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CSPictorial
India
เข้าร่วมเมื่อ 19 ก.ค. 2020
CSPictorial aims at learning computer science in a pictorial way. This channel will provide computer tutorials to make students understand computer concepts in a simple way. CSPictorial will cover concepts ranging from basics to advanced level.
Self-Dual Boolean Functions | (Explained with solved examples)
Boolean Algebra: th-cam.com/video/UZtWgDADr1o/w-d-xo.html
Laws of Boolean Algebra: th-cam.com/video/hVc8b4ePoFQ/w-d-xo.html
Simplification of Boolean expressions: th-cam.com/video/j7Qkrm1YJ0c/w-d-xo.html
A Boolean expression is a logical statement that can either be TRUE or FALSE.
The complement of a Boolean expression is the negation of the variables with the replacement of ANDs with ORs and vice versa.
If F = (A + B)(C + D). The complement F’ = A’B’ +C’D’
The dual of a Boolean function is derived by Replacing ANDs with ORs and vice versa. Switching identity elements 0s to 1s and vice versa.
Always remember, for duality, the variables or literals will remain as such. You should never change the variables to find the dual of a Boolean function.
This is the major difference between the complement and dual of a Boolean function.
If F = (B’ +C).A, the dual is derived as Fdual = (B’.C) + A
Self-duality principle:
Case 1: The Boolean function is given as an expression in terms of variables/literals
Self- duality principle states that the function is said to be Self dual if and only if its dual is equivalent to the given function.
Case 2: Boolean function is given in terms of minterms as ∑ (0, 1, 6, etc) or maxterms as π(2, 3, 4, 5, etc).
Self- duality principle states that the function is said to be Self-dual if it satisfies two conditions:
The given function should be a neutral function and
the function should not contain two mutually exclusive terms.
Neutral function: a function is neutral if it contains exactly 2n-1 minterms and maxterms. And also, Number of minterms must be equal to the number of maxterms.
Mutually exclusive terms: Two mutually exclusive terms are the complement of each other. Mutually exclusive pairs for a Boolean function with three variables are (0,7); (1,6); (2,5); (3,4). The self-duality principle states that terms inside these mutually exclusive pairs cannot appear together in the given Boolean function.
This video explains these two cases of self-duality with simple examples. Watch this video until the end for better understanding.
Interesting fact: Self-duality is closed under complement which means If a function is self-dual, then its complement will also be a self-dual function.
Additional information: The no. of Self-dual functions possible with n variables is 2^2^(n-1).
Laws of Boolean Algebra: th-cam.com/video/hVc8b4ePoFQ/w-d-xo.html
Simplification of Boolean expressions: th-cam.com/video/j7Qkrm1YJ0c/w-d-xo.html
A Boolean expression is a logical statement that can either be TRUE or FALSE.
The complement of a Boolean expression is the negation of the variables with the replacement of ANDs with ORs and vice versa.
If F = (A + B)(C + D). The complement F’ = A’B’ +C’D’
The dual of a Boolean function is derived by Replacing ANDs with ORs and vice versa. Switching identity elements 0s to 1s and vice versa.
Always remember, for duality, the variables or literals will remain as such. You should never change the variables to find the dual of a Boolean function.
This is the major difference between the complement and dual of a Boolean function.
If F = (B’ +C).A, the dual is derived as Fdual = (B’.C) + A
Self-duality principle:
Case 1: The Boolean function is given as an expression in terms of variables/literals
Self- duality principle states that the function is said to be Self dual if and only if its dual is equivalent to the given function.
Case 2: Boolean function is given in terms of minterms as ∑ (0, 1, 6, etc) or maxterms as π(2, 3, 4, 5, etc).
Self- duality principle states that the function is said to be Self-dual if it satisfies two conditions:
The given function should be a neutral function and
the function should not contain two mutually exclusive terms.
Neutral function: a function is neutral if it contains exactly 2n-1 minterms and maxterms. And also, Number of minterms must be equal to the number of maxterms.
Mutually exclusive terms: Two mutually exclusive terms are the complement of each other. Mutually exclusive pairs for a Boolean function with three variables are (0,7); (1,6); (2,5); (3,4). The self-duality principle states that terms inside these mutually exclusive pairs cannot appear together in the given Boolean function.
This video explains these two cases of self-duality with simple examples. Watch this video until the end for better understanding.
Interesting fact: Self-duality is closed under complement which means If a function is self-dual, then its complement will also be a self-dual function.
Additional information: The no. of Self-dual functions possible with n variables is 2^2^(n-1).
มุมมอง: 41
วีดีโอ
Sample problems| Canonical |Standard| SOP| POS
มุมมอง 982 หลายเดือนก่อน
This video gives you sample problems related to Canonical and standard SOP and POS forms with simple step by step solutions. These type of conversion problems can surely be expected in competitive exams. Canonical and Standard form of SOP (with examples): th-cam.com/video/-VlAtQl3qwo/w-d-xo.html Canonical and Standard form of POS (with examples): th-cam.com/video/1tXz4Mdh6j0/w-d-xo.html This vi...
