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Digital Electronics -- DeMorgan's Theorem

  Рет қаралды 103,500

MovieHQ

MovieHQ

Күн бұрын

Пікірлер: 179
@robdouma6382
@robdouma6382 8 жыл бұрын
You are VERY good at teaching....made it so clear. Thank you!
@MovieHQ
@MovieHQ 8 жыл бұрын
Thanks! I really appreciate it.
@mohammedsayed4793
@mohammedsayed4793 10 жыл бұрын
when i dont understand something in class i just come to your videos and it all becomes clear, my professor is horrible, thank you!
@andrewclark3162
@andrewclark3162 9 жыл бұрын
i learnt more in this 15 min video than 3 hours of lecture
@MovieHQ
@MovieHQ 9 жыл бұрын
Andrew Clark Thank you very much!
@Paraclete333
@Paraclete333 9 жыл бұрын
DeMorgan's theorem in a nutshell: BREAK A LINE, CHANGE THE SIGN (I love the way it rhymes!) It took my professor over a month to teach this.
@harshpherwani6590
@harshpherwani6590 7 жыл бұрын
Lmao I feel ya
@james77011
@james77011 3 жыл бұрын
I heard about De Morgan's Theorem many years ago but, it was so confusing... Gave me a headache trying to understand it 🤦
@ghost93700
@ghost93700 9 жыл бұрын
Sir, I can't thank you enough for these tutorials..I'm saving a lot of time using these and all thanks to you!... Please upload more videos in the future.. You're the KZbin's official Digital Electronics Professor who saved students and time.... 1hour=15minutesof your class.....WOWWWW!!. Love you Thanks
@MovieHQ
@MovieHQ 9 жыл бұрын
Thank you very much. I really appreciate you kind words.
@TheSaady20
@TheSaady20 8 жыл бұрын
I'm an electronic engineer and i thank god that you made these videos!
@MovieHQ
@MovieHQ 8 жыл бұрын
+Saad Ahmedsw Very glad to help. Thanks for watching.
@MrJosh6889
@MrJosh6889 8 жыл бұрын
This is a lot better than a stale computer organization text book. Thanks for putting this out.
@MovieHQ
@MovieHQ 8 жыл бұрын
+MrJosh6889 Thank you very much!
@ognimoddd
@ognimoddd 7 жыл бұрын
You explained in about 16 minutes what took my professor an hour and a half. Thank you!!
@MovieHQ
@MovieHQ 7 жыл бұрын
You are welcome. Glad to help.
@davidhe7935
@davidhe7935 8 жыл бұрын
understood the concept in seconds, just break the line and change the sign! Thank you, very helpful and saved a lot of time!
@MovieHQ
@MovieHQ 8 жыл бұрын
You are welcome
@kirin347
@kirin347 9 жыл бұрын
"When you break a line, you change a sign." Love it!
@MovieHQ
@MovieHQ 9 жыл бұрын
+kirin347 Old school. There should be a rap song!! :)
@jaiankrishna1462
@jaiankrishna1462 7 жыл бұрын
kirin347 i
@GarrettMorrisey
@GarrettMorrisey 9 жыл бұрын
Thank you so much for these videos! I have NOTHING AGAINST FOREIGN PEOPLE, but I have a foreign teacher and it is sometimes harder to catch things or understand due to an accent. Your videos clear this up for me.Thank you.
@MovieHQ
@MovieHQ 9 жыл бұрын
Thank you for watching!
@chocobo1
@chocobo1 9 жыл бұрын
A few months ago I remember struggling with truth tables and I found your video which helped me. Now a few months later I youtube "DeMorgans theorem" and your video comes up. Once again you have saved my school life, thank you so much dude.
@MovieHQ
@MovieHQ 9 жыл бұрын
So glad to hear they helped. Thanks for watching!
@TheElz8
@TheElz8 10 жыл бұрын
You Sir are a Prince!, I have struggled for years to remember DeMorgan's Theorem. It seems like child's play now..thank you!
@MovieHQ
@MovieHQ 10 жыл бұрын
Glad to be of help. Now if I can get my wife to agree with you!!
@androiduberalles
@androiduberalles 10 жыл бұрын
Excellent. This was 15 minute video was way more helpful than the 1.5hr lecture my professor did. Thanks.
