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Jan. 2011
Computer Architecture, Background and Motivation
Slide 1
Part I
Background and Motivation
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Computer Architecture, Background and Motivation
Slide 2
About This Presentation
This presentation is intended to support the use of the textbook
Computer Architecture: From Microprocessors to Supercomputers
,
Oxford University Press, 2005, ISBN 019515455X. It is updated
regularly by the author as part of his teaching of the upperdivision
course ECE 154, Introduction to Computer Architecture, at the
University of California, Santa Barbara. Instructors can use these
slides freely in classroom teaching and for other educational
purposes. Any other use is strictly prohibited. © Behrooz Parhami
Edition
Released
Revised
Revised
Revised
Revised
First
June 2003
July 2004
June 2005
Mar. 2006
Jan. 2007
Jan. 2008
Jan. 2009
Jan. 2011
Second
Jan. 2011
Computer Architecture, Background and Motivation
Slide 3
I
Background and Motivation
Topics in This Part
Chapter 1
Combinational Digital Circuits
Chapter 2
Digital Circuits with Memory
Chapter 3
Computer System Technology
Chapter 4
Computer Performance
Provide motivation, paint the big picture, introduce tools:
• Review components used in building digital circuits
• Present an overview of computer technology
• Understand the meaning of computer performance
(
or why a 2 GHz processor isn’t 2
×
as fast as a 1 GHz model)
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Computer Architecture, Background and Motivation
Slide 4
1
Combinational Digital Circuits
First of two chapters containing a review of digital design:
• Combinational, or memoryless, circuits in Chapter 1
• Sequential circuits, with memory, in Chapter 2
Topics in This Chapter
1.1
Signals, Logic Operators, and Gates
1.2
Boolean Functions and Expressions
1.3
Designing Gate Networks
1.4
Useful Combinational Parts
1.5
Programmable Combinational Parts
1.6
Timing and Circuit Considerations
Jan. 2011
Computer Architecture, Background and Motivation
Slide 5
1.1
Signals, Logic Operators, and Gates
Figure 1.1
Some basic elements of digital logic circuits, with
operator signs used in this book highlighted.
x
≡
y
/
AND
Name
XOR
OR
NOT
Graphical
symbol
x
∧
y
Operator
sign and
alternate(s)
x
⊕
x
∨
y
xy
x
+
x
′
¬
x
or
x
_
x
×
y
xy
Arithmetic
expression
x
+
y
−
2
xy
x
+
y
−
1
−
Output
is 1 iff:
Input is 0
Both inputs
are 1s
At least one
input is 1
Inputs are
not equal
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Computer Architecture, Background and Motivation
Slide 6
The Arithmetic Substitution Method
z
′
= 1 –
z
NOT converted to arithmetic form
xy
AND same as multiplication
(when doing the algebra, set
z
k
=
z
)
x
∨
y
=
x
+
y
−
xy
OR converted to arithmetic form
x
⊕
y
=
x
+
y
−
2
xy
XOR converted to arithmetic form
Example: Prove the identity
xyz
∨
x
′∨
y
z
′≡
?
1
LHS = [
xyz
∨
x
′
]
∨
[
y
z
′
]
= [
xyz
+ 1 –
x
–(1–
x
)
xyz
]
∨
[1 –
y
+ 1 –
z
y
)(1 –
z
)]
= [
xyz
+ 1 –
x
]
∨
[1 –
yz
]
= (
xyz
+ 1 –
x
) + (1 –
yz
) – (
xyz
+ 1 –
x
)(1 –
yz
)
= 1 +
xy
2
z
2
–
xyz
= 1 = RHS
This is addition,
not logical OR
Jan. 2011
Computer Architecture, Background and Motivation
Slide 7
Variations in Gate Symbols
Figure 1.2
Gates with more than two inputs and/or with
inverted signals at input or output.
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This note was uploaded on 02/22/2011 for the course ECE 154 taught by Professor Staff during the Spring '08 term at UCSB.
 Spring '08
 Staff
 Computer Architecture, Microprocessor

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