Fundamentals of Computer Systems
Thinking Digitally
Martha A. Kim
Columbia University
Fall 2015
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Fundamentals of Computer Systems: Lecture Notes on Computer Systems, Digital Circuits, and, Lecture notes of Computer Architecture and Organization
A course syllabus for Fundamentals of Computer Systems at Columbia University in Fall 2015. The course covers topics such as computer systems, digital circuits, logic, and architecture. The syllabus includes administrative information, office hours, and recommended texts. The document also includes examples of binary and hexadecimal numbers, as well as algorithms for addition in decimal and binary. The typology of the document is 'lecture notes'.
Typology: Lecture notes
2014/2015
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Fundamentals of Computer Systems
Thinking Digitally
Martha A. Kim
Columbia University
Fall 2015
Computer Systems Work Because of Abstraction
Application Software
Operating Systems
Architecture
Micro-Architecture
Logic
Digital Circuits
Analog Circuits
Devices
Physics
Simple information processing system
Discrete Information Processing System
System State
Discrete Inputs
Discrete Outputs
First half of the course
Simple information processing system
Discrete Information Processing System
System State
Discrete Inputs
Discrete Outputs
First quarter of the course
Office Hours
The six (and counting) TAs and I will all offer office hours.
Always consult the course calendar (linked from course webpage) for the latest schedule.
https://www.google.com/calendar/embed?src=8g48vdedcbb85k7jn4or
Assignments and Grading
Weight What When 40% Six homeworks See Webpage 30% Midterm exam #1 October TBA 30% Midterm exam #2 December TBA
Homework is due at the beginning of lecture. We will drop the lowest of your six homework scores; you can one assignment with no penalty. There will be no extensions.
The Text(s): Alternative
No required text. There are two recommended alternatives. … (^) David Harris and Sarah Harris. Digital Design and Computer Architecture.
Almost precisely right for the scope of this class: digital logic and computer architecture.
The Text(s): Alternative
… (^) M. Morris Mano and Charles Kime. Logic and Computer Design Fundamentals, 4th ed.
… (^) Computer Organization and Design, The Hardware/Software Interface, 4th ed. David A. Patterson and John L. Hennessy
The Decimal Positional Numbering System
Ten figures: 0 1 2 3 4 5 6 7 8 9
7 × 102 + 3 × 101 + 0 × 100 = (^73010)
9 × 102 + 9 × 101 + 0 × 100 = (^99010)
Why base ten?
Which Numbering System Should We Use?
Some Older Choices:
Roman: I II III IV V VI VII VIII IX X
Mayan: base 20, Shell = 0
Babylonian: base 60
Binary and Octal
DEC PDP-8/I, c. 1968
Oct^ Bin 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111
PC = 0 × 211 + 1 × 210 + 0 × 29 + 1 × 28 + 1 × 27 + 0 × 26 +
1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20
= 2 × 83 + 6 × 82 + 7 × 81 + 5 × 80
Hexadecimal Numbers
Base 16: 0 1 2 3 4 5 6 7 8 9 A B C D E F Instead of groups of 3 bits (octal), Hex uses groups of 4.
CAFEF00D 16 = 12 × 167 + 10 × 166 + 15 × 165 + 14 × 164 +
15 × 163 + 0 × 162 + 0 × 161 + 13 × 160
C A F E F 0 0 D Hex 11001010111111101111000000001101 Binary 3 1 2 7 7 5 7 0 0 1 5 Octal
Jargon
Bit Binary digit: 0 or 1
Byte Eight bits
Word Natural number of bits for the pro- cessor, e.g., 16, 32, 64
LSB Least Significant Bit (“rightmost”)
MSB Most Significant Bit (“leftmost”)
Decimal Addition Algorithm
- 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18 10 10 11 12 13 14 15 16 17 18 19