Ass2 - Department of Electrical and Computer Engineering...

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Department of Electrical and Computer Engineering ECSE 221 – Introduction to Computer Engineering 1 Assignment 2 – Combinational Logic Due: Monday, February 11 th 2008, 5:00 pm Question 1 Consider the truth table for the function X = f(A,B,C,D) shown below. A B C D X 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 a) Using the Karnaugh Map method, determine the minimal canonical forms (i.e. ∑π and π∑ respectively) corresponding to the truth table shown above. List any multiple solutions. Repeat the analysis using algebraic manipulation for each of the solutions you obtained. b) Using algebraic manipulation, prove the equivalence of the ∑π and π∑ forms obtained. c) Suppose that term #15 was set to d, i.e., don’t care . Determine the resulting minimal canonical forms using the minimization method of your choice. Using algebraic manipulation, prove that the resulting forms are equal. Question 2 In this question you will build implementations for each of the solutions you obtained in Question 1a using a variety of technologies. The LogicWorks simulator, available on all Engineering machines, will be used for this exercise. (Unfortunately LogicWorks is licensed software, so you will have to purchase your own copy if you wish to use it on your personal A shorthand notation for specifying truth tables is to list the minterm of maxterm numbers corresponding to the function’s 1’s or 0’s respectively using the following notation, X "# = {3,4,6,7,11,12,14} A , B , C , D $ , X #" = {0,1,2,5,8,9,10,13,15}, A , B , C , D % where X ∑π corresponds to the Sum of Products form, and X π∑ corresponds to the Product of Sums form. Note: the number associated with a minterm or maxterm is simply the binary value associated with the input, A,B,C,D. For example, the minterm corresponding to A,B,C,D=0,1,1,1 is minterm 7. 1/17
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machines. If you do manage to find an Open Source alternative, please bring it to the attention of the instructor). a) Using the standard gates available in the LogicWorks library, build an implementation for each of the ∑π and π∑ forms you obtained. Prove that the implementation is correct by designing a LogicWorks timing file and a suitable test circuit. b)
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Ass2 - Department of Electrical and Computer Engineering...

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