@MovieHQ
@MovieHQ 10 жыл бұрын
Thanks!. Comments like these keep me going.
@TomOtero1984
@TomOtero1984 4 жыл бұрын
These videos are great! Break the line change the sign. Little phrases like that are what stick when you need to remember on a test!
@MovieHQ
@MovieHQ 4 жыл бұрын
Thanks. That is what I was taught and pass it along.
@kmatera1
@kmatera1 8 жыл бұрын
unbelievable, huge help! thank you for not speaking robot!!!! "break the line, change the sign." genius
@MovieHQ
@MovieHQ 8 жыл бұрын
Thanks!
@michaelangelodino9775
@michaelangelodino9775 10 жыл бұрын
thank you sir. now i can answer my test tomorrow :) God bless you ^^
@Exoorb
@Exoorb 10 жыл бұрын
Honestly, Your videos are amazing. I have learnt so much more watching these videos then I have in lectures. You explain things exceptionally well, you keep it clear, concise, to the point and always provide easy ways to remember things. Thank you so very much!
@MovieHQ
@MovieHQ 10 жыл бұрын
Thank you. Makes it worth doing.
@prestongovender6128
@prestongovender6128 8 жыл бұрын
Amazing tutorials on all these videos. Been binge watching them after being totally clueless trying to understand my textbook. Thank you!
@MovieHQ
@MovieHQ 8 жыл бұрын
+Preston Govender Thanks. Glad I could help.
@innocentkabaso6727
@innocentkabaso6727 2 жыл бұрын
You are an impossible Lecturer,I don't attend Lectures but i have made it Sir;thanks a lot.
@nguyen1314
@nguyen1314 11 жыл бұрын
you are so hlepful ive watch all your digital class it really good keep up the work ! i like how you give us examples and let us do it. THANKS AGAIN!
@jerredblunt1112
@jerredblunt1112 9 жыл бұрын
Simply awesome. True sign of intelligence is making hard stuff easy to learn. Very well done!
@MovieHQ
@MovieHQ 9 жыл бұрын
Jerred Blunt Thank you very much!!
@kimmany1999
@kimmany1999 11 жыл бұрын
Thank you so much for your videos. Your explanations are clear and concise and very easy to follow. You have helped me immensely.
@karenartiom
@karenartiom 10 жыл бұрын
I wish my teacher could explain like you. Thank you very much
@MovieHQ
@MovieHQ 10 жыл бұрын
Thanks. I appriciate it!
@chingizmizambekov6078
@chingizmizambekov6078 8 жыл бұрын
Thanx a lot :) much more explanatory than our course book :)
@MovieHQ
@MovieHQ 8 жыл бұрын
+Chingiz Mizambekov Thank you!
@clarksarge4750
@clarksarge4750 Жыл бұрын
This is a great explanation of digital logic.
@MovieHQ
@MovieHQ Жыл бұрын
Thanks!!
@shadentalal7117
@shadentalal7117 11 жыл бұрын
THAAAANK YOU SO MUCHH!!! God bless u
@metaphyzxx
@metaphyzxx 10 жыл бұрын
This was explained so much more functionally than my teacher did it!
@MovieHQ
@MovieHQ 10 жыл бұрын
Thank you. I appreciate it.
@konev13thebeast
@konev13thebeast 10 жыл бұрын
how does this video only have 8 likes? Its awesome
@MovieHQ
@MovieHQ 10 жыл бұрын
Thanks for the kind words. I really do appriciate them.
@sparshgupta3827
@sparshgupta3827 9 жыл бұрын
man wow... i got it all in one go!
@instaminox
@instaminox 7 жыл бұрын
Simple and straight forward! best wishes :)
@MovieHQ
@MovieHQ 7 жыл бұрын
Thanks!!
@JakobRobert00
@JakobRobert00 10 жыл бұрын
0:50 "When you break the line, you change the sign." Did you make this rhyme on purpose? It is a really good way to memorise it.
@MovieHQ
@MovieHQ 10 жыл бұрын
It was taught to me when I took digital. Not sure where it originated from.
@belhdawa
@belhdawa 10 жыл бұрын
Oh now i will not forget this sentence Thanks XD
@mandochali5343
@mandochali5343 7 жыл бұрын
This is really helpful. keep it up, God Bless You.
