PRODUCT OF SUM (POS) || MODULE 2 || KTU || EET 206 DIGITAL ELECTRONICS

Hello students, today we are going to discuss the concept of POS form based on module 2 of EET 206 digital electronics. What is POS form? It means product of some form. Consider the case, consider a function f of a, b, c which is equal to a plus b dot b plus c complement dot a plus b plus c complement. Consider this function. There are three terms here. a plus b is the first term, b plus c complement is the second term, a plus b plus c complement is the third term. After summing these three terms, what is it doing? It is doing AND. Group of summed terms are multiplied together. Isn't it? This is the first term, this is the second term and this is the third term. The first term is OR and the second term is OR. Similarly, the third term is OR. What is it doing? It is doing AND. Individually, each term is AND. So, what do we call it? Product of summed terms. Now, I said this is a POS form. Next, how is a standard POS form? Consider a function with three variables. f of a, b, c is equal to a plus b complement plus c dot a plus b plus c dot a complement plus b complement plus c. Consider this function. Here, a function with three variables a, b, c is given. Here, these three variables are present in each term. Either it is present in the direct form or in the complement form. So, in each case or in each term, the variables are either in the actual form or in the complement form. If there is a variable in any form, what do we call it? We call it a standard POS form. Now, look at the above case. A function with three variables is given here. The first term here is only a plus b. Which variable is missing here? The variable c is missing here. Now, look at the second term. Here, there is only b and c. The variable a is missing here. Here, c complement term is also present. So, the variable a is missing in the second term. In the third case, all the variables are present. In the first case, c variable is missing. In the second case, a variable is missing. So, what form is this? This is an example of a POS form. Now, look at the second case. In a standard POS form, if all the variables are present in each term, what do we call it? We call it a standard POS form. Now, this case is a product of sum terms. That is, the AND operation is done by summing each term. That is why it is called a product of sum terms. This is the difference between a POS form and a standard POS form. In a standard POS form, each individual term is called the fundamental term. What do we call each individual term? We call it a fundamental term or a max term. We call it a max term in POS. In SOP, we call it a min term. I have explained it in the previous video. Each individual term is called a min term. In a standard POS form, each individual term is called a fundamental term or a max term. The max term is represented by a capital M. The min term is represented by a small m. In a standard SOP form, the min term is represented by a max term in POS. The max term is represented by a capital M and the min term is represented by a small m. Consider a two variable case. In SOP form, the combination of two variables is 2 to the power n. In SOP form, the combination of two variables is 2 to the power 2. That means there will be four cases. There will be four cases for a and b. First, a and b are 0. Second, a is 0 and b is 1. Third, a is 1 and b is 0. Last case, both are 1. In POS form, the max term is represented by a capital M. Here, we are doing OR. In POS form, a plus b is equal to max term 0. In POS form, 0 is the actual variable. In POS form, 0 is the actual variable and 1 is its complement. In POS form, 0 is a and 1 is a complement. In SOP form, 1 is the actual variable and 0 is its complement. Here, both cases are actual variables. Since it is POS form, we said 0 is the actual variable. So, 0 and 0 are actual variables. a plus b is represented by max term 0. In SOP form, a is 0 and 0 is the actual variable. In POS form, b is 1 and 1 is its complement. So, b is complement and its max term is 1. In SOP form, a is 1 and a is 1 is its complement. So, a is complement and b is 0. In SOP form, b is 0 and b is its actual variable. In POS form, b is max term and 2 is its complement. The next case is, both are 1. When 1 comes, it is a complement case in POS form. So, A complement plus B complement, which is represented by max term 3. This is how we represent the truth table of a POS form using max term. Next, let us look at problems based on POS form. y equal to a plus b plus c dot a plus b plus c complement dot a plus b complement plus c complement dot a complement plus b plus c We know that this is a case in POS form. In the question, it is said that y equal to is in POS form. In POS form, the actual variable is 0 and complement is 1. The actual variable is 0 and complement is 1. This is how it is given in POS form. The actual variable 0 is represented by a. In POS form, the actual variable is 0 and complement is 1. In POS form, the actual variable is a and b. In POS form, the actual variable is 0 and complement is 1. In POS form, the actual variable is a and b. The decimal value of 0 is 0. The decimal value of 0 is 1. The decimal value of 0 is 3. The decimal value of 1 is 4. In POS form, the actual variable is pi. In POS form, the actual variable is 0, 1, 3, 4. I hope you understood the SOP form and POS form. In SOP form, the actual variable is 1 and complement is 0. In POS form, the actual variable is 0 and complement is 1. Do not forget these two cases. I hope you understood today's class. See you in the next class with a new topic. Thank you.