor to ask to change the
dimensions of the hall for better flight.
– Or, to widen the elevator shaft after developing the building.
6
7. Top-down and Bottom-up Approaches
• Both strategies of information processing and knowledge
ordering
• A top down approach breaks up a bigger picture into sub-
systems, which are often like black-boxes, initially.
• A Bottom-up approach starts with systems and connects them
together to form bigger systems.
• Top down approach is about planning, and starts
implementations after the complete picture is clear.
– Delays testing
• Bottom up approach on the other hand stresses on
implementation and testing from the beginning.
– Problem may be integration/linking of modules.
– Good for reuse of design.
• Real life design combines both.
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8. Facets of Design
8
Design
Creative Process
(Visualize the
solution)
Engineering
Process
(Explore the
trade-offs, make
decisions)
Optimization
Process
(Choosing best
combination
among
components)
9. Digital/Logic Design
• A digital designer uses components from
digital electronics to solve problems in real
life.
• Transistors from CMOS (Complementary
MOS) forms the core.
• A digital designer abstracts it like a switch.
• Circuit: An inter-connected collection of
switches 9
10. Gate Path
0 Closed
1 Open
Gate
Drain
Source
Gate
Source
Drain
Gate Path
0 Open
1 Closed
pMOS
nMOS
• Transmits 1 well
• Transmits 0 poorly
• Transmits 0 well
• Transmits 1 poorly
Transistors as Switches: 1st Abstraction
11. CMOS Transmission Gate
• Transmit signal from INPUT to OUTPUT when
Gate is closed
Gate (complementary of Gate)
Source Drain
Gate
INPUT OUTPUT
Gate pMOS nMOS OUTPUT
0 OFF OFF Z
1 ON ON INPUT
Z : High-Impedance State,
consider the terminal is “floating”
16. Constraints of a digital design
• Logic designers job is to choose the right components and
connect them to solve the problem meeting:
– Size
– Cost
– Power
– Security
http://www.engadget.com/2014/08/23/elect
rical-potential-data-theft/
Power
consumption
0 1 1 1
Secret
information 0 1
17. Cost, Size, Performance
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Cost and Size are closely related
• Complexity of a digital circuit depends on:
• Number of components used
• Cost of each component
• Wires used to connect these components
As technology becomes
smaller, routing delays
dominate!
18. Moore’s law for Intel Microprocessors
Source: Evolution of Intel Microprocessors (from Jean Baer, Microprocessor
Architecture, Cambridge University Press)
In 1965, Gordon Moore noted that the number of transistors on a chip doubled
every 18 to 24 months.
He made a prediction that semiconductor technology will double its effectiveness
every 18 months
19. Some figures
• 1971: Intel 4004, 1.08 MHz, 2,300 transistors
• 2003: Intel Pentium 4, 3.4 GHz, 1.7 billion transistors
– Frequency increases roughly double per 2.5 years
– Number of transistors roughly double every two years (Moore’s
Law).
• How will the trend continue in the future?
20. Power Dissipation in Intel Processors
Source: Evolution of Intel Microprocessors (from Jean Baer,
Microprocessor Architecture, Cambridge University Press)
Dynamic
Power:
Depends on
how fast the
switches are
turned on and
off!
Static Power:
Device
leakage, which
has started
To dominate!
21. Logic Levels: Another Abstraction
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• The input and output signals are analog signals: continuous voltage
levels (say any real number from 0V to 5V)
• They are abstracted as logic ‘0’ and logic ‘1’:
• Below VL : logic ‘0’
• Above VL: logic ‘1’
• Inputs and Outputs generally have different thresholds to improve the
noise margin*.
• Robust: as variations in analog signals are removed due to the
thresholding!
*voltage difference between output of one gate and input of next. Noise
must exceed noise margin to make second gate produce wrong output.
22. 22
8 9 10 11
12 13 14 15
4 5 6 7
12 13 14 15
2 3 6 7
10 11 14 15
1 3 5 7
9 11 13 15
Think of a number between 1 and 15
23. 23
Binary Numbers
• Number 7 appears on the four cards in the pattern
‘No, Yes, Yes, Yes’
• The number 7 in binary code is 0111
• This is the Digital Language!
Yes = 1 No = 0
24. 24
Why binary?
• Information is stored in computer via voltage levels.
• Using decimal would require 10 distinct and reliable levels
for each digit.
• This is not feasible with reasonable reliability and financial
constraints.
• Everything in computer is stored using binary: numbers,
text, programs, pictures, sounds, videos, ...
25. 25
Bit, Byte, and Word
0
0 1 1 0 1 1 0 0
0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1
0 0 0 0 0 1 0 0
cont’d
A bit is a size that can store 1 digit of a binary number, 0 or 1.
A byte is 8 bits, which can store eight 0’s or 1’s.
A word is either 32 or 64 bits, depending on
computers. Regular PC’s are 32-bit word in size,
higher-end workstations are 64-bit. Word size is the
size of the registers.
What do these bits mean is a matter of interpretation! All information in a
computer are represented in a uniform format of bit patterns.
26. Types of Digital Circuits
• Combinational Circuits: Inputs directly influence the output.
• Example 1: NOT gate
26
Vin
Vcc
27. Example 2: 3 INPUT CMOS NAND GATE
PULL UP
NETWORK
PULL DOWN
NETWORK
A
B
C
Y=~(ABC)
Types of Digital Circuits
28. • Sequential Circuits: These circuits not only depend on current
input, but also to the past history of values on the same inputs.
• An Example: Memory Element
• When EN is high, then DOUT is assigned the value of DIN
• Otherwise, DOUT is held indefinitely.
• Applications:
– Storing and Recalling data
– Sequencing program instructions
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Types of Digital Circuits
DIN
EN
DOUT
30. Summary: Logic Design
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• Set of abstractions and methodologies that help us configure large
number of digital circuits to solve a given problem.
• Need to learn methodologies for developing a systematic design
flow to take a concept and transform into reality.
• We also need to learn optimization techniques, and meet
constraints better!
• Necessity is the mother of invention!
• Constraints give rise to innovations, and make the job worthy!
