Boolean Algebra 1 - The Laws of Boolean Algebra
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- เผยแพร่เมื่อ 9 ก.ค. 2024
- This computer science video is about the laws of Boolean algebra. It briefly considers why these laws are needed, that is to simplify complex Boolean expressions, and then demonstrates how the laws can be derived by examining simple logic circuits and their truth tables. It also shows how some of these laws relate to familiar properties of base 10 numbers, namely the associative, commutative and distributive properties. In addition, this video covers De Morgan’s theorem. It illustrates how De Morgan’s theorem can be proved by comparing the behaviours of the relevant logic circuits. The video that follows on from this one describes how the laws of Boolean algebra can be applied to simplify complex Boolean expressions.
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Please tell me you teach for a living! Your lectures are easier to follow than any professors I've taken.
I have been a teacher for most of my working life. Either in schools, or training software engineers. I am currently Head of Computer Science in UK school. Thanks for the lovely comment. :)KD
@@arjay_2002 So he's still knowledgeable on the topic
I couldn't agree more. I'm doing a digital electronics course right now, and this single 15 minute video cleared up all the confusion my professor has caused in the past two weeks. I have mid-terms coming and this lecture series is going to save me.
Thank you so much!!!
The textbook for my computer hardware class is entirely white page/black text, no color, minimal diagrams. Made it very hard to get boolean logic and algebra down. This video has already taught me so much more than the book did 3 weeks into the semster. Thanks a ton!
You are very welcome. I was the inadequacies of the majority of the textbooks out there that prompted me to make these videos. Having said that, I do like the A level computer science textbooks by Heathcote and Heathcote.
I've got essential computer mathematics, practical discrete mathematics and concrete mathematics for computer science. All 3 are dry. After watching this video, and revisiting the textbooks it all made sense. Maybe I'm a visual learner.
Hi Jachob, I need assistant for my digital class
Having locked maths away in a dusty corner of my brain about 30 years ago, I now find myself needing a serious bootcamp as I teach myself coding and software development. Your videos are an absolute godsend - just head and shoulders above every other resource I've looked at. Thank you so much!
This is one of the most succinct explanations I've found on the topic. Thank you, for the great tutorial!
You are welcome. :) KD
im from germany and its really hard to find good material on all of this, been struggling with my homework and didnt really know what to do but your calm and collective way of explaining things really helps. presentation wise perfect. what a blessing
This is fantastic. It's amazing what proper preparation and presentation can do. This obviously wasn't just banged off in a spare 20 minutes at the end of a day. I really appreciate the work you put into this. Trying to read the material and coming across something like 1 + 1 = 1 for the first time confused me, but you cleared it up with no doubts as to what's going on. Thanks a million!
You are very welcome indeed. Thanks for acknowledging the time and effort. :) KD
I kinda see it as math involving the description of nouns through numbers
-1 being closer to "one in the presence of one" than "1-1=0"
Theres a name for this type of information under statistical sociology being descriptive/representative data instead of a variable data (integers gathered for data)
idk :) just rambling, this is my first video on boolean algebra
this is one of the best explanations of anything I've ever come across. I've been doing electrical engineering for 5 months now and only just come across your channel. Subbed! Thank you!
I'm delighted to hear it was useful. Thanks for the great comment. :)KD
Many thanks for the excellent series of videos on Boolean logic, I've been using these with my A-level classes over a number of years and found them very valuable.
Delighted to hear it. Thanks for commenting. :)KD
THANK YOU !
Your explanation is so clear and easy to follow, much better than what i have from my school :)
I appreciate the simplicity of the name of the channel.
this is making online uni so much more manageable, thank you so much good sir! :)
Studying for an ICT exam tomorrow, these videos are really helpful.
Thank you, this is making much more sense now. Started JavaScript, from there had to understand Boolean algebra. For a person who always struggled with any kind of math this is making sense.
I'm at the University of Edinburgh, and I wish our lectures and tutorials were even 10% as clear as your videos. Thanks!
Your lectures are easier to follow than any professors I've taken. Exactly Thanks Sir God Bless You
You are most welcome. Delighted to help :)KD
Omg I love you sooooo muchhhhhhhhhhhh !!!!! You're a lifesaver my friend
Great video! Clear and very useful. Keep going
People like you make Math and Computer Science bearable for people who cannot understand logic fast enough like a lot of people do. It takes me hours to figure out how a concept works and so videos that explain it in simple terms make it extremely helpful for me to understand these topics. Math and Computer Science is more fun when we have people like you, Ben Eater, Neso Academy, The Organic Chemistry Tutor, and many other amazing people.
Thank you for this series and all the other videos you have put out!
Organic chemistry tutor is the goat
What a great presentation and explanation. Thank you so much!
You are very welcome
This is a great video sir ,very well explained!!
