Assignment2Sol

Assignment2Sol - Department of Electrical Engineering...

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Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering Assignment 2 – Combinational Logic Question 1: Due October 19 th , 2009 A convenient shorthand for specifying truth tables is to list the set of minterms (or maxterms) for which the corresponding Boolean function is true (or false). Consider the following truth table: A B C D F(A,B,C,D) 0 0 0 0 0 d 1 0 0 0 1 0 2 0 0 1 0 1 3 0 0 1 1 1 4 0 1 0 0 0 5 0 1 0 1 1 6 0 1 1 0 0 7 0 1 1 1 0 8 1 0 0 0 d 9 1 0 0 1 0 10 1 0 1 0 1 11 1 0 1 1 1 12 1 1 0 0 0 13 1 1 0 1 1 14 1 1 1 0 0 15 1 1 1 1 0 The shorthand for the sum-of-products ( ∑∏ ) and product-of-sums ( ∏∑ ) forms is shown at the right of the truth table. Given this specification for a Boolean function, answer the following questions. a) Use algebraic methods to derive the minimal forms for both ∑∏ and ∏∑ assuming that don't cares are set to 0 for ∑∏ and 1 for ∏∑ . b) Repeat the above using Karnaugh maps. Here you may choose the don't cares to minimize the resulting expressions. c) Repeat the minimization, this time assuming don't cares are all 0, using any minimization method. Prove algebraically that the resulting forms are equal (same truth table). F ( A , B , C , D ) = 2,3, 5,10,11,13 + 1 0,8 d F ( A , B , C , D ) = 1,4,6,7,9,12,14,15 + 0 0,8 d
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Question 2 Write down the truth table for a full
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This note was uploaded on 05/06/2010 for the course ENG ECSE221 taught by Professor Ferri during the Fall '09 term at McGill.

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Assignment2Sol - Department of Electrical Engineering...

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