EE 2301: Introduction to Digital System Design

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EE 2301 Introduction to Digital System Design
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EE2301 Course Information

• Instructor Prof. Marc Riedel office EE/CSi
  4-167 tel [phone] email mriedel_at_umn.edu
• Syllabus, etc. http//www.cctbio.ece.umn
  .edu/wiki/index.php/EE2301

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All (or mostly) About Bits
0
1
zero
one
false
true
off
on
open
closed
not asserted
asserted
not set
set


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Boxes inside Boxes inside boxes
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Integrated Circuits
Ubiquitous basis for computers (as well as for
every electronic device and appliance.)
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Boxes inside Boxes inside boxes
2000 transistors(Intel 4004, 1971)
800 million transistors(Intel Penryn, 2007)
1 transistor (1960s)
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From Chips to Computers
IBMs Blue Gene 64,000 Processors
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The Computational Landscape
There are known knowns and there are unknown
unknowns but today Ill speak of the known
unknowns. Donald
Rumsfeld, 2002
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(No Transcript)
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One made-up fact
well, an abstraction really
A Logic Gate
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Logic Gates
AND gate
Common Gate
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0
1
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Logic Gates
OR gate
Common Gate
0
0
0
0
1
1
1
0
1
1
1
1
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Logic Gates
NAND gate
Common Gate
0
0
1
0
1
1
1
0
1
1
1
0
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Logic Gates
NOR gate
Common Gate
0
0
1
0
1
0
1
0
0
1
1
0
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Logic Gates
XOR gate
Common Gate
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0
0
1
1
1
0
1
1
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0
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Digital Circuit
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Digital Circuit
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Digital Circuit
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Integrated Circuits
inputs
outputs
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1

• What do Integrated Circuits do?
• accept zeros and ones as inputs
• produce zeros and ones as outputs.

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Integrated Circuits
inputs
outputs
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1
0
1
1
0
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0
1

• Why do we want this?
• zeros and ones represent information
• circuit performs computation.

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Integrated Circuits
inputs
outputs
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1
0
1
1
0
0
0
1

• How do we build (design) such circuits?
• hierarchically, from components.

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Data Structures
Truth Tables
Example
x1
x2
x3
f
0
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0
0
0
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1
0
0
1
0
0
f
0
1
1
1
1
0
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Data Structures
Truth Tables
Example
4 rows
2 variables
8 rows
3 variables
264 rows
64 variables
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Analysis of Digital Circuits
Large domain, small range.
inputs
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Analysis of Digital Circuits
Large domain, small range.
inputs
2m possibilities
2 possibilities
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Synthesis
Analysis
There are known knowns and there are unknown
unknowns but today Ill speak of the known
unknowns. Donald
Rumsfeld, 2004
BooleanInputs
BooleanOutputs
Independent
Unknown
Specified
Unknown
Known
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Example 7 Segment Display
Inputs
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Example 7 Segment Display
Output
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Substitution/Minimization
Basic minimization/restructuring operation
express a function in terms of other functions.
(cost 9)
Substitute b into a
(cost 8)
Substitute c into a
(cost 5)
Substitute c, d into a
(cost 4)