@seandon3827
@seandon3827 7 жыл бұрын
if I do good on my exam its because of you :)
@MovieHQ
@MovieHQ 7 жыл бұрын
Glad to help.
@dabreadman6567
@dabreadman6567 7 жыл бұрын
Man you videos are a God send!
@MovieHQ
@MovieHQ 7 жыл бұрын
Thanks!
@dabreadman6567
@dabreadman6567 7 жыл бұрын
You're welcome, Don't stop what you're doing!
@dorrkboy
@dorrkboy 7 жыл бұрын
This video really helped me, i was making this far to complex ... thanks!
@MovieHQ
@MovieHQ 7 жыл бұрын
Glad I could help!!
@dacintra5110
@dacintra5110 8 жыл бұрын
all your videos are superb! Very helpful.
@MovieHQ
@MovieHQ 8 жыл бұрын
+Omran Basma Thank you very much!
@Owl90
@Owl90 7 жыл бұрын
my dude! You helped me so much! Thanks a lot for these videos!
@MovieHQ
@MovieHQ 7 жыл бұрын
You are welcome. Glad they helped.
@BluEBomBeR41
@BluEBomBeR41 7 жыл бұрын
Thank you! I love how you explain things.
@MovieHQ
@MovieHQ 7 жыл бұрын
Thanks!!!
@1lumpen
@1lumpen 9 жыл бұрын
I'm still having trouble, but you do a good job. I understand a little bit better, and I did okay on your questions, but then the truth table lost me again.
@1lumpen
@1lumpen 9 жыл бұрын
Also, on the bubble pushing. When you have two different initial input gates, how do you determine what kind of gate the third gate becomes??? I don't see anything intuitive in the answers given.
@MovieHQ
@MovieHQ 9 жыл бұрын
Steve Matz It really depends on the goal of the outcome. If you are converting to all NAND gates, then you would convert the ORs to NAND and convert whatever others you must to create NANDS. I was mostly just showing you how to do it, not to really have a purpose.
@sunimalsenaratne3180
@sunimalsenaratne3180 7 жыл бұрын
Thank you so much for great tutorials
@MovieHQ
@MovieHQ 7 жыл бұрын
You are welcome!
@333shiraz
@333shiraz 10 жыл бұрын
sooo awesome teaching thanks man i wish i could give 1000 likes!!!!!
@ronaldrupard5443
@ronaldrupard5443 8 жыл бұрын
I understand how the bubble pushing works schematically, but I am still a little lost on the significance of this. I understand in the one example how you were able to "demorganize" the two and gates and 1 or gate into 3 nand gates. This made sense. But almost every other example you have just as many types of gates as you start with, so is there really no significance here, just learning the innerworkings of bubble pushing? Thanks! the videos are awesome.
@RustedNation
@RustedNation 7 жыл бұрын
Thank you sir for the knowledge!
@MovieHQ
@MovieHQ 7 жыл бұрын
You are welcome!
@ishezthephenom6482
@ishezthephenom6482 7 жыл бұрын
You guys fantastic...keep up
@MovieHQ
@MovieHQ 7 жыл бұрын
Thanks!
@micaman13
@micaman13 10 жыл бұрын
Loving these videos. Do you think you could do a sop to pos practice problem using De Morgan's Theorem? My professor has done it once or twice but went to fast for me to get what he was doing. I would love to see how you would teach it.
@MovieHQ
@MovieHQ 10 жыл бұрын
Can you give me more detail! Do you mean to take a sop with most if not all inverted then break lines or sop with lines already broken and convert to pos by combining lines. Give me an example and I will see what I can do.
@ramyapriya7824
@ramyapriya7824 6 жыл бұрын
GOOD WORK PLS UPLOAD MORE VIDEOS AND THANK YOU
@MovieHQ
@MovieHQ 6 жыл бұрын
Thanks!
@LostInLeiden
@LostInLeiden 9 жыл бұрын
Really good video, thanks a lot!
@MovieHQ
@MovieHQ 9 жыл бұрын
Thanks for watching.
@MovieHQ
@MovieHQ 11 жыл бұрын
Great to know it helped.
@RealLoveDragon
@RealLoveDragon Жыл бұрын
Thanks king!👑
@GD-jx1sb
@GD-jx1sb 7 жыл бұрын
Starting at the six minute mark, the third and fourth examples are wrong. Why is there no sign change or complement for B + C? Shouldn't the final answer be A + B'C'? Same with the fourth example why are you not changing the AND operator to an OR operator for A'C'?
