Introduction to Computer Engineering – EECS 203

Introduction to Computer Engineering – EECS 203http://ziyang.eecs.northwestern.edu/ ∼ dickrp/eecs203/Instructor: Robert DickOffice: L477 TechEmail: dickrp@northwestern.eduPhone: 847–467–2298TA: Neal OzaOffice: Tech. Inst. L375Phone: 847-467-0033Email: nealoza@u.northwestern.eduTT: David BildOffice: Tech. Inst. L470Phone: 847-491-2083Email: d-bild@northwestern.edu

OutlineNumber SystemsHomework1. Number Systems2. Homework2 R. Dick Introduction to Computer Engineering – EECS 203

Number SystemsHomeworkIntroduction to number systemsConsider a base-10 number: 1,2931, 293 = 1 · 10 3 + 2 · 10 2 + 9 · 10 1 + 3 · 10 0For base-10, given an n-digit number in which d i is the ith digit, thenumber isn∑10 i−1 · d ii=03 R. Dick Introduction to Computer Engineering – EECS 203

Number SystemsHomeworkIntroduction to number systemsThis works for any base. Convert 2, 012 3 from base-3 to base-10.2 · 3 3 + 0 · 3 2 + 1 · 3 1 + 2 · 3 02 · 27 + 0 · 9 + 1 · 3 + 2 · 154 + 0 + 3 + 259 104 R. Dick Introduction to Computer Engineering – EECS 203

Number SystemsHomeworkIntroduction to number systemsConvert 59 10 from base-10 to base-3. Repeatedly divide by thegreatest power of b (the base) that is less than the number.Remainder Try dividing Digit Comment59 3 4 = 81 0 Too big59 − 0 · 81 = 59 3 3 = 27 2 O.K.59 − 2 · 27 = 5 3 2 = 9 0 Too big5 − 0 · 9 = 5 3 1 = 3 1 O.K.5 − 1 · 3 = 2 3 0 2 O.K.02012 3 = 2012 35 R. Dick Introduction to Computer Engineering – EECS 203

Number SystemsHomeworkConversion works for any baseReview: For base-10, given an n-digit number in which d i is the ithdigit, the number isn∑10 i−1 · d ii=1For base-b, given an n-digit number in which d i is the ith digit, thenumber isn∑·b i−1 · d ii=16 R. Dick Introduction to Computer Engineering – EECS 203

Useful basesNumber SystemsHomework2: Also called binary. Most fundamental base in digital logic.Know this like the back of your hand.8: Also called octal. Sometimes used by programmers. Preferbase 16.10: Also called decimal or Arabic.16: Also called hexadecimal or simple hex. One of the mostcompact and beautiful representations for digital computerprogrammers.7 R. Dick Introduction to Computer Engineering – EECS 203

BinaryNumber SystemsHomework1 2 4 8 16 32 64 128 256 512 1,024 (1K)2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10k ≠ K1 k = 10 3 = 1,0001 K = 2 10 = 1,0248 R. Dick Introduction to Computer Engineering – EECS 203

DecimalNumber SystemsHomeworkMost commonly used by human beings.Also called Arabic.Actually developed in India and brought to Europe via Arabianempire.Largely replaced Roman numerals, which were more cumbersomewhen writing the large and complicated numbers used inastronomy and wide-spread trade.9 R. Dick Introduction to Computer Engineering – EECS 203

Number systemsNumber SystemsHomeworkRepresentation of positive numbers same in most systemsA few special-purpose alternatives exist, e.g., Gray codeAlternatives exist for signed numbers10 R. Dick Introduction to Computer Engineering – EECS 203

Base-16: HexNumber SystemsHomework0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150 1 2 3 4 5 6 7 8 9 A B C D E FOften prefixed with 0x.What is 0xFF?11 R. Dick Introduction to Computer Engineering – EECS 203

OutlineNumber SystemsHomework1. Number Systems2. Homework12 R. Dick Introduction to Computer Engineering – EECS 203

Number SystemsHomeworkReading assignmentM. Morris Mano and Charles R. Kime. Logic and ComputerDesign Fundamentals. Prentice-Hall, NJ, third edition, 2004Sections 5.1–5.613 R. Dick Introduction to Computer Engineering – EECS 203

Number SystemsHomeworkComputer geek culture referenceSpelling things in ASCII (hex or binary)This is one of the lower forms of geek culture, akin to bad punsHowever, at least one university has things written into itsbuildings with subtle brick patterns in ASCII binary4a6934207375616e34206a69312073686534206a69342068656e332068616f332077616e322114 R. Dick Introduction to Computer Engineering – EECS 203