Karnaugh Map (K' Map) - Part 1

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  • Опубліковано 27 жов 2024

КОМЕНТАРІ • 1,1 тис.

  • @anjaneedevi4402
    @anjaneedevi4402 Рік тому +254

    This nvr gets old...8 yrs gone..
    Still NO ONE can replace NESO ACADEMY..!!🔥
    Salute bro..!

  • @sarvagyamaithani2093
    @sarvagyamaithani2093 4 роки тому +1248

    tomorrow is my digital's end sem. exam and here I am learning everything at once just because of your very simplifying teaching skills

  • @karan51ngh
    @karan51ngh 4 роки тому +477

    trust me, this is the best video for K-Maps on UA-cam....dont go anywhere else...
    Thanks man!
    I'm a CSE student who hates electronics....
    This thing's a blessing in disguise!

    • @magendiravarman2775
      @magendiravarman2775 2 роки тому +4

      CT,Me too... and tomm my digi exam gonna to happen 😬

    • @vkmsd007
      @vkmsd007 2 роки тому

      I am believing you man even I am cse student i am having sem exam in just 1 day

    • @hardikrajpal2410
      @hardikrajpal2410 2 роки тому +8

      ✋🏽CSE student from IITB. This man teaches better than our prof.

    • @infinityxtanishq8712
      @infinityxtanishq8712 2 роки тому +5

      @@hardikrajpal2410 sab jga ye bakchodi padhate hai? Sed

    • @manjuuday3565
      @manjuuday3565 2 роки тому +2

      @@hardikrajpal2410 chal jootha

  • @Arien17k
    @Arien17k 4 роки тому +248

    The sad thing is that I have to bleed (pay) 1300€ each semester for crappy lessons and crappy "professors" that don't teach me anything, thanks to covid19 now they don't even do lessons just upload crappy slides, such a scam... At least i can stay at home and study quality material. Many thanks Neso Academy.

    • @varunprasannan
      @varunprasannan 3 роки тому +12

      But still had to pay the full fess right? :/

    • @Arien17k
      @Arien17k 3 роки тому +9

      @@varunprasannan obviously

    • @granjeethreddy6730
      @granjeethreddy6730 3 роки тому +1

      Yeah man!!

    • @otismilburn1052
      @otismilburn1052 3 роки тому +9

      You should know
      "We pay not for the lectures, we pay for the degree"
      UA-cam won't provide you degree

    • @sohamshinde1258
      @sohamshinde1258 3 роки тому +2

      they are the biggest burden on economy

  • @d_evil2416
    @d_evil2416 3 роки тому +3369

    Most of engineering student would be watching this vdo a night before their exam😂😂😂

  • @WasifAnton
    @WasifAnton 7 років тому +412

    lol every time i set at the class im like WTF is going on..im not ganna pass the exams, then i remember that i got the Neso Academy
    Thank you man :)

    • @samimahassan1716
      @samimahassan1716 5 років тому +17

      when i dont understand anything i feel stupid but when i came here i understand that im not stupid but the teachers dont explain well

    • @saicharanmarrivada5077
      @saicharanmarrivada5077 4 роки тому

      @@samimahassan1716 so damn true

    • @balapranav7096
      @balapranav7096 4 роки тому +7

      Same here bro. Our DSD sir is like blah blah blah, and with online classes, it's still worse. And I am like holy shit, this time I am gonna flunk my exams and then I remember Neso Academy and their beautiful way of explaining things.

    • @MohdDanish-hv9ym
      @MohdDanish-hv9ym 4 роки тому

      @@samimahassan1716 correct

    • @majormac7814
      @majormac7814 3 роки тому

      as a current students its absolutely ridiculous how much higher education over complicates this stuff

  • @shreyxnsh.14
    @shreyxnsh.14 Рік тому +27

    Neso Academy helping engineers pass since a decade!!! Mind blowing 🤯🤯

    • @anishagupta3951
      @anishagupta3951 11 місяців тому +1

      Can someone please explain it to me how's in the last step we got BC' (c bar) [it should be BC according to the coloum right ?? ]

    • @amaanjamal7744
      @amaanjamal7744 Місяць тому +1

      @@anishagupta3951 because C is written as 0 ... thats why we put compliment over c