@MovieHQ
@MovieHQ 7 жыл бұрын
These are both correct. For #3: B+C has 2 lines over them. If you were to break those 2 lines, you would need to change the sign 2 times. Or just cancel the 2 lines (since they are the same length. Same for #4.
@DanDaddyD
@DanDaddyD 7 жыл бұрын
this is gold
@MovieHQ
@MovieHQ 7 жыл бұрын
Thanks!
@Mental1993
@Mental1993 10 жыл бұрын
You are awesome! thank you!
@MovieHQ
@MovieHQ 10 жыл бұрын
Thank you.
@victoryoyah6600
@victoryoyah6600 7 жыл бұрын
like your lectures....now which is the most preffered method to use in simplifying logic equations?
@MovieHQ
@MovieHQ 7 жыл бұрын
Really it depends. I use k-maps for most things. It is just quicker. If there are small expressions that are basic, I will use Boolean algebra.
@MovieHQ
@MovieHQ 11 жыл бұрын
Thanks. Glad to help.
@MovieHQ
@MovieHQ 11 жыл бұрын
Great! Glad it helped.
@12131ize
@12131ize 9 жыл бұрын
I LOVE YOU MAN !!!
@MovieHQ
@MovieHQ 9 жыл бұрын
Thanks!! I think!! :)
@Adeo83jcso
@Adeo83jcso 9 жыл бұрын
cs made simple hats off^^^
@zishy92
@zishy92 7 жыл бұрын
how would you use de morgans law on this expression !C(AB+!A!BD+!AB!D) != this means it has a single line above please help
@solomonthell7589
@solomonthell7589 9 жыл бұрын
Why didn't you change the sign between (B+C) When you broke the line? 3:46
@MovieHQ
@MovieHQ 9 жыл бұрын
I did not break a line for that one. A and B+C both had 2 lines over them. When you have 2 lines, they cancel each other out. If you broke lines, you would have to break 2 lines and change the sign twice (going back to waht you had in the first place).
@solomonthell7589
@solomonthell7589 9 жыл бұрын
Ok ic now...Thanks man God bless u.
@shutdahellup69420
@shutdahellup69420 7 жыл бұрын
15:31 in question no.02 how did the NAND gate after bubble pushing became OR gate? can u please explain??
@MovieHQ
@MovieHQ 7 жыл бұрын
When bubble pushing, you change the gate, add bubble where there were none and remove bubbles that were there. NAND becomes OR with output bubble removed and input bubbles added. The input bubbles then "float" back to the outputs of the other 2 gates.
@shutdahellup69420
@shutdahellup69420 7 жыл бұрын
MovieHQ oh!!! thanks a lot for quick reply... love these videos...keep up the good work.
@User89018
@User89018 3 жыл бұрын
I am confused when the problems get larger I can do the simple ones but my teachers makes this hard very hard to understand I need help with it maybe I am not smart enough to get these things
@MovieHQ
@MovieHQ 3 жыл бұрын
Just take them line by line and and don't try to break too many things at once. Start with the lines closest to the terms (under other lines) and work up breaking one line and changing the sign at a time. You will get there.
@DC_Gaming2447
@DC_Gaming2447 9 жыл бұрын
I know you said you can break a line but can you reconnect it while changing the gate again? like saying: A(not) * B(not) is the same as (not) A+B?
@MovieHQ
@MovieHQ 9 жыл бұрын
+John Cobb Yes. Connect a line and change the sign.. Same thing in reverse.
@DC_Gaming2447
@DC_Gaming2447 9 жыл бұрын
+MovieHQ what if you run into a 1+A(not) or a 1*A(not)
@MovieHQ
@MovieHQ 9 жыл бұрын
+John Cobb Anythings ORed with a 1 is a 1... Anything ANDed with a 1 is just the thing (A(not)).
@kapilkumaroctober
@kapilkumaroctober 8 жыл бұрын
Why can't we break the line and change the sign to plus for the 4th example where you have ________ ______ ? AC
@MovieHQ
@MovieHQ 8 жыл бұрын
+Kapil Kumar If you are talking about the 4th one on the list at around 5:07, you could break the line and change to + however, there are 2 lines. You would need to then break the second solid line therefore changing it back to *. Remember that lines of the same length (covering the same items) just cancel out. Hope that helps and thanks for watching.
