Boolean Function Representation: SOP and POS Form | Minterms and Maxterms Explained

[@ALLABOUTELECTRONICS]

Timestamps: 0:00 Introduction 1:05 Sum of Product (SOP) form 4:01 Product of Sum (POS) form 7:16 What is Minterm 12:21 What is Maxterm 18:27 Canonical SOP to Canonical POS conversion

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[@LynaLy-o2g]

i dont understand why did we take only m0 m2 m4 and m7 in 11:02 what about the other minterms ?

[@ALLABOUTELECTRONICS]

Because if you see the truth table at 10:41, then the output F1 is 1 for these four minterms. That is why only these four minterms have been considered. I hope, it will clear your doubts.

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[@halildalklc4591]

Thanks for the video! But how do you determine whether the output is 1 or 0? For example; the output for (001) was 0 at 10:35 and the output for (001) was 1 at 11:48

[@ALLABOUTELECTRONICS]

Here, just to explain the concept, some random 3-varibale functions F1 and F2 were taken.

[@Cannonbolt-i1t]

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[@avijidshil2751]

how did you calculate the output of the Function F1 as 1 when ABC is 000? how did you calculate the F1 in the truth table?

[@avijidshil2751]

timestamp 10:05

[@ALLABOUTELECTRONICS]

@@avijidshil2751 Here it has been assumed that for some circuit, we are getting this truth table. Or in other words, we have one circuit which behaves in a way, when input ABC is 000 then its output is 1. And similarly, for the certain input combinations (like 010, 100, 111), its output is 1.

[@avijidshil2751]

@@ALLABOUTELECTRONICS So those combinations need to be memorised rather than calculated? I'm sorry i just don't understand.

[@jigarprajapati4591]

I think he is trying to say that we have assumed that circuits and the output@@avijidshil2751

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[@jef798]

Sorry if I missed something, I don't get why we have to complement the variables from 0 to 1 when writing minterm expression at 8:00. Like is it just a rule or is there a reason behind it?

[@ALLABOUTELECTRONICS]

First, for the two variables, A and B we have total 4 different possibilities. So, these 4 possibilities (00, 01, 10, 11) have been shown in the table. Now, during the representation, if the value of the variable is 0 then it is represented by the complement of the variable. (e.g A-bar). And if the value of the variable is 1, then it is represented as it is (e.g A) So, for the inputs AB, if the value of these two variables are 00, then corresponding minterm is A-bar B-bar. So, that is how different input combinations are represented.

[@jef798]

@@ALLABOUTELECTRONICS thank you!

[@snehasagar4230]

10:27 how did you wrote F1 by which method did you wrote that

[@ALLABOUTELECTRONICS]

Here this specific truth table is taken as an example. Generally, for a given specific digital circuit either you know the truth table, or based on our requirement we are designing the digital circuit. In second case, we are already knowing the truth table. (That means for what specific input combination the output is 1 ) I hope, it will clear your doubt.

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[@ronodipsanpui7850]

15:36 why there is need of cmplementing the function first then solving directly we can do from the function given nah?

[@ALLABOUTELECTRONICS]

We want to represent the same function is POS form. That is why the function was complemented and then F1 was found in POS form. If you want to write directly from F1, using shortcut method then you can do so, by writing the Boolean expression for 0s. But here when variable is 0, you need to consider it as 1. For example, F1 is 0 when A = B = 0 and C = 1. So, in POS form, one of the term will be (A + B + C'). and likewise, you can write for all other terms. Here just to avoid confusion, the proper procedure was followed.

[@LANCEJERELLMACASPAC-vo7br]

why get only 4 minterms?? how do u determine the in which what to choose in minterms? what combination of number to choose as minterm,, 10:48

[@ALLABOUTELECTRONICS]

Because if you see the truth table on the left hand side, then in that truth table the function F1 is 1 (high) only for the four input combinations. Or we can say that, F1 =1 only for four minterms. One of them is A = 0, B = 0 and C = 0. In decimal 000 corresponds to 0, so it represents minterm m0. Likewise another input combination for which the F1 is 1, (A = 1, B = 1 and C = 1), 111 in decimal corresponds to 7, so it represents minterm m7. So, in this case, the F1 is 1 for four different minterms. (m0, m2, m4 and m7) I hope, it will clear your doubt.

[@LabdhiShah-p5q]

But how is F1 determined?

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[@rakshitagarg2942]

How did you find the value of F1 in truth table ? 11:14

[@ALLABOUTELECTRONICS]

For explanation, some random function F1 is taken.