  • @yannimohamed2349
    @yannimohamed2349 5 років тому +102

    I smiled at the end of the lecture, after understanding this ordeal for so long. You have decoded a mystery for many of us in the digital electronics course. Much respect and many thanks. :)

  • @kerenchristina536
    @kerenchristina536 4 роки тому +4

    Wherever u r .. and whoever u r.. just be blessed.. god bless u.. and oh my.. the best lectures ever...thank u

  • @fr3nesi
    @fr3nesi 5 років тому +85

    i have a midterm tomorrow on this, explained it better than my prof did :)

  • @larsfinlay7325
    @larsfinlay7325 Рік тому +13

    I got a 97% in upper level formal logic when I was in university. I asked the professor at the end of the course (I majored in English Literature) what applications does formal logic have in the real world? he told me that it's used for upper level philosophy courses and proofing. then he kinda just was done talking to me. I wish I'd found this video back in 2014 but finding it now is the next best thing. thanks for making this resource freely available on youtube. best wishes.

  • @christiangallo241
    @christiangallo241 2 роки тому +22

    I have to say. I have a midterm exam in a couple of days and was having difficulty understanding the reasoning behind k-maps. You really put things in the simplest form, making it very easy to understand. I really appreciate your work, and hope u keep helping us on our educational journey. Thanks again!

    • @sravanr2275
      @sravanr2275 Рік тому

      i have mid exams in 2 days bro Today February 11th Saturday i have exam on February 13th Monday bro but i can't able to concentrate on this i don't know what to do now

    • @MUNIR_FF011
      @MUNIR_FF011 Рік тому

  • @rudravyas1715
    @rudravyas1715 3 роки тому +31

    The moment i saw the playlist i stopped attending digital lectures in college 🤣🤣 thanks to neso academy 🥳🥳🥳

  • @yaminimenda257
    @yaminimenda257 2 місяці тому +1

    From the Engineering 1st year I'm watching neso.. Best Source ever... ❤.... It'll never gets old...

  • @richaprasad4344
    @richaprasad4344 4 роки тому +12

    Sir, this is geniuly the best lecture please don't stop making videos as we need your videos more than any book or professor 😄.You are doing a great job .

  • @swetachaudhary9220
    @swetachaudhary9220 3 роки тому +5

    thank you so much sir. your teaching method, your style, your knowledge, your explanations are just wonderful. now, i don't have to attend online lecture with not much information. I can just watch your videos and make my exam better and I am learning with interst, too. thank you for adding this much value, knowledge and information with fun. we engineears are greatful to you. thank you so much.

  • @jwfcp
    @jwfcp 8 років тому +5

    Thanks, I'm really enjoying these.
    A simpler way of explaining why the rows are the way that they are is to say that the person writing the chart is organizing them in a way so that going from one cell to its adjacent neighbor will only change the state of one variable at a time. By placing all of the divergences of abc immediately next to it, you can readily pick out the reductions for a'bc, ab'c and abc' if they are available.

  • @horizon9370
    @horizon9370 9 місяців тому +1

    It's a 9 year Old Video still it is the best all over The UA-cam..... Thankyou Neso Academy For saving my semester Huge thank You 🙌🙌🙌🙏🙏

  • @msatyabhaskarasrinivasacha5874
    @msatyabhaskarasrinivasacha5874 2 роки тому +6

    Complex topics with simple 5 min video....I still admire how's that possible... hats off to your hardwork...

  • @abulkalam6693
    @abulkalam6693 2 роки тому +22

    The quality of your lecture is so amazing that even after seven years of this video, it seems latest and also it is the best 👍

  • @pature9658
    @pature9658 2 роки тому +10

    "You just fill the cells throughout your life without actually knowing what is going on inside it." Thank you man. That is really eye opening. Best k map video 👍

  • @vishalsathiaseelan679
    @vishalsathiaseelan679 3 роки тому +1

    Sir you are the best. Thank you so much. I am doing Electrical Electronic Eng, & my professor doesnt know how to teach us. Just told us to memorize. Thank you so much for explaining HOW the KMAP is formed. You are the BEST sir. Love from MALAYSIA.

    • @circuitsanalytica4348
      @circuitsanalytica4348 3 роки тому +1

      Dont memorize concepts, understand it and you will never forget it. You are really blessed to have platforms like Neso......

