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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PROPORTION METHOD The proportion method is used in both of these expressions. A proportion is an equation that says that two ratios are equivalent. The use of cross multiplying is in use in both expressions as well. I believe the first expression (#56) uses the extreme-means property; the product of the means is equal to the product of the extremes. #56. To estimate the size of the bear population on the Keweenaw Peninsula‚ conservationists captured‚ tagged‚ and released 50 bears
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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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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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KEY HONORS ALGEBRA 2 B 1. a. d. 2. a. d. a1 3‚ Semester Exam Review b. b. an 4 an1 an 3 4n 1 an 1 3 n 1 3n 2 c. 805‚306‚368 1‚073‚741‚823 a1 1 an an 1 3 c. 178 5370 3. 4624.577 cm3 4. 2805 seats 5. a. 6. a. 3 7. a. 81 b. 8. a. a 4b9 b. 1 3 17 3 7 b. 4 or 3 7 b. 4 1 9 x4 5 c. 24 5 c. x 2 or
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(Salman‚ Mohammed‚ Ogunlade & Ayinla; 2012). These internal and external examinations focus on component of mathematics like i. Number and numeration ii. Algebra iii. Geometry and mensuration iv. Statistics This means that a student ’s overall performance is dependent on a proper understanding of each of the components above. Since algebra is an important component of mathematics that is examined at all levels in our Secondary School System‚ it is pertinent to examine the difficulties student
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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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Elementary Education: Shaping the Minds of the Future Kayla Lovell Composition II Ms. Reed 22 January 2012 Outline Thesis: Elementary teachers may not have highest income‚ but they have one of the most fulfilling careers. Introduction: When thinking back to elementary school‚ what most people remember the best‚ are the teachers they had along the way. Elementary teachers not only introduce their students to the basic concepts of core subjects‚ they also help pave the path to each student’s
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Elements of Mathematics for Economists Bernard Cornet January 18‚ 2011 Contents Notation 1 Euclidean Spaces 1.1 Scalar Product and Associated Norm . . . . . . . . . . . . 1.1.1 Scalar Product . . . . . . . . . . . . . . . . . . . . 1.1.2 Norm Associated to a Scalar Product . . . . . . . . 1.1.3 Convergence in a Normed Space . . . . . . . . . . . 1.1.4 Euclidean Spaces and Hilbert Spaces . . . . . . . . 1.2 Matrices and Scalar Product . . . . . . . . . . . . . . . . . 1.2.1 Generalities on Matrices
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titled “Basic Algebra Skills-Real numbers & Algebraic Equations‚ Exponents & Scientific Notation‚ Radicals & Radical Exponents‚ and Polynomials”. I chose this presentation because I felt I needed to remember algebraic equations‚ exponents and polynomials. I have not had algebra for many years so this presentation was a very good refresher. It reminded me about real numbers and algebraic expressions and square roots. It was good to be reminded about the steps you take in algebra to solve an equation
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