Tnx. :)
Brilliant video, thank you so much for your help!
😆
I am sort of late to the party but i still felt the need to praise you for this video, you've done a great job. I had absolutely no idea about logic gates etc. beforehand but got everything after these 15 minutes
That's really nice to hear. Thank you :)KD
Thanks from Bharat I left this topic because single distributive formula which is given in wrong in my book now I corrected this it saved my time a lot thanks sir
This helped visualize the text I'm using so well. Thank you.
To the host of CS,I say Thankyou for taking me to class. This is the first of your vids I've watched,I Believe. Yet I'll be watching more for sure!!!
*Subbed*
You are most welcome :)KD
thx alot, mr brown for explaining this. I understood with ease in just about 30 minutes
6yrs later still so much useful
Thank you :)KD
Thank you sir for this video. It's helpful.
Brilliant video sir. Really well explained. I've been stuggling with grasping A2 Boolean Algebra laws because our teacher was rushing the topic too fast, and our Computer Science A level coursebook hardly explains it in such detail...
Glad to help :)KD
Thanks for the great explanation!
I want to cry happy tears, thank you so much Sir❤️
You're welcome :)KD
what an easy to follow break down! thank you
What have I been watching? Whaoooo! I hit the subscribe button 3 minutes into your first video. The voice and explanation...Whaooo! Thanks sooOOoooOOOOooo much.
You are most welcome, and thank you :)KD
Thank you so much! This is very well-explained
Thx sir your voice is so clear and the De Morgan's law really blown my mind
Thanks for the comment. :)KD
I was struggling to understand the equations and tables my school uses to teach. Now I got the grasp! You're an amazing teacher, thank you.
Thank YOU. Delighted to help :)KD
Explained really well. Thank you so much
Brilliantly simple, well explained. Very helpful.
You are most welcome. Thanks for the comment :)KD
Thanks alot sir. Made it very easy to understand. Love the Ascent too.
You are very welcome.
accent*
Great video! Thank you very much :)
You are the best teacher on Earth!
Amaizing video!
Many Million Thanks :)
Perhaps not. But I appreciate the sentiment :)KD
This is a great video, and the narrator has a fantastic voice.
The narrator thanks you for the comment.
Thank you for making this make sense!
You're very welcome :)KD
i like all yo videos sir
they are easy and very modern,you make me like the subject i had faileed and had no intrest in it
THANKS ALOT,WE/I need more videos from you please
Very Good Video, will help me in my digital class, Very well explained..
Now am satisfied with your explanation. Thank you sir.
You are most welcome
You are awesome man!!
Thank u so much for this video, i have a test on this stuff coming up and my teacher is completely useless : 'D Your explanations were much clearer and helped me figure out the concepts much better
Thank you! I have an exam tomorrow and your video is really helpful.
Good luck :)KD
Such a useful video. Thank you so much. I can go and explain Logic gates to my Y10 Computer Science group
Thanks for the comment. I'm not sure I would go this far with ALL of my Y10 class (writing expressions from simple gate combinations is usually enough for mine), but many would benefit from an insight into this.
I'm not sure if this can be considered algebra but I believe it is.
*S* is for *Step*
12:24
(A+B) * (A+C)
*1S1* : = AA + AB + AC + BC
{In binary A squared (A*A) is equal to A, so replace it}
*1S2* : =A + AB + AC + BC
{In addition I can place parenthesis anywhere}
*1S3* : = (A + AB + AC) + BC
*1S4* : = A(1 + B + C) + BC
{In binary any thing plus one is equal to one.
So (1 + B + C) = 1 ... (A * 1 = A)}
*1S5* : = A + BC
And we are done!
Edit: 13:06
A * (A+B)
*2S1* : = AA + AB
*2S2* : = A + AB {Same as *1S2* }
*2S3* : = A(1+B)
*2S4* : = A*1 {Same as *1S5* }
*2S5* : = A
*3S1* ... {Start from *2S2* and continue}
thank you for the explanation. I got stuck there for a moment.
Awesome videos! Thank you for sharing
You're very welcome :)KD
I think it's much easier to understand with circle pictures, or if wires were colored (green = 1, red = 0)
Thanks you for video
Thanks!
This is so helpful!!!
:) Tnx for saying so
Thank you for the understandable video
You're welcome. :)KD
so helpful thank you!
You are most welcome :)KD
I've found that the *absorption law* is the most difficult one to spot. Thankfully, once you learn about K-maps, simplification becomes a much easier and less error prone process. :)
For me, the biggest problem is knowing when to stop. K-Maps are definitely more conclusive.
Thank you so much 🙏🏽🙏🏽
You are very welcome :)KD
damn this is so pog thank you so much
Thanks a bunch!
You're very welcome :)KD
Very nice video
thankyou for this awesome explanation
You're very welcome :)KD
This is so badass!!
