Fundamentals of Computer Systems, Summaries of Computer Architecture and Organization

Download Fundamentals of Computer Systems and more Summaries Computer Architecture and Organization in PDF only on Docsity! Fundamentals of Computer Systems Thinking Digitally Stephen A. Edwards Columbia University Summer 2020 The Subject of this Class 0 Meee in Engineering Works Because of Abstraction Application Software Operating Systems Architecture Micro-Architecture Logic Digital Circuits Analog Circuits Devices Physics 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. Rules and Regulations Each assignment turned in must be unique; work must ultimately be your own. Don’t cheat: Columbia Students Aren’t Cheaters Test will be closed-book; you may use a single sheet of your own notes Optional Texts: Alternative 1 No required text. One option: � David Harris and Sarah Harris. Digital Design and Computer Architecture. Either 1st or 2nd ed. Almost precisely right for the scope of this class: digital logic and computer architecture. Optional Texts: Alternative 2 � M. Morris Mano and Charles Kime. Logic and Computer Design Fundamentals. 4th ed. � David A. Patterson and John L. Hennessy. Computer Organization and Design, The Hardware/Software Interface. 4th ed. The Decimal Positional Numbering System Ten figures: 0 1 2 3 4 5 6 7 8 9 73010 = 7×102+3×101+0×100 99010 = 9×102+9×101+0×100 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 Binary and Octal: Electronics Likes Powers of Two D EC PD P- 8/ I, c. 19 68 Oct Bin 0 0 1 1 2 10 3 11 4 100 5 101 6 110 7 111 PC = 0101101111012 = 0×211+1×210+0×29+1×28+1×27+0×26+ 1×25+1×24+1×23+1×22+0×21+1×20 = 26758 = 2×83+6×82+7×81+5×80 = 146910 Jargon Bit Binary digit: 0 or 1 Byte Eight bits Word Natural number of bits for the processor, e.g., 16, 32, 64 LSB Least Significant Bit (“rightmost”) MSB Most Significant Bit (“leftmost”) Decimal Addition Algorithm 434 +628 4+8 = 12 + 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 1 434 +628 2 4+8 = 12 1+3+2 = 6 + 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 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 Binary Addition Algorithm 10011 +11001 1+1 = 10 + 0 1 0 00 01 1 01 10 10 10 11 Binary Addition Algorithm 1 10011 +11001 0 1+1 = 10 1+1+0 = 10 + 0 1 0 00 01 1 01 10 10 10 11 Binary Addition Algorithm 0011 10011 +11001 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 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 Signed Numbers: Dealing with Negativity How should we represent negative numbers? aren 4 EQUAL Ee ou Fan t ZERO CALORIES. MAXIMUM PEPSI'TASTE. 4 Two’s Complement Numbers Really neat trick: just make only the most significant bit represent a negative number instead of positive; treat the rest as binary. 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. Subtraction done with negation and addition. Very good property: no −0 Two’s complement numbers are equal if and only if all their bits are the same. Number Representations Compared Code Binary Signed One’s Two’s Mag. Comp. Comp. 0000 0 0 0 0 0001 1 1 1 1 ... 0111 7 7 7 7 1000 8 −0 −7 −8 1001 9 −1 −6 −7 ... 1110 14 −6 −1 −2 1111 15 −7 −0 −1 Smallest number Largest number F F a u c Interesting The ancient Egyptians used binary fractions: The Eye of Horus Binary-Coded Decimal thinkgeek.com Humans prefer reading decimal numbers; computers prefer binary. BCD is a compromise: every four bits represents a decimal digit. Dec BCD 0 0000 0000 1 0000 0001 2 0000 0010 ... ... 8 0000 1000 9 0000 1001 10 0001 0000 11 0001 0001 ... ... 18 0001 1000 19 0001 1001 20 0010 0000 ... ... BCD Addition Binary addition followed by a possible correction. Any four-bit group greater than 9 must have 6 added to it. Example: 158 +242 000101011000 +001001000010 1010 First group BCD Addition Binary addition followed by a possible correction. Any four-bit group greater than 9 must have 6 added to it. Example: 1 158 +242 0 1 000101011000 +001001000010 1010 First group + 0110 Correction 10100000 Second group + 0110 Correction BCD Addition Binary addition followed by a possible correction. Any four-bit group greater than 9 must have 6 added to it. Example: 11 158 +242 00 1 1 000101011000 +001001000010 1010 First group + 0110 Correction 10100000 Second group + 0110 Correction 01000000 Third group BCD Addition Binary addition followed by a possible correction. Any four-bit group greater than 9 must have 6 added to it. Example: 11 158 +242 400 1 1 000101011000 +001001000010 1010 First group + 0110 Correction 10100000 Second group + 0110 Correction 01000000 Third group (No correction) 010000000000 Result