  • @sananaz4291
    @sananaz4291 3 роки тому +3

    You made my day by making it easy to understand the K map. Thank you so much for your deep concept about it.

  • @aadhilm4319
    @aadhilm4319 2 роки тому

    Trust me guys... This channnel is beyond worsds and helps me to pass my exam, they provide every bit of details so there is no chance of doubts. In my case, due to lack of internals, I had to repeat the subject once again, one of friends recommended the channel and rest is history.

  • @markgesaka8836
    @markgesaka8836 Рік тому +10

    I am watching this video 8 years later but guess what? It is really helpful and am grateful that i have understood. OLD IS GOLD.....VIVA!

  • @markfinn825
    @markfinn825 Рік тому

    Your videos have always been good. Since your English seems to have improved they are now easier for me to understand. Good work

  • @tarunraghav7093
    @tarunraghav7093 7 років тому +3

    best online lecture . I missed my school class so I searched it on you tube and what I got is best.

  • @harshitnema4197
    @harshitnema4197 5 років тому +18

    Last moments of lectures contain very good example of not giving up from learning new things just by having some difficulties in starting, hail to you NESO .

  • @TinksDizzyGizmo
    @TinksDizzyGizmo 9 років тому +19

    Writing exams on this soon, was so in the dark around this after this vid, I understand so much better. Awesome, THANK YOU.

  • @seacaptain72
    @seacaptain72 5 років тому +4

    I take my FE exam here in a month, and Neso, you have had the most concise, clear, explanatory videos I've found on youtube. I can't tell you how much I appreciate these. And when I pass that exam, I'm going to throw some money your way. Thank you so much for making these videos.

  • @memo6032
    @memo6032 2 роки тому +3

    I saw multiple videos on this but I just couldn't get it. For sure, I could get 'how' to do a kmap, but I had no idea 'why' it works. It had seemed like magic even though there should be a simple logic to it. So, thanks a lot! I had to watch this twice for it to click but at least finally now I can skip to the other lesson in my text book with a clear conscience.

  • @ansh6848
    @ansh6848 2 роки тому +1

    That's super cool that this man explained what's going inside a K'Map and that's what I was looking for cause in schools they told us to learn that.

  • @rohitshimpi788
    @rohitshimpi788 4 роки тому +7

    Better than any other explanations on UA-cam ❤️

  • @vyaparimaithree9881
    @vyaparimaithree9881 4 роки тому +1

    The content and the way u r explaining reaches us very easily.Thank u so very for helping us.

  • @kingshukbiswas2723
    @kingshukbiswas2723 3 роки тому +9

    At first, the lecture was tricky, but at then end, it all got cleared. A big shout-out to Neso Academy for making learning a bit easier❤

  • @cook2connectwithsrivastava181
    @cook2connectwithsrivastava181 11 місяців тому

    u were so right abt the college teachers...they didnt tell us even the full form of K...so forget abt the basics ...u taught very well sir..thx for the lecture sir

  • @MohitK96
    @MohitK96 8 років тому +570

    I feel to donate my tution fee to Neso academy

    • @harishbirhman
      @harishbirhman 7 років тому +48

      www.nesoacademy.org/donate donate there.

    • @magmathrower2382
      @magmathrower2382 7 років тому +14

      good idea

    • @SpaceJesus25
      @SpaceJesus25 6 років тому +16

      im the better harish

    • @Malik-dn8ne
      @Malik-dn8ne 5 років тому +2

      they are already getting alot from advertisements xD

    • @senkottuvelan
      @senkottuvelan 5 років тому +3

      @@Malik-dn8ne Not the investment they made.

  • @ningammakenchannavar934
    @ningammakenchannavar934 5 років тому +4

    I thank to nesco academy , you people explained it in easy and understanding way I understood this concept clearly thank you so much

  • @DineshRamSai
    @DineshRamSai 5 років тому +39

    Mr.Stark, I feel soo..... good after listening to this lecture.

  • @jadenjoseph2746
    @jadenjoseph2746 4 роки тому +4

    Best explaination ever in UA-cam . This lec solved all my doubt. 5/5
    Stars amazing.

  • @deepakkumarmehto9919
    @deepakkumarmehto9919 8 років тому +4

    Sir, i liked your video very much. It is most useful for me.
    It's a suggestion that when you tell that you teach this in previous video so you have to mentioned that video or lecture number for refrences.

