[0:07]Dear students, welcome to Gate Smashes. Aaj ki is video me explain karne ja raha hu. Properties of various logic gates. Toh dekho logic gates ke bare me maine last video me aapko explain kiya ki unki categorization hum kaise karte hai. Unke truth table kya hai basic jo hai wo points aapko bataye the. Lekin competitive exams ke liye specially aapko na properties ke upar kai bar question aa jata hai. Properties me waise to commutative property aur associative property jyada popular hai, lekin ek aur property hai idempotent property ya fir closure bhi aap usko bol sakte ho. Wo bhi aapko pata honi chahiye kyunki competitive exams may be kai bar college university exam me bhi iske upar pucha ja sakta hai. Toh guys, fatfat se video ko like kar de, channel ko subscribe kare, agar abhi tak aapne nahi kiya aur agar kar bhi diya hai toh aur devices se subscribe karwa sakte ho, subscribers bahut jaruri hai. Toh chaliye, start karte hai yaha pe gates maine already likh diye Not gate, And, OR, NAND, NOR, XOR aur XNOR. Yaha pe aapko properties maine tino mention kar di hai aur ye aapko tick dikh rahi hogi, cross dikh rahe honge, isko cram jo hai wo nahi karna. Ye sirf aapko samjhane ke liye table banaya hai, aap isko fatfat se proof kar sakte ho ki kaha pe property follow ho rahi hai, kaha pe property follow nahi ho rahi. Jaise, start karte hai Not gate se. Ab Not gate ke case me maine kya likha hai, Idempotent aur closure. Sabse pehle to samjho Idempotent property ka matlab kya hai? Idempotent property ka matlab kya hota hai generally, ki let's say maine koi operator use kiya. Jaise maine dot operator use kiya, kaunsa operator use kiya dot. Theek hai, multiplication wala. Toh let's see agar main iske left mein A likhta hu, right mein main A likhta hu. Toh maine yaha pe output jo hai wo kya achieve kiya? Output maine kya achieve kiya? A hi achieve kiya. Kehne ka matlab kya tha? Maine input di A. Us A ko maine A ke sath khud ke sath hi maine operator ke sath use kiya aur fir final result bhi mujhe same wahi mila input wala.
[2:10]Agar aisa hota hai toh fir ye kya hota hai Idempotent property ko follow karta hai. Main dubara se fir bata du koi bhi operator aap use kar rahe ho, koi bhi operator. Toh yaha pe let's say dot aapne use kiya. Ab dot mein aapne input kya di? A. Kya di? A input di aur A input ko aapne A ke sath khud ke sath hi aapne dot ke sath usko multiply kiya ya use kiya keh sakte ho. Aur output bhi same wahi aai toh means Idempotent property follow ho rahi hai. Jaise aapka And gate. Ab And gate mein mere pas and ka matlab kya hota hai? Dot. Toh A dot A karoge to output kya aayegi A. Matlab aapne input di thi A aur output bhi A hi aai toh yani Idempotent property ko follow kar raha hai. Ab aapne input di A aur Not gate lagaoge, kaunsa gate lagaoge? Not gate agar lagaoge, toh output kya aayegi? A bar aayegi. Pata hai aapko, zero doge toh one aayegi, one doge toh zero aayegi. Aapne input di thi A aur operator konsa lagaya ya gate konsa aapne use kiya? Not gate. Toh output kya aayi A bar. Kya A aur A bar barabar hai? Nahi. That's why it is crossed. Matlab ye nahi hai Idempotent property ko follow nahi karta. Bas ye kahani hai. Aise hi ab OR gate. OR gate ki baat karo. Aapne input di A aur A ko A ke sath hi aapne plus kiya toh output dekho kya aayegi? A hi aayegi. That's why it is also following the Idempotent property. Then NAND gate ki agar hum baat kare. Input di aapne A aur usko aapne kya kiya? A ke sath hi NAND gate kiya. NAND gate me aapko pata hai, ye aap isse denote karte ho aur output kya aayegi? Aapko pata hai ki A. A ka bar aayega.
