Boolean Function Representation: SOP and POS Form | Minterms and Maxterms Explained
ฝัง
- เผยแพร่เมื่อ 25 ก.ค. 2024
- In this video, the Sum of Product (SOP) and Product of Sum (POS) form of Representation of Boolean Function is explained using examples. And what is minterm and maxterm in the Boolean Expression is also explained.
The following topics are covered in the video:
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
Boolean Expression Representation:
The Boolean Expression is typically represented in two forms.
1) Sum of Product Form (SOP)
2) Product of Sum Form (POS)
There are two types of SOP and POS forms of representation.
Canonical and Non-Canonical
In this video, the Boolean Expressions in both Canonical and Non-Canonical SOP and POS forms are explained. And the concept of minterms and maxterms is also explained.
What is minterm?
It is the product term that contains all the variables of the function either in true form or complemented form.
The canonical SOP form is Sum of Minterms.
What is Maxterm?
It is the sum term that contains all the variables of the function either in true form or complemented form.
The canonical POS form is Product of Maxterms.
In the later part of the video, how to write the Boolean expression in Canonical SOP or POS form from the truth table is also explained.
Digital Electronics (Playlist):
• Digital Electronics
This video will be helpful to all the students of science and engineering in understanding the SOP (Sum of Product) and POS (Product of Sum) form of representation of the Boolean Function and the concept of minterms and maxterms.
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#SOPandPOS
#Minterms
#Maxterms
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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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Thank you!
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Just one word- PERFECT, but if you could just provide notes also like everything in few pages or even these slides also would be a great help. Anyways, A big thanks!!
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Thank you
I have watched my videos and search on many website about max term after find min term.
This one is single video which gives full details of both with conversion.
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From an engineering student
Good luck
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sir can please cover k map next month [1 dec] we have exam and im having difficulty ,,,also show simplification using k map {adder subtractor circuiyt} please
Yes, it will be covered soon.
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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?
timestamp 10:05
@@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.
@@ALLABOUTELECTRONICS So those combinations need to be memorised rather than calculated? I'm sorry i just don't understand.
I think he is trying to say that we have assumed that circuits and the output@@avijidshil2751
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
Here, just to explain the concept, some random 3-varibale functions F1 and F2 were taken.
How to realisation for this using NAND/ NOR gates
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.
15:36 why there is need of cmplementing the function first then solving directly we can do from the function given nah?
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.
How you calculated F1 for min term or max term
Would you please mention the timestamp where you are referring to in the video ?
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
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.
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?
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.
@@ALLABOUTELECTRONICS thank you!
F ka value kaise aaya koi bta do yrr exm h
How did you find the value of F1 in truth table ? 11:14
For explanation, some random function F1 is taken.
How we r getting that F1 values?
he's just giving them out as an example
Studying 1 hour before exams 😅😭
how to get the function ?
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.
@@ALLABOUTELECTRONICS sir, is it a trick that we get the exact function from sum of terms or is it a fully proved argument.....
Amazing
Mai exam se 3 ganta phele dekh rahi hu 2024 me
How to find value of F
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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how to fine f1 10:35
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.
In 11:15 s,how we know that m0=1? Please give me explanation sir🙏
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.
Sir how can we find F1 in minterm?
Hi, would you please mention the timestamp, where you are referring to in the video ? At 18:27, I have already explained the conversion.
@@ALLABOUTELECTRONICS what do you mean about it
F1 is given in exam ?
@@ALLABOUTELECTRONICS or what is F1= xyz'…?
@@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.
7:14
10:00
super fucking bro
How do you calculated f1 colmun values 11:14?
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.
@@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.
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.
@@ALLABOUTELECTRONICS hi
F1 kasay aya
Would you please mention the timestamp where you are referring to in the video ?
olmayan allahın razı olsun
Hindi me bolo yar hm sb Hindustani hai...
Kal kiska exam h😢😂