hello all Welcome to our YouTube channel learned infinite this is Dr Deepa lakmi in today's episode we are going to see derived Gates so in previous episode we have seen the introduction about Gates logic gates and basic Gates so as I told you already the derived gates are derived from the basic Gates so we will have a clear explanation about what are derived Gates how it is derived what are the symbols that are used on the truth taper that is used for the derived Gates right so moving on to the session first we will be having four types of derived Gates the first one is nand second is nor third is exor and fourth is exor so usually I used to tell my students relate and learn as we are having many Concepts it's difficult to remember all the concepts at once so we can remember any one concept and relate to the other concept so that it will be easy for us so first is going to be the Nan gate so Nan gate is the complement gate of and it is the complement of and gate clear so you having the symbol for and gate is a d symbol so the Nan symbol will be a complement so a small circle in the and gate will be your nand gate so if you are giving a A and B as inputs so and is for multiplication so the output will be a do B the old Dash so in n gate you will be having a do B so since nand is the complimentary gate the output will be a do B the old Dash right so moving on to the truth table if there are two inputs A and B so the a do B the old Dash will be the output for your land Gates so the probability is two inputs so 2 power to four probabilities so it will be 0 0 0 1 1 0 1 1 so in and gate only if both the inputs are true the output will be true so here it is the complement vice versa so if both the inputs are true the output is false and for other inputs the output will be true hope you would understood this so Nan gate is the complimentary gate of an gate so if both the inputs are true the output is false for the other inputs the output is true clear so this is about the Nan gate so moving on to the Nar gate so as nand is a complement of anate nor is the complement of orgate so it is the complement of orgate okay so the r symbol is as we had discussed in the previous class this is your R symbol and a small circle indicates it is a Norgate okay so if a and b are two inputs in Norgate usually in orgate it is a addition the two inputs will be added so in N it is a + b the whole dash clear okay so the truth table for this will be a b a + b the whole dash so the probability is 0 0 0 1 1 0 and 1 1 so usually in orgate if either one of the input is true the output will be true so when it comes to the compliment only if both are false the output is true otherwise it is false okay so this is the exact complement of your orgate so when you relate and study it is enough if you study and gate and orgate the complement will be your nand and nor so you can easily relate to that right so these are the first two derived Gates nand and nor I think it will be uh easy for you to remember because you previously know what is and gate and orgate so just a complimentary gate gate is going to be your nand and nor gate so moving on to the third gate it is a different gate it is XR gate okay so X or gate the symbol will be a orgate under curve added curve to the orgate this is the symbol for your X orgate okay so if a and b are given as input the output will be a XR B so you can see the symbol for XR it is plus under Circle this is a symbol for your XR okay so it is going to be a XR B moving on to the truth table for XR a b the output will be a XR is plus under Circle X or B so the possible inputs are 0 0 0 1 1 0 and 1 1 so what will be the output so as the name indicates XR means if any one of the input is going to be true the output will be true else false that means if both the inputs are false the output is going to be false even if both the inputs are true the output is going to be false so only if one of the input is going to be true the output is going to be true right so that means only in second and third condition in second condition you having the output B to be true and in third condition you're having the output a to be true so one only in these two conditions the output is going to be that is a ex or B is going to be true in other two conditions it's going to be zero so that is XR XR that means exclusively or the expansion for your XR gate is exclusively or that means exclusively only one of the input should be true okay so only in second and third condition we can exclusively see B is true and in third condition we can see exclusively a is true so the output is true for both the conditions so this is going to be your XR gate so remember the symbol for XR will be plus under Circle embedded in that right so the last derived gate is going to be xn so xn gate is going to be the complimentary gate of XR okay so this is your complimentary gate of XR so since it is a compliment gate so whenever you are having your complimentary you just going to insert a circle over that particular gate so this is going to be your X gate so when the inputs A and B are given the output will be a xn B so you can see the difference between XR and X symbol in XR it is going to be plus under Circle whereas in xn it is going going to be dot embedded in a circle okay so this symbol indicates the dot and the circle indicates it is going to be your xn so it is easy to derive because it is just the complement of XR gate so you can easily say only if both the inputs are true or both the inputs are false the output is going to be true else it is going to be false that is the exact complement of your XR gate right so when two inputs are given a and b the output is going to be a x nor b a DOT and a circle so the possible combinations 0 0 0 1 1 0 1 1 right so what is going to be xor as I told you it is a complement complement of your XR so whether it is zero if it is zero here it is going to be one year if it is one it is going to be zero year so if both the inputs are false the output is true if both the inputs are true the output is true if either one of the input is true the output is going to be false because it is a x nor gate so this with this we can conclude with the derived Gates so what is derived Gates derived gates are the gates which are derived from your basic Gates basic Gates we have seen in the previous session previous video and or and not so these derived gates are derived from your basic Gates so there are four forms of derived Gates first is your land second is n third is xor and fourth is xar so Nan is the exact complement of your an gate n is your exact complement of your orgate so exclusive orgate is true only if either one of the input is true right and xor is the exact complement of your XR gate where the output will be true if both the inputs are true or both the inputs are false so I think uh this video will help you to uh uh find an easy way to how to arrive at your derived Gates so this derived Gates is useful for forming a circuit as well as this truth table is used for forming the output for the specified inputs okay so we will be seeing many interesting and many important topics in the further sessions so till then this is Dr Deepa lakmi signing off happy learning