  • @youbobasumatary
    @youbobasumatary 3 роки тому

    Today is my digital electronic exam and i'm learning it now...thanks a lot brother..may god bless u

  • @tamarazin2797
    @tamarazin2797 9 років тому +4

    sir u r the life savior.... tomorrow i will hv my DLD xm and ur lectures helped me a loot. pls keep me in ur prayer..

  • @shivamthakurthakur7797
    @shivamthakurthakur7797 4 роки тому +1

    The way of explaining is unique.
    Thankyou so much sir..

  • @ujjwalnath4240
    @ujjwalnath4240 7 років тому +12

    This dude is legit. You might just have saved me in day after tomorrow's exam.

  • @kdrama_kpopworld_
    @kdrama_kpopworld_ 3 роки тому +3

    Why didn't i know about neso academy before 😭 it a little bit late..my digital electronics are on feb 11th...your explanation helped me a lot!!!

  • @abdxlive
    @abdxlive Рік тому +3

    Some Videos Never Old ✨ Thanks Neso Team

  • @cruzmonte4614
    @cruzmonte4614 7 років тому +2

    Just wanna say THANK YOU VERY MUCH for these wonderful lecture i understood it much better than been taught in a class....
    Thank you once again NESO ACADEMY, keep these good works up
    Much love

    • @circuitsanalytica4348
      @circuitsanalytica4348 3 роки тому +1

      Students of your generation are really lucky to have a platform like Neso...

  • @arundhutimukherjee1412
    @arundhutimukherjee1412 3 роки тому +12

    undoubtedly 1000x times better than my college... once i pass out and get a job I will donate money here rather than going to alumni in my college to tell how great my college is.

  • @opbankolia
    @opbankolia 8 років тому +1

    Sir,
    I am from India & I have seen about all videos of electronics on Neso Academy.Your videos are awesome .Your voice is so clear and sweet.your explanation is brilliant & nice.I support u.God bless u sr.thank u

  • @ramyaanandan7800
    @ramyaanandan7800 7 років тому +3

    great!!!! explanation sir!!! no one will explain this topic with this much clarity...
    thanks a lot sir..

    • @circuitsanalytica4348
      @circuitsanalytica4348 3 роки тому

      Yes, really nice video, you people are really lucky to have platforms like this....

  • @thehope7689
    @thehope7689 4 роки тому +1

    Your way of teaching is very nice that's why I love neso academy

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    @kushalswarup2662 3 роки тому +75

    I can't imagine my btech withiut this playlist🤩🔥.

  • @kapilumrania
    @kapilumrania 2 роки тому +1

    You're One of the finest teacher available on this planet

  • @canoselshekinah96
    @canoselshekinah96 3 роки тому +4

    It made perfect sense sir. Thank you very much for your amazing lecture!

  • @himanshus428
    @himanshus428 5 років тому +2

    my concepts of kmaps are now clear after completing 4 years of my BE. Thanks @Naso acadamy

  • @ankanmukherjee873
    @ankanmukherjee873 7 років тому +4

    Sir u are the real teacher..!!!

  • @susenakodumuri2667
    @susenakodumuri2667 5 років тому

    Dear, you are teaching is really excellent... Now I know that what is proper teaching way.... It's very clear....

  • @mohitranjan8876
    @mohitranjan8876 5 років тому +3

    Never got such an in-depth explanation of K-Maps!!!
    Sir, you are simply great

  • @nitismita1035
    @nitismita1035 2 роки тому

    I wish I got this kind of teaching in every subject. Engineering would be bliss. But thanks a lot sir, you saved so many engineers.

  • @ceezgeez1793
    @ceezgeez1793 7 років тому +27

    You just said exactly what happened in my class. Professor showed how to do it but not explain it!!! WOW!!! at 13:55

    • @zattiya
      @zattiya 5 років тому +1

      Did you mug it up?

  • @Adborn-cg7wo
    @Adborn-cg7wo Рік тому +17

    13:36 Absolutely true brother and thanks for your effort

  • @davidduarte543
    @davidduarte543 7 років тому +2

    Thank you very much since the begining of the semester i was using karnaugh maps and i didn't know why we were going from 01 to 11

    • @circuitsanalytica4348
      @circuitsanalytica4348 3 роки тому +1

      List of the students dont know this and Neso explained it very well....

