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Math Help - Sum of products expansion help

  1. #1
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    Sum of products expansion help

    How do I find the sum of products expansion of this Boolean function F(x,y) that equals 1 if and only if x = 1
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  2. #2
    MHF Contributor
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    The sum of products expansion is easily obtained from the truth table. For each line of the table where the function value is 1, e.g.,

    Code:
    x | y | F(x,y)
    --------------
       ....
    1 | 0 | 1
       ....
    you add one product to the sum. In this product, you write x is the x's column has 1, and \bar{x} if the x's column has 0. (I assumed that the negation of x is denoted \bar{x}; you may have a different notation.) Also, you do the same for y. So, for the line above, you add the following product: x\bar{y}.

    To repeat, you add all such products for lines where F(x,y)=1.
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