hi everyone Welcome to our YouTube channel learn to infinite this is Dr Deepa lakmi hope you have enjoyed our previous videos so we have discussed about logical gates gates basic Gates and derived gates in previous discussion we are discussing about derived Gates so derived gates are the gates which are derived from the basic Gates and or and not so we have seen the derived gates are exactly comp mentary Gates like nand n exor and exnar so today we are going to see another important part of gates that is universal Gates so as the name indicates why it is called as the universal Gates so this Gates that is the universal gate is used to represent all the basic Gates that means the universal gate is used to represent and or and not gate so what are the two basic Universal Gates nand and N are the two basic Universal Gates so as I told you the definition of universal Gates nand and nor are called as universal Gates because using these two gates we can represent the basic Gates and or and not right so I think you would have now known what is universal gate what is the definition of universal gate and the why the name the Universal gate has arrived right so first we have to prove why this nand and nor is called as the universal gate so as I told you this Universal gate that is nand or nor can be represent and or and no gate so first we will see how nand is used as a nod gate so in previous videos we have discussed about nand Gates so this is a symbol of Nan gate so any Circle indicates it is a compliment gate so when an input A or B is passed onto the n gate the output we arrive is the a complement or B complement depending upon the input right so by this you can see the nand acts as the not gate because what is the working of no gate we have seen in our basic Gates no gate is a complimentary gate where whatever the input we are giving the exact compliment output we are going to arrive at right so here n is used as a not gate second how nand is used as the hand gate okay so and is the product gate so when A and B are passed through the Nan gate your output will be a do B the whole dash this we have seen in our derived Gates a do B the old Dash so now when you are substituting this input in this gate see this so consider this as a instead of a do B consider this as a so a the old Dash when it is passed to the Nan gate it will be giving the a dash the old Dash which is equivalent to a okay so similarly a do B the old Dash when it is passed through the n gate it will be equivalent to a dob it's a compliment gate so by this what is the output for and gate the output of and gate is a do B so by using these two Nan Gates we can arrive at the output of and gate so by this manner Nan acts is the and gate right so we have seen nand acting as not and Nan acting as and gate now coming on to nand as or gate so R is the sum gate summative gate so when two inputs are passed your output will be A+ B when X and Y is passed your output will be x + y right so see here it's the same way when a is passed to the Nan gate you will be getting a complement B is passed to the an gate Nan gate you'll be getting B compliment when these two inputs are pass separately to the L gate you will be getting a dash B Dash the old Dash right right product gate so a d b Das since it is a n the old Dash so here you are applying the complimentary principle complimentary principle is there that is uh listen here when you are applying the complimentary a dash the old Dash is equal to a right so that is what we are applying a dash the old Dash is equal to a similarly B Dash the old Dash is equal to B here you are having the dot product so applying the dot product to the complement you'll be getting plus okay this is The Duality principle we are using here so by using The Duality principle of nandate A- do B- the whole dash is equal to a plus b so in this manner we can see nand is used as the orgate so by this we can prove that nand is a universal gate because nand is used to represent not gate and gate and or gate right so now we will see the next part the second part how n is used as the universal gate so now we are going to prove how n is used as the universal gate the same way as we approved for nand so you all know what is a Nar gate we have seen in a previous video the derived gate of Nar gate so for any input a is given the output will be a dash since it is a complementary gate whatever input you will be getting the complemented output so by this manner n acts as a n gate this is the first part second we are going to prove how n is used as the r gate okay so R is the some gate so when A and B are passed Nar gate it is a plus b since it is a Nar gate the old complement again when you are passing to Norgate this complement will be canceled and your output will be a plus b which is in turn the output of orgate so by this manner n is used as the or gate and finally we are seeing how n is used as the and gate so a when it is passed to Nan gate it will be a dash B when it is passed to n Norgate it will be B Dash when both are IND indvidually passed down to the Norgate it is a dash plus b Dash the old Dash similarly as we have applied The Duality principle over here we are applying here a Das the old Dash is equal to a b Das the old Dash is equal to B plus when it is complemented it becomes dot product which is a do B which is in turn the output for your hand gate right so we are proved that nand and N are Universal Gates because nand and nor gates are used to represent the base Gates and or and not so hope this video will be useful for you and uh you would have well known what is universal Gates what are derived Gates what are basic Gates what are logic gates so any doubts and any clarifications you can post it hope you would have enjoyed this video we will meet in the next session till then this is Professor Deepa lakmi signing off have a good day