  • @ceezgeez1793
    @ceezgeez1793 7 років тому +3

    My professor showed how to solve with a K map but never fully explained it like you did. THANK YOU!!!!!

  • @shubham_dev_
    @shubham_dev_ 4 місяці тому +1

    13:50 You are right! I could not understand this in college. Thanks for such a nice explanation.

  • @anthonysteinerv
    @anthonysteinerv 4 роки тому +4

    Thanks for this video, I was kinda closed mind about this K-map thing, I've always thought that Graphical Methods are a waste of time, and I always preferred to do the Algebra, now I'm kinda interested in this one at least, it's crazy how we want to apply the a+a(bar) = 1 axiom, but tbh what I don't like about them is precisely how some things seem magical until somebody explains them, for example: I don't get why we have to group thing in powers of 2, like for me, it doesn't make sense how can group 4 ones. And my teacher is kinda good, but tbh you explained it better, for example when u showed which ones have adjancy, u made it simpler, my teacher was like drawing crazy stuff lmao, thanks again.

  • @aayamoza8495
    @aayamoza8495 8 років тому +2

    Very very good lecture... I was so confused about K map but now its so crystal clear. Thank you!

  • @mesolagic
    @mesolagic 6 років тому +3

    This was a lot easier to follow compared to my in class lecture. Thank you!

  • @lakshyakaparwan8984
    @lakshyakaparwan8984 7 місяців тому

    i got a test at 2 oclock today and its 12 now all i can say is thank you for making this content

  • @deepaksahoo9336
    @deepaksahoo9336 6 років тому +3

    You teaching is so good that even if i play in x2 speed, i can understand everything

    • @musk-xx
      @musk-xx 5 років тому +1

      Yr concentration is high man
      If i left 2 sec m like , wait wht? 😂😂

  • @RoshaedAlFardin-e5u
    @RoshaedAlFardin-e5u 24 дні тому +1

    Our faculty linked this as reference video :)
    Would've come here anyway. Exam in three and half hours.

  • @fatmaabdi2256
    @fatmaabdi2256 7 років тому +7

    That was so helpful. Thank you so much. love from kenya

  • @arunmishra9240
    @arunmishra9240 3 роки тому +2

    Oooohooo kya bataya h sir ❤️❤️❤️❤️❤️
    Hats off sir🙏🙏🙏🙏🙏❤️❤️❤️❤️❤️❤️🔥🔥🔥🔥

  • @mathematicsphobia5495
    @mathematicsphobia5495 5 років тому +3

    23.32 what a line sirrrrr....
    Pranam guruji

  • @shanshabrin4847
    @shanshabrin4847 Рік тому

    You're my saviour 💗. I don't attend lectures , You're the only my discrete maths professor

  • @HimanshJainYTube
    @HimanshJainYTube 7 років тому +10

    Bhai, maza aa gaya. Hats off!

  • @umamaheswari2715
    @umamaheswari2715 3 роки тому

    Very much useful for engineering students..Ur teaching was better than college faculties

    • @circuitsanalytica4348
      @circuitsanalytica4348 3 роки тому +1

      Uma, you people are really blessed to have platforms like UA-cam and Neso...

  • @Astonish2828
    @Astonish2828 2 місяці тому +3

    30 mins to my exam 😂 This is an emergency learning

  • @mehulkushwah6947
    @mehulkushwah6947 Рік тому

    Sir you are become a game changer to build my intrest in digital electronics thanks a lot 😊

  • @top_gee006
    @top_gee006 6 місяців тому +6

    Watching today 2024, a few hours before my digital electronics exam 😅

    • @Leomenz43
      @Leomenz43 3 місяці тому

      im watching before my discrete strutures exam

  • @murshedaziz3742
    @murshedaziz3742 3 роки тому +1

    I passed my digital course with your help. I owe you, man.

  • @nanaarhin5567
    @nanaarhin5567 Рік тому +5

    In drawing the K-Map, what determines where A should be and where the other inputs should be too?

    • @ammarzavahir8928
      @ammarzavahir8928 Рік тому +1

      I think he ordered them from A to BC because A is the MSB and BC is LSB

  • @manjulababushet8597
    @manjulababushet8597 4 роки тому

    U derserve more likes and subscribers .... Very clear and unambigious explaination

  • @aliwaqas46
    @aliwaqas46 7 років тому +3

    neso deserve donations

  • @AbhishekKumar-ft8uc
    @AbhishekKumar-ft8uc Рік тому

    Great sir, you explained in very simple way.

