Fundamentals of Computer Systems, Lecture notes of Algorithms and Programming

Download Fundamentals of Computer Systems and more Lecture notes Algorithms and Programming in PDF only on Docsity! Fundamentals of Computer Systems Thinking Digitally Martha A. Kim Columbia University Fall 2013 1 / 1 The Subject s of this Class 0 1 2 / 1 Engineering Works Because of Abstraction Application Software COMS 3157, 4156, et al. Operating Systems COMS W4118 Architecture Second Half of 3827 Micro-Architecture Second Half of 3827 Logic First Half of 3827 Digital Circuits First Half of 3827 Analog Circuits ELEN 3331 Devices ELEN 3106 Physics ELEN 3106 et al. 3 / 1 Simple information processing system Discrete Information Processing System System State Discrete Inputs Discrete Outputs First half of the course 4 / 1 Simple information processing system Discrete Information Processing System System State Discrete Inputs Discrete Outputs First quarter of the course 4 / 1 Rules and Regulations You may collaborate with classmates on homework. Each assignment turned in must be unique; work must ultimately be your own. List your collaborators on your homework. Do not cheat. Tests will be closed-book with a one-page “cheat sheet” of your own devising. 7 / 1 The Text(s): Alternative #1 No required text. There are two recommended alternatives. É David Harris and Sarah Harris. Digital Design and Computer Architecture. Almost precisely right for the scope of this class: digital logic and computer architecture. 8 / 1 The Text(s): Alternative #2 É M. Morris Mano and Charles Kime. Logic and Computer Design Fundamentals, 4th ed. É Computer Organization and Design, The Hardware/Software Interface, 4th ed. David A. Patterson and John L. Hennessy 9 / 1 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 12 / 1 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? 13 / 1 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 14 / 1 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? 17 / 1 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”) 18 / 1 Decimal Addition Algorithm 1 1 434 +628 1062 4+ 8 = 12 1+ 3+ 2 = 6 4+ 6 = 10 + 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 19 / 1 Decimal Addition Algorithm 1 1 434 +628 1 062 4+ 8 = 12 1+ 3+ 2 = 6 4+ 6 = 10 + 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 19 / 1 Decimal Addition Algorithm 1 1 434 +628 1062 4+ 8 = 12 1+ 3+ 2 = 6 4+ 6 = 10 + 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 19 / 1 Binary Addition Algorithm 10011 10011 +11001 101100 1+ 1 = 10 1+ 1+ 0 = 10 1+ 0+ 0 = 01 0+ 0+ 1 = 01 0+ 1+ 1 = 10 + 0 1 0 00 01 1 01 10 10 10 11 20 / 1 Binary Addition Algorithm 10 011 10011 +11001 101 100 1+ 1 = 10 1+ 1+ 0 = 10 1+ 0+ 0 = 01 0+ 0+ 1 = 01 0+ 1+ 1 = 10 + 0 1 0 00 01 1 01 10 10 10 11 20 / 1 Binary Addition Algorithm 1 0011 10011 +11001 10 1100 1+ 1 = 10 1+ 1+ 0 = 10 1+ 0+ 0 = 01 0+ 0+ 1 = 01 0+ 1+ 1 = 10 + 0 1 0 00 01 1 01 10 10 10 11 20 / 1 Binary Addition Algorithm 10011 10011 +11001 101100 1+ 1 = 10 1+ 1+ 0 = 10 1+ 0+ 0 = 01 0+ 0+ 1 = 01 0+ 1+ 1 = 10 + 0 1 0 00 01 1 01 10 10 10 11 20 / 1 One’s Complement Numbers Like Signed Magnitude, a leading 1 indicates a negative One’s Complement number. To negate a number, complement (flip) each bit. 00002 = 0 00102 = 2 11012 = −2 10002 = −7 11112 = −0? Addition is nicer: just add the one’s complement numbers as if they were normal binary. Really annoying having a −0: two numbers are equal if their bits are the same or if one is 0 and the other is −0. 23 / 1 24 / 1 Two’s Complement Numbers Really neat trick: make the most significant bit represent a negative number instead of positive: 11012 = −8+ 4+ 1 = −3 11112 = −8+ 4+ 2+ 1 = −1 01112 = 4+ 2+ 1 = 7 10002 = −8 Easy addition: just add in binary and discard any carry. Negation: complement each bit (as in one’s complement) then add 1. Very good property: no −0 Two’s complement numbers are equal if all their bits are the same. 25 / 1