[@omm9974]

Sir Please help in process of maxterm how did u write F1 in truth table 0+0+0 it will be 0 na but u have written 1

[@ALLABOUTELECTRONICS]

For writing a function in terms of a Maxterm from the truth table, you need to look for the combination in a truth table, where the output is 0. (For finding the expression in terms of minterms, we are considering the combination, where the output is 1). So, basically here we are using a inverted logic. So as per this, for example, if the F is 0 for A= B= C = 0, then maxterm is A + B + C. Here, in maxterm representation, when the variable is 0, then represent it as it is, and when it is 1, then we need to complement it. So, that is why if function is 0 for A= B = C = 0, then corresponding maxterm is (A+B+C). Likewise, if function is 0 for A = 0, B= 0 and C= 1 then corresponding maxterm will be A + B + C'. I hope, it will clear your doubt.

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[@ALLABOUTELECTRONICS]

Yes, it will be covered soon.

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[@sutopasarkar497]

In 11:15 s,how we know that m0=1? Please give me explanation sir🙏

[@ALLABOUTELECTRONICS]

From the truth table as you can see, when all A, B and C are 0, then output of the function is 0. The ( A, B,C ) = ( 0,0,0) represents the minterm m0. I hope, it will clear your doubt.

[@KuewuPamela-wq7xi]

Please will you be given a particular function to calculate for the minterm or it would be calculated for you automatically,then afterwards questions would be given based on that

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[@pkus]

How do you calculated f1 colmun values 11:14?

[@rushalmshah]

In the function, if the particular minterm is present then write 1 in front of that minterm. For example, minterm m0 is part of the function. Therefore, 1 is written in front of that. I hope, it will clear your doubt.

[@pkus]

@@rushalmshah what is the difference between 000(m0) and 001(m1) why 1 is put infront 000 why not 001? I dont get your explanation.

[@ALLABOUTELECTRONICS]

Just go through the definition of minterm first. You will get better idea. (7:17 onwards). If you see the function F1, then it consist of 4 terms. A'B'C' corresponds to minterm m0. That means in this function, minterm m0 is present. And that's why in the table in front of 000 (m0) 1 is written. Similarly, for the remaining terms, 1 is written.I hope, it will clear your doubt.

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[@purvishroff5238]

How you calculated F1 for min term or max term

[@ALLABOUTELECTRONICS]

Would you please mention the timestamp where you are referring to in the video ?

[@KeerthanaKeerthana-v6f]

Why we need to express 0 in true form and 1 in complement form in maxterms

[@ALLABOUTELECTRONICS]

Because the maxterms and minterms are complement of each other. So, in maxterms, the representation of 0 and 1 is also exactly opposite to the minterm representation.

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How to realisation for this using NAND/ NOR gates

[@ALLABOUTELECTRONICS]

I have already made a video on NAND and NOr gate as universal gate, where I have explained that, how the AND and OR functions can be implemented using NOR and NAND gate. Under digital electronics playlist, you will get all those videos and solved examples. Please check that on the playlist page of the channel.

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how to fine f1 10:35

[@ALLABOUTELECTRONICS]

F1 function is 1 for the specific input combinations. (minterms). In algebraic form, it is the summation of all the minterms for which F1 is 1. For example, the F1 is 1 when A =B = C = 0. So, that corresponds to A'B'C'. And similarly, all the minterms have been summed together. I hope, it will clear your doubt.

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[@nadasr8742]

how to get the function ?

[@ALLABOUTELECTRONICS]

I didn't exactly get what you are saying. But if the function is not given for specific logic circuit then from the truth table, you can find the function.

[@Ben-786]

@@ALLABOUTELECTRONICS sir, is it a trick that we get the exact function from sum of terms or is it a fully proved argument.....

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How we r getting that F1 values?

[@MomoMoshiMomo]

he's just giving them out as an example

[@rizahamii2987]

Sir how can we find F1 in minterm?

[@ALLABOUTELECTRONICS]

Hi, would you please mention the timestamp, where you are referring to in the video ? At 18:27, I have already explained the conversion.

[@rizahamii2987]

@@ALLABOUTELECTRONICS what do you mean about it F1 is given in exam ?

[@rizahamii2987]

@@ALLABOUTELECTRONICS or what is F1= xyz'…?

[@ALLABOUTELECTRONICS]

@@rizahamii2987 If F1 = xyz' then corresponding minterm is m6 (x = 1, y = 1 and z = 0). So, similarly, if you have a function F1 = xyz + x'y'z' + xyz' then in terms of the minterm it is equal to m7 + m0 + m6. That means F1 = m0 + m6 + m7. I hope, it will clear your doubt.

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How to find value of F

[@ALLABOUTELECTRONICS]

Typically, when you are designing a circuit, then based on the required outcome, you know the expression of F (from the truth table). For example, when you are designing a half adder, then you know that, for what inputs, the output F is 1. So, from the truth table, you know that, for which minterms the output is 1. But academic perspective, sometimes you have been given the entire truth table. So, you just need to check for which minterms, the output F is 1.

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Would you please mention the timestamp where you are referring to in the video ?

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