Digital Design and Computer
Architecture
Lecture 1
Digital Design and Computer Architecture
Harris & Harris
Morgan Kaufmann / Elsevier, 2007
1
Logistics
• Handouts:
– Syllabus, Lecture Notes
• Lab 1 posted on the website:
– www.jlc.tcu.edu.tw
• Reading for next Monday (9/29:點名)
– 1.6-1.7, 1.9, 2.1-2.3
2
Overview
• More Logistics:
– Course Objectives
– Course Requirements
– Schedule
• Digital Design
– Managing Complexity
– Number Systems
– Logic Gates
3
Course Objectives
• To become a competent digital designer
• To learn to recognize and apply the principles of
abstraction, modularity, hierarchy, and regularity
in digital design
• To hone your debugging skills by designing,
building, and testing digital circuits
• To design, build, and test your own clock
• To understand what’s under the hood of a
computer
• To have fun while you’re doing it!
4
Course Requirements
• Class Participation
– If you need to miss class, email me beforehand
• Assignments:
– Weekly problem sets (10%), due Monday Morning
– Semester labs (電子鐘15% + 組合語言程式15%)
– Reading
• Exams
– Midterm (25%)
– Final (35%)
• Team policy for bi-weekly discussion
–
–
–
–
(75%個人成績+25%團體成績) for Midterm and Final
Number of team member 5~6,
Bonus for participation: +3;
leader +5
5
Syllabus
• Read the syllabus!
6
Digital Design
General engineering principles for complex
systems:
– Abstraction
– Discipline
– The three -Y’s
• Hierarchy
• Modularity
• Regularity
7
Abstraction
• Hiding details when
they aren’t important
Application
Software
programs
Operating
Systems
device drivers
Architecture
instructions
registers
Microarchitecture
datapaths
controllers
Logic
adders
memories
Digital
Circuits
AND gates
NOT gates
Analog
Circuits
amplifiers
filters
Devices
transistors
diodes
Physics
electrons
8
Discipline
• Intentionally restricting your design choices
(so that you can work more productively at
a higher level of abstraction)
9
The Three -Y’s
• Hierarchy
– Dividing a system into modules and
submodules
• Modularity
– Well-defined functions and interfaces
• Regularity
– Uniformity, so modules can be easily reused
10
Digital Abstraction
• 1’s and 0’s
• bits: binary digit
11
Number Systems
• Decimal numbers
1's column
10's column
100's column
1000's column
537410 = 5 × 103 + 3 × 102 + 7 × 101 + 4 × 100
five
thousands
three
hundreds
seven
tens
four
ones
• Binary numbers
1's column
2's column
4's column
8's column
11012 = 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20 = 1310
one
eight
one
four
no
two
one
one
12
Number Conversion
• Decimal to binary conversion:
– Convert 101012 to decimal
• Decimal to binary conversion:
– Convert 4710 to binary
13
Hexadecimal Numbers
Hex Digit
Decimal Equivalent Binary Equivalent
0
0
0000
1
1
0001
2
2
0010
3
3
0011
4
4
0100
5
5
0101
6
6
0110
7
7
0111
8
8
1000
9
9
1001
A
10
1010
B
11
1011
C
12
1100
D
13
1101
E
14
1110
F
15
1111
14
Number Conversion
• Hexadecimal to binary conversion:
– Convert 4AF16 (0x4AF) to binary
• Hexadecimal to decimal conversion:
– Convert 0x4AF to decimal
15
Bits, Bytes, Nibbles…
• Bits
10010110
most
significant
bit
• Bytes & Nibbles
least
significant
bit
byte
10010110
nibble
• Bytes
• (how they are put in memory?)
CEBF9AD7
most
significant
byte
least
significant
byte
16
Addition
• Decimal
• Binary
11
3734
+ 5168
8902
carries
11
1011
+ 0011
1110
carries
17
Binary Addition Examples
• Add the following
4-bit binary
numbers
1001
+ 0101
• Add the following
4-bit binary
numbers
1011
+ 0110
18
Signed Binary Numbers
• Sign and Magnitude:
– 1 sign bit, N-1 magnitude bits
– Example: -5 = 11012
+5 = 01012
• Two’s Complement( why? )
– Same as unsigned binary, but most
significant bit (msb) has value of -2N-1
– Most positive 4-bit number: 01112
– Most negative 4-bit number: 10002
19
“Taking the Two’s Complement”
• Reversing the sign of a two’s
complement number
• Method:
1. Invert the bits
2. Add 1
• Example: Reverse the sign of 0111
1. 1000
2. + 1
1001
20
Two’s Complement Examples
• Take the two’s complement of 0101.
• Take the two’s complement of 1010.
21
Two’s Complement Addition
• Add 6 + (-6) using two’s complement
numbers.
111
0110
+ 1010
10000
• Add -2 + 3 using two’s complement
numbers.
22
Logic Gates
BUF
NOT
A
Y
Y
Y=A
Y=A
A
0
1
A
Y
1
0
A
0
1
Y
0
1
23
Two-Input Logic Gates
OR
AND
A
B
Y
A
B
Y=A+B
Y = AB
A
0
0
1
1
B
0
1
0
1
Y
Y
0
0
0
1
A
0
0
1
1
B
0
1
0
1
Y
0
1
1
1
24
More Two-Input Logic Gates
XOR
A
B
NAND
A
B
Y
Y=A+B
A
0
0
1
1
B
0
1
0
1
NOR
Y
Y = AB
Y
0
1
1
0
A
0
0
1
1
B
0
1
0
1
A
B
XNOR
Y
Y=A+B
Y
1
1
1
0
A
0
0
1
1
B
0
1
0
1
A
B
Y
Y=A+B
Y
1
0
0
0
A
0
0
1
1
B
0
1
0
1
Y
25
Multiple-Input Logic Gates
AND4
NOR3
A
B
C
Y
Y = A+B+C
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
A
B
C
D
Y
Y = ABCD
Y
How about 4-input XOR?
26
Next Time
• Beneath the digital abstraction
• Transistors
• Boolean algebra
27