Canonical and Standard form of POS (with examples)
มุมมอง 6223 หลายเดือนก่อน
This video is about the Canonical and Standard forms of POS Boolean expressions. A Boolean expression is a logical statement that can either be TRUE or FALSE. Examples of Boolean expressions are: A BC; AB AB' A'B; (A B)(B C)(A B') Every Boolean expression can be represented in two forms: SOP form or POS form. Boolean Algebra playlist: th-cam.com/play/PLmX-4JIvNy3HytNDD_LbjGFp7q3r-LYHY.html Cano...
Canonical and Standard form of SOP (with examples)
มุมมอง 6604 หลายเดือนก่อน
This video is about the Canonical and Standard forms of SOP Boolean expressions. A Boolean expression is a logical statement that can either be TRUE or FALSE. Examples of Boolean expressions are: A BC; AB AB' A'B; (A B)(B C)(A B') Every Boolean expression can be represented in two forms: SOP form or POS form. Boolean Algebra playlist: th-cam.com/play/PLmX-4JIvNy3HytNDD_LbjGFp7q3r-LYHY.html SOP ...
Don't Care Condition in K-Map | (Solved Examples)
มุมมอง 3088 หลายเดือนก่อน
In K-Map, the don’t care conditions allow us to replace the empty cell of a K-Map to form larger group of cells. A “Don’t-Care’’ cell is represented as “X”. While forming groups of cells, “Don’t Care” cell can be treated as 1 or 0 or that cell can even be ignored. Karnaugh Map introduction: th-cam.com/video/a1Zwqjw_sp0/w-d-xo.html K-Map Simplification Procedure: th-cam.com/video/GpPshBH4FEo/w-d...
Boolean Simplification using K-Map (Step-by-Step)
มุมมอง 3458 หลายเดือนก่อน
This video explains the K-Map simplification procedure step by step if the given Boolean function is in SOP form and in POS form. Karnaugh Map Introduction: th-cam.com/video/a1Zwqjw_sp0/w-d-xo.html Boolean Simplification using Boolean laws: th-cam.com/video/j7Qkrm1YJ0c/w-d-xo.html K-Map Rules for grouping of cells: th-cam.com/video/u2ExFST7K-k/w-d-xo.html K-Map Simplification in SOP form Step 1...
Karnaugh Map Simplification Rules | Grouping Cells
มุมมอง 15K9 หลายเดือนก่อน
Karnaugh Map is the method used to minimize and simplify the Boolean functions. It works on the basis of complement laws: X X’ = 1 and X.X’ =0. Thereby, to cancel a variable in K-Map, we need pairs of variables and their complements which is done by grouping. K-Map uses some rules for grouping of adjacent cells. In this video, we will check out simple explanation for these rules, one by one. Ka...
Karnaugh Map | Introduction (Basic)
มุมมอง 27110 หลายเดือนก่อน
Karnaugh Map is a tabular structure used to minimize and simplify the Boolean functions. For an n variable K-map, there are 2n cells. K-Map key terms: 1. Minterms, 2. Maxterms, 3. SOP Form, 4. POS Form Types of K-Map: 1. Two-variable K-Map 2. Three-variable K-Map 3. Four-variable K-Map 4. Five-variable K-Map, etc. Karnaugh map approach may be applied for any number generally it is used up to si...
Simplification Of Boolean Expressions | Using Laws of Boolean Algebra
มุมมอง 1Kปีที่แล้ว
This video is about the simplification of Boolean expressions using Boolean laws. This video covers 15 examples of Boolean expression simplification of which many are solved examples from previous NET and GATE question papers. The main aim of simplifying Boolean expressions is to obtain a final logical expression that has the minimum number of terms and thereby requires minimum number of logic ...
It's all about CSPictorial | Channel Trailer
มุมมอง 456ปีที่แล้ว
It's all about CSPictorial | Channel Trailer
Interesting facts about Computers and Technology
มุมมอง 537ปีที่แล้ว
Interesting facts about Computers and Technology
Computer Abbreviations | Part - II (From I - Z)
มุมมอง 5162 ปีที่แล้ว
Computer Abbreviations | Part - II (From I - Z)
Computer Abbreviations | Part - I (From A - H)
มุมมอง 1.5K2 ปีที่แล้ว
Computer Abbreviations | Part - I (From A - H)
MCQs on MS-Office | Computer Awareness| (50 Questions)
มุมมอง 2493 ปีที่แล้ว
MCQs on MS-Office | Computer Awareness| (50 Questions)
Boolean Algebra | (Simple introduction)
มุมมอง 7613 ปีที่แล้ว
Boolean Algebra | (Simple introduction)
MCQs on Binary Number system | Questions from NTA-NET & GATE | (Detailed solutions)
มุมมอง 8K4 ปีที่แล้ว
MCQs on Binary Number system | Questions from NTA-NET & GATE | (Detailed solutions)
Octal to Hexadecimal | Hexadecimal to Octal | (step-by-step procedure with examples)
มุมมอง 2364 ปีที่แล้ว
Octal to Hexadecimal | Hexadecimal to Octal | (step-by-step procedure with examples)
Hexadecimal to binary | Binary to hexadecimal | Easy!!