  • @alterguy4327
    @alterguy4327 7 років тому +21

    I regret taking your tutorials for free

    • @candypaii
      @candypaii 7 років тому +1

      he gets money from youtube ads :)

    • @alterguy4327
      @alterguy4327 7 років тому

      Corruption dude Not much..as an avg lecturer in India gets

    • @alterguy4327
      @alterguy4327 7 років тому +5

      He deserves more

    • @gagandeepsingh7789
      @gagandeepsingh7789 6 років тому +2

      @@alterguy4327 he is a professional teacher hired by a company for making these videos

    • @Nobodyxu987ui
      @Nobodyxu987ui 6 років тому

      Corruption i hardly see any ads in his videos :(

  • @circuitsanalytica4348
    @circuitsanalytica4348 3 роки тому +1

    Nice video, explained the topic in depth....

  • @nikhilsahu4491
    @nikhilsahu4491 5 років тому +6

    Hello sir u r name is sujeet😍😍 ,nice i noticed at 14:15

  • @hitanshuvibhute1489
    @hitanshuvibhute1489 3 роки тому

    bro your technique to solve k-map is amazing . i used to make mistakes in simplification... now it wont happen. awesome brother keep going

  • @aneeshsagiraju3985
    @aneeshsagiraju3985 3 роки тому +6

    FACT : when u want to understand a concept from basics then its more confusing compared to mugging up, but once u understand it u will remember it for the rest of your life. LIFE LESSON

  • @fancyAlex1993
    @fancyAlex1993 2 місяці тому +2

    Just saying that after 9 years, this video still stands

  • @SaikatPodder
    @SaikatPodder 8 років тому +8

    Sir when ur website will recover?...

  • @bhavanihaibatti3543
    @bhavanihaibatti3543 4 роки тому +1

    Nice explanation tq 🙏 sir ,I didn't understand earlier in my online classes but now after seeing urs video I understood Correctly 🙂👍

  • @hardishah3442
    @hardishah3442 3 роки тому +3

    What is boolean algebra?😭 Can't someone teach me from the very base

    • @arunmishra9240
      @arunmishra9240 3 роки тому +1

      See the playlist of digital electronics by neso academy

  • @rohitantony7004
    @rohitantony7004 6 років тому +2

    It's 4:45 AM while I write this. I've got my end semester exam at 9 in the morning. Words can't express how thankful I am. You're doing God's work.

    • @circuitsanalytica4348
      @circuitsanalytica4348 3 роки тому

      Students of your generation are really lucky to have platforms like Neso and UA-cam....

  • @raonegamming729
    @raonegamming729 9 років тому +16

    A'+ABC=A+BC I'M NOT UNDERSTANDNG THIS STEP....PLEASE TELL ME

    • @diksha6717
      @diksha6717 9 років тому +9

      +Souvik Saha It should be A' + X as ( X + X'Y = X+Y)

    • @idlewolf7196
      @idlewolf7196 7 років тому +11

      X + (X'Y) = (X+X') ( X + Y) = (1) (X + Y)
      In this particular case: A/A' would be X/X' and B(not)C would be Y

  • @abrarulhaqsofi
    @abrarulhaqsofi Місяць тому +2

    Watching this 2 hours before exam. Wish me luck

  • @panchcw
    @panchcw 9 років тому +4

    i cant figure out how u simplify boolean algebra in last 2 ,3 steps pleas help me

    • @satyamsovan123
      @satyamsovan123 7 років тому +3

      Simply follow this guide : -
      (A+B)(A+C)
      =A.A+A.C+B.A+B.C
      =A+A.C+B.A+B.C
      =A.(1+C)+B.A+B.C
      =A+B.A+B.C
      =A.(1+B)+B.C
      =A+B.C
      Hope this helps !!

  • @barsilgen120
    @barsilgen120 2 роки тому

    great video and explanation why we are using K-map and what the behind is in K-map!

  • @shubhamyadav-zo7nn
    @shubhamyadav-zo7nn 7 років тому +5

    sir aapki voice kaise chenge ho gyi vhi shi thi