@Lone1025
@Lone1025 7 жыл бұрын
You're awesome!
@MovieHQ
@MovieHQ 7 жыл бұрын
Thanks!
@Jinz007
@Jinz007 10 жыл бұрын
This helped a lot...
@MovieHQ
@MovieHQ 10 жыл бұрын
Thank you!
@chummyigbo8844
@chummyigbo8844 8 жыл бұрын
You very good. Thank you
@MovieHQ
@MovieHQ 8 жыл бұрын
Thanks for watching!
@MrDivad006
@MrDivad006 9 жыл бұрын
Great video! What is your profession if I may ask?
@MovieHQ
@MovieHQ 9 жыл бұрын
Lowinator Thank you. I am a professor and assistant dean at a college.
@T1000315
@T1000315 9 жыл бұрын
MovieHQ You are currently saving my life on my DE final tomorrow. I hope there is some way I can repay you. Also, where do you teach? I wish the guys teaching me posted gaming videos in their spare time haha.
@MovieHQ
@MovieHQ 9 жыл бұрын
T1000315 Glad I could help you out. I am located in Lexington Kentucky. I agree, not many teachers play games in their spare time and post them. I wish I had more time to play/post. I do what I can.
@MovieHQ
@MovieHQ 9 жыл бұрын
+razorIaIa I use these as my lecture videos as well. I am sure I have students who feel the same way about me. :)
@james77011
@james77011 3 жыл бұрын
At time 3:50 I thought the sign below B+C should have been changed to B•C Or did i miss something? 🤔
@MovieHQ
@MovieHQ 3 жыл бұрын
There are 2 lines that are both the same length so they cancel out. If you changed the sign, you would need to change it twice since there are 2 line taking you back to +
@TacoDaddy-mr8ig
@TacoDaddy-mr8ig 5 ай бұрын
Im watching your video again. I have also been watching another video and reading a book that has some rules about what you showed at time 3:50 i jus want to make sure the rules in the book applies to your video as well. I will take pictures and send to you for more clarification ​@@MovieHQ
@MovieHQ
@MovieHQ 5 ай бұрын
@@TacoDaddy-mr8ig Those rules all still apply to Boolean algebra so they should apply to your book. It might be written differently. I have tried to make it as simple as possible.
@MovieHQ
@MovieHQ 11 жыл бұрын
Thank you!
@johnlang555
@johnlang555 8 жыл бұрын
at 9:17 wouldn't you have been left with just BC(A+1), how did you cancel the 3 A's ?
@MovieHQ
@MovieHQ 8 жыл бұрын
+Maximilian Ortiz Remember the rule of ORs. Anything ORed with a 1 is a 1. Does not matter how many terms or what the terms are.
@johnlang555
@johnlang555 8 жыл бұрын
Oh ok so if it is A + 1 or B + 1 it will always result to 1. Now how about if it was A + B + 1 will the result also be 1?
@MovieHQ
@MovieHQ 8 жыл бұрын
+Maximilian Ortiz Those will always result in a 1.
@johnlang555
@johnlang555 8 жыл бұрын
MovieHQ thanks for your help
@brokenangel2513
@brokenangel2513 7 жыл бұрын
very good
@MovieHQ
@MovieHQ 7 жыл бұрын
Thanks!
@maxduncan7090
@maxduncan7090 6 жыл бұрын
lifesaver
@MovieHQ
@MovieHQ 6 жыл бұрын
Thanks!
@rakeshkumarray1016
@rakeshkumarray1016 8 жыл бұрын
very nice
@MovieHQ
@MovieHQ 8 жыл бұрын
+Rakesh Kumar Ray Thanks!
@NebulaWorm
@NebulaWorm 6 жыл бұрын
oh ini dosen mekatron gue
@ohmakademi
@ohmakademi 9 жыл бұрын
good lesson. Thank you so much
@MovieHQ
@MovieHQ 9 жыл бұрын
+DİJİTAL ELEKTRONİK Thank you for watching and the comment!