มุมมอง 924 ปีที่แล้ว
Hexadecimal to binary | Binary to hexadecimal | Easy!!
Hexadecimal to decimal | Decimal to hexadecimal | (step-by-step procedure with examples)
มุมมอง 3114 ปีที่แล้ว
Hexadecimal to decimal | Decimal to hexadecimal | (step-by-step procedure with examples)
Octal to binary | Binary to octal | (conversions with examples)
มุมมอง 2164 ปีที่แล้ว
Octal to binary | Binary to octal | (conversions with examples)
Octal to decimal | Decimal to octal | (conversions with examples)
มุมมอง 2134 ปีที่แล้ว
Octal to decimal | Decimal to octal | (conversions with examples)
Two's complement form | Subtraction | Addition | (Examples)
มุมมอง 2.1K4 ปีที่แล้ว
Two's complement form | Subtraction | Addition | (Examples)
One's complement form | Subtraction | Addition | (Examples)
มุมมอง 4.7K4 ปีที่แล้ว
One's complement form | Subtraction | Addition | (Examples)
MCQs | Computer awareness for competitive exams | (50 questions)
มุมมอง 8754 ปีที่แล้ว
MCQs | Computer awareness for competitive exams | (50 questions)
The Central Processing Unit | (components and functions)
มุมมอง 83K4 ปีที่แล้ว
The Central Processing Unit | (components and functions)
Thanks mom ❤
This is the best explanation i have seen.Thank you so much for this.
Thank you
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Thank you
Our teacher made us play to study and imagen
Thank you so much. I was actually looking for this. Nobody explained me properly how k map actually works
Thnx,it was great✨
Thank you
Our teacher used this video in class
3:43 why did u skip the wrap around group.
I appreciate your interest. I skipped explaining the terms because it works the same way as other groups. That wrap around group gives the term B'C'D cancelling out A and A'.
Boolean functions in Cryptology can be studied by considering their various representations including Truth Table, Algebraic Normal Form and Walsh Spectrum. The Truth Table is a list of bits giving the output for every input. n input variables require 2^n outputs. For convenience pack them into an array of unsigned 64-bit integers. The ANF is a formula using only AND and XOR. This makes the ANF representation formula unique. There is a DUALITY property between TT and ANF since the matrix operation that switched between these two forms is its own inverse. The Walsh spectrum is a list of 2^n signed integers obtained by applying a Fourier Transform to a truth table. For convenience we use the polarity truth table {-1,1} instead of the binary truth table {1,0} so that the Walsh spectrum value at position W is directly proportional to the correlation that the Boolean function has with the Linear function designated by W which is denoted by L_w(x). Correlation with linear functions is vital in Cryptology since there exist strong attacks on ciphers which employ functions that are too close to linear. There is a class of Boolean functions that achieve the maximum possible distance from linear functions, and these are called the Bent functions. When the polarity (+ve or -ve) of the Walsh spectrum of a Bent function is considered, it is also a Bent function, and so this is the DUAL Bent function. ... etc...etc...
Thank you for helping me with my computer
thanks love from kerala as a BCA student❤️
Thank you mam.
Thanks very much
Using this so i can convince my parents to buy me a pc 🖥
At the min 4:45 after taking the 2s compliment why you again add 1 ???
At that step, we are finding 2s complement = 1s complement +1
I appreciate your interest. Check the steps one more time. Hope you get it clear
Today is my exam at 10 15 and iam watching in 9 o clock
All the Best
Thanks for this beautiful explanation
the video is fake
why?
Can we use mainframe computers to do work and mini computers as a memory
Thank you helped me in my computer project
Literally the best video on yt related to this topic. Thankyou soo much ma'am for your efforts. We really appreciate you
Thank you so much for your encouragement
Hello dear, welcome to you.
Miss badhiya ❤
Thank you
L
Keep it up😍😍😍
Thank you
Thank you
Very impressive clip that simplifies long lecture within few minutes.
Thank you for this encouraging comment
Wow this helps me in my revision short and clear
Thank you
superb job well expalnation about cpu thnks
Thank you
Good teacher
Thank you
Thank you
Thank you mam ❤
❤wow
Thank you
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THANKYOU SOOO MUCH OMG I HAVE BEEN STRUGGLING TO FIND A CLEAR EXPLANATION😢😢🙏🙏
Thank You for your encouraging comment
0:50 fake m@+#@& f=×#!=@ computers
Thanks for good information❤
thank you madam
Thank you!!
3:15 I don't understand it
Watch the video from the beginning. It's easy to understand
❤❤❤
❤️❤️❤️ 0:15
Can u pair cell 2 and 8
We cannot group cells diagonally
@@cspictorial2540 thanks
Thank you so much ma' am
Tq mam❤
Good
Thank You
Amazing video appreciated
Thank You
Tq sir