Cheers me dear :)KD
Sooo algebraically product rules are covered under addition rules? ..is all that i understoon
Plus that the -. symbol means a type of "sum of.."
Superb clear speaker. Little confused with the NOT graphic and wires jumping over others. Otherwise I will refresh my degree course some 50 years ago in Bolton
Thank you. Hopefully, you made sense of the crossing wires :)KD
I really appreciate you explanation
Delighted to help. Thanks for commenting :)KD
You you suggest a good book that is as good as your explanation in this video. I need to clear many more concepts such as that of Conditional Statements. There is no video I can find where you have covered that concept. Thanks.
might be a silly question but how do you know what input values goes on the truth table?
Not a silly question, but fundamental. Take a quick look at this video:
th-cam.com/video/BnB2m1nXZ84/w-d-xo.html
The idea is to include all of the input possibilities. :)KD
Thank you so much
You're most welcome :)KD
Thank you a lot
You are most welcome :)KD
Thanks sir you lecture really professionally
Thank you :)KD
❤❤❤Thank you so much
You are very welcome :)KD
You are an amazing person
Thank you so much :)KD
Nicholas from Kenya,,, thank you for the good video
My pleasure :)KD
6:57 I don't understand why in Boolean addition 1+1 =1. So, it is not addition mod 2. Is it just the desired definition to correspond to what we want to represent, in this case an OR?
I just noticed, if we follow a mod 2 arithmetic, so that 1+1 =0, then we get XOR.
I'm a beginner but I think I have a good way of thinking about it:
If we think of 1 or TRUE as just any random voltage and 0 or FALSE as no voltage at all - we can say that NO VOLTAGE + NO VOLTAGE = NO VOLTAGE (0+0=0) and that SOME VOLTAGE + SOME VOLTAGE = SOME VOLTAGE (1+1= 1)
So basically 1 just represents SOMETHING and 0 represents NOTHING and when you add SOMETHING with SOMETHING the answer will always be SOMETHING :)
@@other39201 I like that!
Thank you! This is showing genius idea .( greater than in my school BTW )
You are most welcome. :)KD
Dude you rock👍
Thank you :)KD
I didn't know that David Attenborough did boolean algebraic commentary as well. Interesting.
He's one of my heroes. Thanks for taking time to comment. :)KD
Thank you,😘😘
You're welcome :)KD
I really like the way you explain things with your voice it’s like you are voice acting a lore or something.
Thanks for the lovely comment. :)KD
Some one mentioned Boolean algebra and I didn’t know what it was. I watched this, and still don’t know what it is. Thanks, it’s me not you. I swear.
Hi Paradox. You need to be familiar with the fundamentals of logic gates first, and be aware that logic gates can be combined to make useful circuits. Boolean algebra gives us a way to describe combinations of logic gates, that is, a way to describe electronic circuits that perform specific tasks. Simplifying Boolean algebra expressions is a technique that circuit designers can use to simplify circuits. Of course, all that is easier said than done; it takes plenty of practice to become proficient with Boolean algebra (and, to be honest, circuit designers use clever software to do it for them these days). :)KD
@@ComputerScienceLessonsWould you recommend and resources to read / watch before this?
How did (A.B) + (A.C) +B became (A.C)+B in the last. I couldn't understand this step, shouldnt it become A.(B+C)+B ?
I must say I've been around the game for a few years now and I'm being actively involved in teacher training taking many courses on the Isaac platform running many CPD's curriculum's
and...?
thanx ;)
That feel when youtube is far better than listening to the actual teacher.
Sadly, teachers don't come with a 'pause' button :)KD
I wish you were my teacher back then
14:39 Summary Page of all 19 laws
Maybe it belongs on a T-shirt!
How can this be? B V ( B ^ C ) = B ( If we dont have truth table)
You sound like one of the lecturers that used to do the database classes in Murdoch Uni.
I hope they sounded good :)KD
@@ComputerScienceLessons he was the best. Sadly from what I heard he left probably because od funding issues and whatnot. Thanks for your tutorials. I feel like I got a fighting chance now.
good
Trying not to freak out, here spending my Christmas learning my A level course 🤣
Kaway-kaway sa mga gikan sa Moodle. ✋✋✋
3:31
1 ^ A = 1 is true fo 2nd column ?
1 AND A is not necessarily 1. If A = 0, then 1 AND A = 0.
Way better than my proffesor
Thank you :)KD
What of (AUB) =A
thanks , it is very difficult to learn for a child of class IX
Stick with it and take your time. Make sure you are comfortable with the standard searching and sorting algorithms and Big O will be much easier :)KD
Only reason i picked your video was because of the British accent. Hate to admit it but it is what it is.
thumbs up if you just zoomed into the thumbnail for your online test