@ohmakademi
@ohmakademi 9 жыл бұрын
thanks
@americanclicker516
@americanclicker516 9 жыл бұрын
I have seen your videos and they are perfect.In fact i use bulean algebra in school and except that i also use other things that you unfortunately didnt have like for ex The diamond code,huffman code,hamming,bistables etc :/ can you help me with a good channel that has these?
@MovieHQ
@MovieHQ 9 жыл бұрын
American Clicker Unfortunately, I do not know of any other videos that cover those. I am sure there are some out there. Those are items we do not cover as part of or basic digital class.
@wanyoikedanny472
@wanyoikedanny472 6 жыл бұрын
thanks
@MovieHQ
@MovieHQ 6 жыл бұрын
You are welcome.
@brendajahongo942
@brendajahongo942 8 жыл бұрын
you really are a good teachercan you please show me how to draw a logic gate using one gate onlyI always get that question wrong
@MovieHQ
@MovieHQ 8 жыл бұрын
+Brenda Jahongo Thank you. I cannot post another video, but I can give you some tips. First step is to bubble push the gates until you have the type you need (OR or AND). Then keep in mind that a NAND or NOR gate with the inputs tied together acts as a NOT gate. That should get you through pretty much anything.
@brendajahongo942
@brendajahongo942 8 жыл бұрын
+MovieHQ that's bad ,your videos are really good ...thanks for the tips , I think I am getting something.But I have one more question on 2's complement..Have do I solve this: -(05.50)decimal -(15.25)decimal?
@MovieHQ
@MovieHQ 8 жыл бұрын
+Brenda Jahongo I am not sure what you mean. 2's compliment would be for Binary numbers not decimal.
@brendajahongo942
@brendajahongo942 8 жыл бұрын
+MovieHQ but i just got a question like...
@MovieHQ
@MovieHQ 8 жыл бұрын
+Brenda Jahongo Sorry I could not be of more help. Maybe you need to convert to Binary first then do 2's compliment? I have no idea.
@brokenangel2513
@brokenangel2513 7 жыл бұрын
شكرا ممتاز شرح
@kaadshah7737
@kaadshah7737 9 жыл бұрын
sorry but i really understood nything after 12.02dat concept of bubble pushing would plz explain me ...:( for the very first time it happened that i couldnt understand ur explainatioin..i felt bleak
@MovieHQ
@MovieHQ 9 жыл бұрын
kaad shah Bubble pushing is using logic diagrams to perform DeMorgan's Theorem. Probably not something you will see too often honestly. Not sure I could explain it any better in text than I did in the video.
@kaadshah7737
@kaadshah7737 9 жыл бұрын
MovieHQ yess finally got d point
@MrSarimjavaid
@MrSarimjavaid 8 жыл бұрын
Thaaankkkk Youuuu
@MovieHQ
@MovieHQ 8 жыл бұрын
+Sarim Javaid welcome
@prinxegupta
@prinxegupta 8 жыл бұрын
You can be a real teacher man. But just one complaint I have from you. Please focus a little bit more on fundamentals and working of things. You are a wonderful teacher but the main issue with our education sytem is that we learn things but never understand how things work. You can work on that and be a wonderful and great teacher. Please pls don't only focus on the concept. Focus on the fundamentals as well.
@MovieHQ
@MovieHQ 8 жыл бұрын
+Prince Gupta This whole series is not designed for engineering level students. It is more for the technician level whop does not really need to know every detail of the whys. They just need the hows. I appreciate the comment about being a teacher. I have been a college professor for almost 20 years. :) This is the method that works best for the students I teach in the technical college.
@harshpherwani6590
@harshpherwani6590 7 жыл бұрын
you're doing a wonderful job, keep up the good work thank you for helping us all
@MovieHQ
@MovieHQ 7 жыл бұрын
Thanks!!
@harshpherwani6590
@harshpherwani6590 7 жыл бұрын
you deserve it :)
@98xcxc
@98xcxc 7 жыл бұрын
?Can I get your power point
@MovieHQ
@MovieHQ 7 жыл бұрын
I am sorry, but I do not have them any more.
@sluttyfuck19
@sluttyfuck19 9 жыл бұрын
I like
@MovieHQ
@MovieHQ 9 жыл бұрын
Thanks!
@3333218
@3333218 10 жыл бұрын
(8:20) You lost your chance to do an ACDC joke.
@MovieHQ
@MovieHQ 10 жыл бұрын
Yes, there are a lot of those in digital.
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