explain with an example how to express a boolean function in its sum of product form
Answers
OR Gate (Sum) Thus the Boolean equation for a 2-input OR gate is given as: Q = A+B, that is Q equals both A OR B. For a sum term these input variables can be either “true” or “false”, “1” or “0”, or be of a complemented form, so A+B, A+B or A+B are all classed as sum terms.
In the tutorial about the Sum-of-Product (SOP) expression, we saw that it represents a standard Boolean (switching) expression which “Sums” two or more “Products” by taking the output from two or more logic AND gates and OR’s them together to create the final output. But we can also take the outputs of two or more OR gates and connect them as inputs to an AND gate to produce a “Product of the Sum” (OR-AND logic) output.
In Boolean Algebra, the addition of two values is equivalent to the logical OR function thereby producing a “Sum” term when two or more input variables or constants are “OR’ed” together. In other words, in Boolean Algebra the OR function is the equivalent of addition and so its output state represents the “Sum” of its inputs.
The logical sum of two or more logical product terms is known as sum of products expression. SOP is an ORing of of AND ed variables. The boolean expression containing all the input variables either in complemented or un complemented form in each of the product term is known as canonical SOP expression and each term is called minterm. For example, express the product of sum from the boolean function f(x,y). For example, express the product of sum from the boolean function F(X, Y) and the truth table for which is given below: Now by adding minterm for the output 1’s, we get the desired sum of product expression which is X’Y’ + XY.