Basic Engineering Boolean Algebra and Logic Gates F Hamer‚ M Lavelle & D McMullan The aim of this document is to provide a short‚ self assessment programme for students who wish to understand the basic techniques of logic gates. c 2005 Email: chamer‚ mlavelle‚ dmcmullan@plymouth.ac.uk Last Revision Date: August 31‚ 2006 Version 1.0 Table of Contents 1. 2. 3. 4. 5. Logic Gates (Introduction) Truth Tables Basic Rules of Boolean Algebra Boolean Algebra Final Quiz Solutions to Exercises Solutions
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HISTORY OF ALGEBRA M AT H 1 WHAT IS ALGEBRA? • Denotes various kinds of mathematical ideas and techniques • more or less directly associated with formal manipulation of abstract symbols and/or with finding the solutions of an equation. HISTORICAL OBJECTIVES 1. attempts to deal with problems devoted to finding the values of one or more unknown quantities. 2. the evolution of the notion of number 3. the gradual refinement of a symbolic language THE SEARCH OF “EQUATION” • Egyptian Mathematics
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CMU Spring’14 18-760 VLSI CAD [100 pts] Homework 1 Out Wed‚ Jan 22; Due Mon‚ Feb 3 (by noon in HH1112) 1. Properties of Boolean Difference [15 pts] (i) Use Boolean algebra and the basic properties of Shannon cofactors from the notes to show that this identity is true. Again‚ f and g are functions of x1‚x2‚...xn‚ and x refers to some arbitrary variable in x1‚x2‚...xn. ∂ ( f + g) ∂g ∂f # ∂f ∂g & = f • ⊕ g• ⊕% • ( ∂x ∂x ∂x $ ∂x ∂x ’ Hints: (a) Notice that there are no “x” variables
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Inequality Equation: 12x + 15y ≤ 3000 (1). 12x+ 15(0) 15y ≤ 3000 (2). 12(0) + 15y≤ 3000 12x ≤ 3000 15y≤ 3000 12x / 12 ≤ 3000/12 15y / 15 ≤ 3000/15 12x ≤ 250 15y≤200 The problem 46 on page 240 in the text book‚ Elementary and Intermediate Algebra asks that I evaluate an inequality equation that can satisfy the Ozark Company needs. (Dugopolski‚ M. 2012 )The paragraphs ask for an inequality that can allow the company to use 3000 board feet of maple lumber. Of the 3000 board feet of lumber‚ the
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KENYA METHODIST UNIVERSITY END OF 3RD TRIMESTER 2012 (EVENING) EXAMINATIONS FACULTY:SCIENCE AND TECHNOLOGY DEPARTMENT:PURE AND APPLIED SCIENCES UNIT CODE: MATH 110 UNIT TITLE:LINEAR ALGEBRA 1 TIME:2 hours Instructions: Answer question one and any other two questions. Question One (30 marks) Find the determinant of the following matrices. -4 8 (2 marks) 0 1 1 -3 -2 (3 marks) 2 -4 -3 -3 6 +8 Find the values of x and y if:(5 marks) x + 2y 14 = 4
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Illinois Rules of Professional Conduct Rule 1.1 – Competence Provide competent representation Legal knowledge‚ skill‚ thoroughness reasonably necessary Comments Determining whether requisite knowledge and skill exists: relative complexity/specialized nature of matter‚ lawyer’s own training and experience‚ preparation and study time‚ available help Do not need special training or prior experience to handle a new problem – just study up Emergency matters – you can help to the extent reasonably
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Name/Student Number: Algebra 2 Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the trigonometric expression. 1. a. b. c. d. Answer B In ‚ is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. 2. a = 3‚ c = 19 a. = 9.1°‚ = 80.9°‚ b = 18.8 c. = 14.5°‚ = 75.5°‚ b = 18.8 b. = 80.9°‚ = 9.1°‚ b = 18.8 d. = 75.5°
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Algebra Review 1. Evaluate the expression 1 2 17 B) − 2 1 C) 2 17 D) 2 3a + 2b when a = -3 and b = -4. 2 A) − 2. Simplify: A) B) C) D) 17 29 16 30 3+5• 6 −4 3. Simplify: A) 40 B) 18 C) 34 D) 12 Evaluate: 1 7 − 1 5 − 1 5 1 7 6 − 2 • 2 + 25 4. 3x − y if x = 2‚ y = 8‚ and z = –2. 6z − x A) B) C) D) CPT Review 4/17/01 1 5. Simplify: A) B) C) D) –2 2 11 2 11 − 2 14 − 30 2(− 4 ) 6. Use the distributive property to simplify. A) B) C) D) − 4x + 30 −
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4/14/2014 Advanced Algebra [print page] Option 1: Completed Independently You are an investment broker who has been asked to create a diverse investment portfolio for a new client. Before investing your client’s $5‚000 in a variety of stocks‚ bonds‚ and cash equivalents that will make up the portfolio‚ you must first get to know your client. Part I: Client Profile Create a fictional client for whom you will create an investment portfolio. You must provide the client’s name age occupation
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Computer Linear Algebra-Individual Assignment Topic: Image Sharpening and softening (blurring and deblurring). Nowadays‚ technology has become very important in the society and so does image processing. People may not realize that they use this application everyday in the real life to makes life easier in many areas‚ such as business‚ medical‚ science‚ law enforcement. Image processing is an application where signal information of an image is analyzed and manipulated to transform it to a different
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