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Table of Contents. Sum of Product is the abbreviated form of SOP. Sum of product form is a form of expression in Boolean algebra in which different product terms of inputs are being summed together. To understand better about SOP, we need to know about min term. Minterm means the term that is true for a minimum number of combination of inputs. That is true for only one combination of inputs.
In other words, these are the ways to represent the deduced reduced logic function. We can use the deduced logic function in designing a logic circuit. Before understanding SOP and POS, we must learn various related terms so that the entire thing would collectively make some sense. Expression includes Product terms are taken where the input set produces a value 1. Only Sum terms which generate a value 0. Method 1 represents the variable and 0 is the complement of it. Obtained through Adding corresponding product terms.
Any kind of logical expression can be represented through these terms and there are many ways of expressing a logical function. AND represents the product relationship between the terms whereas OR represents sum relationship. So, Sum of Products and Product of Sums are the equivalent approaches of representing a logical expression. To be clearer in the concept of SOP, we need to know how a minterm operates. So, the term SOP is also defined as the expression which is completely of minterms. The word minterm holds true for a minimal number of combinations of input terms. The below table clearly describes the concept of minterms.
The use of switching devices like transistors give rise to a special case of the Boolean algebra called as switching algebra. In switching algebra, all the variables assume one of the two values which are 0 and 1. A Boolean expression is an expression which consists of variables, constants 0-false and 1-true and logical operators which results in true or false. A Boolean function is an algebraic form of Boolean expression. A Boolean function of n-variables is represented by f x1, x2, x3….
We will get four Boolean product terms by combining two variables x and y with logical AND operation. These Boolean product terms are called as min terms or standard product terms. Similarly, we will get four Boolean sum terms by combining two variables x and y with logical OR operation. These Boolean sum terms are called as Max terms or standard sum terms. From the above table, we can easily notice that min terms and Max terms are complement of each other.
Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It only takes a minute to sign up. I think the easiest way is to convert to a k-map, and then get the POS. In your example, you've got:.
The logic gate symbol of AND gate is shown in figure.
For example, if we have two variables namely X & Y then the canonical expression comprising of min terms will be XY+X'Y', whereas the canonical expression.
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