00:01
Hello, the question is taken from physics and the question is write an expression for the output in terms of input variable for each circuit below.
00:10
Okay, so let me first write the, draw the circuit in order to evaluate the output.
00:17
Okay, so for first case, it is, once again, single input and then there is an all gate and then note gate and the situation is.
00:33
Like this and there is only one input okay so the output will be a complement okay so this is the first one it behaves like a note gate okay let us draw the b1 and b1 is nandgate one one input a other input b then there is a note gate a so output of this become b complement so output of this nandgate is a dot b complement so output of this nandgate is a dot b complement whole complement so that will be a dot b complement whole complement is equal to a complement plus b complement complement complement by d morgan identity okay so that will be a complement plus b which is the required value for this last is first and gate and then a then b and then there is a node gate and the output of it is connected to a nandgate okay then there is a c and after that output of it and output of it will connect to a no or gate okay so this is a b this will be b complement output of and gate is a dot b so this is b complement c complement this is a nondate so b complement dot c whole complement okay so we know that output of a no gate is a dot b plus b complement c complement whole complement okay so we can solve it like this a dot b plus b complement c whole complement then there is again a whole complement okay so that will be first a dot b complement complement dot b complement c complement complement complement so that will be b complement c so that will be we can write it as a complement plus b complement by demorgan identity and this become dot b complement c complement complement complement mean same value okay so further solving it we get the value a complement b complement b complement c b complement dot b complement is b complement plus b complement into c further taking b complement c are common a complement plus one anything as added to one give you one so the final result is b complement c which is the required output draw logic circuit to implement the expression below just implement the function as as written don't rearrange or simplify okay so next second first is a plus b complement c okay so first is this is b complement c so this there is a note gate b okay and then there is a output of it and other is c will be be ended together so this corresponding to b complement and c after that there is an input a and both of them are all together.
04:22
So the output of it is a plus b complement into c.
04:29
Further, second is let me write first the expression b, a, b complement, then b plus b c whole complement plus a complement plus c whole complement.
04:50
So this is the required expression.
04:52
Now we have to draw figure so first this is a and this is b so there is a note gate okay so we have to first corresponding to this we have to use an and gate so the output of it is a b complement second b c complement so first here we have to use a nand gate okay so first we have to take this one and then c okay so this will give you output b dot c complement third is a complement so first for a complement we have to use a note gate here okay so let us bring it downward these are not connected okay so what was the expression a complement so this is a complement and then only see so there is a no gate one input is a complement and this is c so output is a complement plus c whole complement now all of these three are add together so the output become add addition addition is done by all the gate so its output is a b complement plus b dot c complement plus a complement plus c whole complement okay next is an important theorem of bullion algebra is d morgan the which says that a b complement is a complement plus b complement and a plus b complement is a complement dot b complement use truth table to demonstrate both these theorem are two okay so first so this is for a b b then a b complement after that sorry that is one a b then not a so that is my a complement b complement b complement it may be morgan identity okay and then there here is a dot b complement a complement plus b complement last one is a plus b whole complement a complement dot b complement okay so if we need to prove that this two are equal and these two are equal okay so let me 0 0 0 1 1 1 0 1 1 a dot b is 0 -0 -0 -1.
08:48
A complement is 1 1 -0 -0...