Arithmetic logic unit potx

Algorithms Department of Computer Science University of Illinois at Urbana-Champaign Instructor: Jeff Erickson Teaching Assistants: • Spring 1999: Mitch Harris and Shripad Thite • Summer 1999 (IMCS): Mitch Harris • Summer 2000 (IMCS): Mitch Harris • Fall 2000: Chris Neihengen, Ekta Manaktala, and Nick Hurlburt • Spring 2001: Brian Ensink, Chris Neihengen, and Nick Hurlburt • Summer 2001 (I2CS): Asha Seetharam and Dan Bullok • Fall 2002: Erin Wolf, Gio Kao, Kevin Small, Michael Bond, Rishi Talreja, Rob McCann, and Yasutaka Furakawa • Spring 2004: Dan Cranston, Johnathon Fischer, Kevin Milans, and Lan Chen • Fall 2005: Erin Chambers, Igor Gammer, and Aditya Ramani • Fall 2006: Dan Cranston, Nitish Korula, and Kevin Milans • Spring 2007: Kevin Milans • Fall 2008: Reza Zamani-Nasab • Spring 2009: Alina Ene, Ben Moseley, and Amir Nayyeri • Spring 2010: David Morrison, Kyle Fox, and Rachit Agarwal • Fall 2010: Alina Ene c Copyright 1999–2011 Jeff Erickson. Last update July 8, 2011. 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[...]... in 1971 The O(n log n) running time requires the standard assumption that O(log n)-bit integer arithmetic can be performed in constant time; the number of bit operations is O(n log n log log n) 8 A multiplicative group (G, ⊗) is a set G and a function ⊗ : G × G → G, satisfying three axioms: 1 There is a unit element 1 ∈ G such that 1 ⊗ g = g ⊗ 1 for any element g ∈ G 2 Any element g ∈ G has a inverse... categories imposed by their languages According to an extreme formulation of this principle, some concepts in one language simply cannot be understood by speakers of other languages, not just because of technological advancement—How would you translate ‘jump the shark’ or ‘blog’ into Aramaic?—but because of inherent structural differences between languages and cultures For a more skeptical view, see Steven... same techniques to analyze those resources as we use to analyze running time 0.5 A Longer Example: Stable Matching Every year, thousands of new doctors must obtain internships at hospitals around the United States During the first half of the 20th century, competition among hospitals for the best doctors led to earlier and earlier offers of internships, sometimes as early as the second year of medical... hospitals would regularly call doctors, offer them internships, and demand immediate responses Interns were forced to gamble if their third-choice hospital called first—accept and risk losing a better opportunity later, or reject and risk having no position at all.11 Finally, a central clearinghouse for internship assignments, now called the National Resident Matching Program, was established in the early... product of experience, not its replacement We can’t teach you how to do well in this class All we can do (and what we will do) is lay out some fundamental tools, show you how to use them, create opportunities for you to practice with them, and give you honest feedback, based on our own hard-won experience and intuition The rest is up to you Good algorithms are extremely useful, elegant, surprising,... anker, firkin, half-barrel, barrel, hogshead, pipe, well, river, and ocean (Every container in this list is twice as big as its predecessor, except that a firkin is actually 2.25 ankers, and the last three units are just silly.) BARLEYMOW(n): “Here’s a health to the barley-mow, my brave boys,” “Here’s a health to the barley-mow!” “We’ll drink it out of the jolly brown bowl,” “Here’s a health to the barley-mow!”... each one-digit addition Similarly, multiplying an n-digit number by a one-digit number takes O(n) time, using essentially the same algorithm What about multiplying two n-digit numbers? At least in the United States, every grade school student (supposedly) learns to multiply by breaking the problem into n one-digit multiplications and n additions: 31415962 × 27182818 251327696 31415962 251327696 62831924... exclusively on algorithms that can be reasonably implemented on a computer In other words, each step in the algorithm must be something that either is directly supported by common programming languages (such as arithmetic, assignments, loops, or recursion) or is something that you’ve already learned how to do in an earlier class (like sorting, binary search, or depth first search) 0.3 Writing down algorithms Computer . naive set theory, Boolean algebra, first-order predicate logic, sets, functions, relations, modular arithmetic, recursive definitions, trees (as abstract objects, not. licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 United States License. For license details, see http://creativecommons.org/licenses/by-nc-sa/3.0/us/. For