Columbia University: Fundamentals of Computer Systems - Lecture Notes, Lecture notes of Algorithms and Programming

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Fundamentals of Computer Systems

Thinking Digitally

Stephen A. Edwards and Martha Kim

Columbia University

Spring 2012

The Subject of this Class

But let your communication be, Yea, yea; Nay, nay: for whatsoever is more than these cometh of evil.

— Matthew 5:

Engineering Works Because of Abstraction

Application Software

Operating Systems

Architecture

Micro-Architecture

Logic

Digital Circuits

Analog Circuits

Devices

Physics

Boring Stuff

Mailing list: csee3827-staff@lists.cs.columbia.edu http://www.cs.columbia.edu/~sedwards/classes/2012/3827-spring/

Prof. Stephen A. Edwards First Half of Semester sedwards@cs.columbia.edu 462 Computer Science Building

Prof. Martha Kim Second Half of Semester martha@cs.columbia.edu 469 Computer Science Building

Lectures 1:10–2:25 PM, Mon, Wed, 614 Schermerhorn Jan 18–Apr 30 Holidays: Mar 12–16 (Spring Break)

Assignments and Grading

Weight What When 40% Six homeworks See Webpage 30% Midterm exam March 7th 30% Final exam During Finals Week (May 4–11)

Homework is due at the beginning of lecture. We will drop the lowest of your six homework scores;

you can

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skip omit forget ignore blow off screw up feed to dog flake out on sleep through

            

one with no penalty.

The Text

David Harris and Sarah Harris.

Digital Design and Computer Architecture.

Morgan-Kaufmann, 2007.

Almost precisely right for the scope of this class: digital logic and computer architecture

thinkgeek.com

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?

Hexadecimal, Decimal, Octal, and Binary

Hex Dec Oct Bin 0 0 0 0 1 1 1 1 2 2 2 10 3 3 3 11 4 4 4 100 5 5 5 101 6 6 6 110 7 7 7 111 8 8 10 1000 9 9 11 1001 A 10 12 1010 B 11 13 1011 C 12 14 1100 D 13 15 1101 E 14 16 1110 F 15 17 1111

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

Computers Rarely Manipulate True Numbers

Infinite memory still very expensive

Finite-precision numbers typical

32-bit processor: naturally manipulates 32-bit numbers

64-bit processor: naturally manipulates 64-bit numbers

How many different numbers can you

represent with 5

binary octal decimal hexadecimal

digits?

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

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