[3:49]Which is what? A bar. Toh kya wo A ke barabar aaya? Nahi aaya. That's why not following. Aise hi aap XOR ka kar sakte ho, NOR ka kar sakte ho, XOR ya XNOR kisi ka bhi aap check kar sakte ho. Bas ye property aapko is tarike se check karni hoti hai. Then commutative property ki baat kare, toh Commutative property aapki generally kya bolti hai? Commutative property aapki generally bolti hai ki yaar agar mai A.B kar raha hu toh B.A aana chahiye. Matlab A.B kar raha hu aur B.A kar raha hu toh dono barabar aane chahiye. Toh dekho aap And gate ke case me karoge toh obviously follow hoga. Aap jaise dekho 0.1 kar lo ya 1.0 kar lo, kya aayega? Answer zero hi aayega. Matlab barabar hi aayega. Toh ye follow kar rahi hai. OR ke case me dekho, 0 + 1 kar lo ya 1 + 0 kar lo, answer aapka one matlab barabar hi aayega. Toh ye bhi aapki follow kar rahi hai. Achcha Not ke case me maine NA kyun likha hai? Kyunki jo commutative property aur associative property hai na, wo ek tarah se aap keh sakte ho ki binary properties hai. Binary matlab, ki isme aapko do values chahiye, A aur B chahiye ya X aur Y chahiye. Lekin Not gate me hum single input dete hai, toh is case me aap keh sakte ho NA, matlab Not applicable, Not applicable. But baakiyo ke case me aapko puchhenge bhi nahi. Aapko mainly And gate, OR gate ya aapko general way se hi puch sakte hai ki basic logic gates follow commutative property ya universal gate follow commutative property, true or false. Ya fir aapko puch sakte hai arithmetic gates follow associative property, true or false. Is tarike ke questions kafi aate hai. Toh bas aapko koi bhi check karna hai. Jaise aapko NAND check karna hai. Toh NAND ke case me commutative ki agar hum baat kare toh NAND ke case me kya aayega? Jaise A.B ka bar ya fir B.A ka bar. Matlab agar aap isme value daloge bhi toh iski value aap zero rakh lo iski value one rakh lo, one rakh lo iski value zero rakh lo. Toh ye kya answer aayega aapka? Zero ka bar yaha pe bhi zero ka bar, matlab dono jagah one one barabar. Aap koi bhi value put karke check kar sakte ho toh ye bhi aapka follow karega. Aise hi NOR gate me bhi, XOR me bhi, XNOR me bhi aap check kar lo. Answer aapka jaise XOR me aapko check karna hai, A XOR B is equal to B XOR A. Kya ye barabar hai? Aap A aur B ki value put kar lo. Let's say aapne zero one put kiya. Toh zero one ke case me alag-alag value ke case me one deta hai. Yaha pe one zero ho gaya. Toh one zero ke case me bhi kya deta hai? One hi deta hai. Toh dono barabar ho gaye. Toh yes, it follows. Toh aap hamesha yaad rakhna, commutative properties followed by every logic gate. Toh ye question aapse puch sakte hai aur Idempotent properties only followed by what? And gate and OR gate. Then associative property aap keh sakte ho followed by all the gates except universal gate. Kaunse aapke? NAND and NOR. Isko bhi aapne check karna hai. Simple. Let's say associative ke case mein A NAND B NAND C aur yaha pe hum likh denge A bahar likh denge B NAND C. Theek hai? Is tarike se hum yaha pe check karenge. Toh dekho kya ye dono barabar hai? Waise to aap expression khol ke bhi isko kar sakte ho. Otherwise value put karke aap isko kar lo. Yaha pe A B C ki value aap kya karo? One one zero put kar lo. Jaise aapne yaha pe one one zero aur yaha pe one one zero. Is tarike se aap check kar sakte ho. Toh aapko pata hai A NAND B, matlab one NAND one. Toh yaha pe output kya aayegi? Aapki output aayegi zero aur fir zero ko aapne NAND kiya zero ke sath toh output kya aayegi aapki one. Yaha pe dekho pehle isko solve karoge one zero toh NAND ke case me aapki output jo hai wo kitni aayegi? One aur fir one aur one ko NAND karoge toh output kya aayegi aapki zero. Toh dekho dono barabar nahi aa rahe. Otherwise aap value bhi jo hai wo isko simple solve bhi kar sakte ho. Ye kya banega aapka? A B, kyunki yaha pe bar ke upar bar hai, wo aapka A B ban jayega. Plus C bar yaha pe ban jayega aur yaha pe kya ban jayega? Yaha pe B C ka bar pehle aa jayega. Fir A dot ke sath aapka pura bar jo hai wo is tarike se aa jayega. Jisko aap kya likh sakte ho? A B kyunki yaha pe bar ke upar bar hai, wo aapka A B ban jayega. Plus C bar yaha pe ban jayega aur yaha pe kya ban jayega? A bar plus B C. Toh dekho dono expression hi alag-alag aa rahe hai toh aap keh sakte ho ki they are not equal aur equal nahi hai toh ya ni ye associative property ko follow nahi kar rahi. Same aap NOR ke case me bhi check kar sakte ho. XOR XOR jo hai wo follow karte hai. Toh ye is tarike se aapko just isliye bata raha hu. Ki aapko koi bhi is tarike ka question aata hai toh aapko yaad rakhne ki jarurat nahi hai. Aap simply solve bhi kar sakte ho. Lekin kai bar kya hota hai competitive exam me kuch aise exams hote hai jahan pe time jo hai wo bahut hi bada constraint hai. Jaise GATE vagairah me bahut jyada aap keh sakte ho time ka constraint nahi hai. Aapke pas sufficient time hota hai agar is type ka question aata hai. Lekin IT officer ke exam me ya fir kuch aisa TGT PGT ke exam me jahan pe aapko limited time hota hai toh agar aapko yaad rahenge points toh bina check kiye ya bina time lagaye aap easily answer jo hai wo kar sakte ho. Thank you.
