COMPENG 2DI4 Lecture Notes - Esc Key
17 Sep 2013
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Click the mouse to move to the next page. Use the esc key to exit this chapter. Given an expression in product-of-sums form, the corresponding sum-of-products expression can be obtained by multiplying out, using the two distributive laws: X(y + z) = xy + xz (x + y)(x + z) = x + yz (3-1) (3-2) In addition, the following theorem is very useful for factoring and multiplying out: (x + y)(x + z) = xz + x y (3-3) In the following example, if we were to multiply out by brute force, we would generate 162 terms, and 158 of these terms would then have to be eliminated to simplify the expression. Instead, we will use the distributive laws to simplify the process. The same theorems that are useful for multiplying out expressions are useful for factoring. By repeatedly applying (3-1), (3-2), and (3-3), any expression can be converted to a product-of-sums form.
