hw9sol - ECEN 248 Introduction to Digital System Design...

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ECEN 248: Introduction to Digital System Design Department of Electrical Engineering Texas A&M University Assignment #9 Solutions 1. Suppose I have a SOP expression for a funciton f on n -variables, x 1 ,x 2 , · · · x n . Assume that there are k cubes in the expression of f . I would like to represent the SOP expression as an k × n matrix B , with each row representing a cube of f , and each column representing a variable. The rules for constructing the matrix B are: If the literal x j is present in a cube i , then I write a ’1’ in the ( i,j ) entry of B . If the literal x j is present in a cube i , then I write a ’0’ in the ( i,j ) entry of B . If the literal x j is not present in a cube i , then I write a ’-’ in the ( i,j ) entry of B . For example, suppose I had a 4-variable function f = x 1 x 3 + x 2 x 4 . The corresponding matrix B would be: B = bracketleftbigg 1 - 0 - - 1 - 1 bracketrightbigg (a) Write down the matrix B for the function x 1 x 2 x 3 + x 2 x 3 x 5 + x 4 + x 1 . (b) Write down a rule for computing the cofactor of a function f , represented in the above fashion (with respect to a literal x i ). The result should also be in the same format as above. (c) Write down a rule for computing the cofactor of a function f , represented in the above fashion (with respect to a literal x i ). The result should also be in the same format as above.
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