 Now we discuss about the decoder combinational circuit. So decoder is a combinational logic circuit that receives coded information of n input lines and converts damage to maximum of 2 to the power n unique output lines. So decoder is functions just opposite to a encoder and the decoder output will have less than 2 to the power n outputs when some of the n bits decoded informations are unused or are do not care combinations. Now we see the block diagram truth table and logic circuit of decoder. So now this is a block diagram of n to 2 to the power n decoder. Here n numbers of inputs then it decodes 2 to the power n outputs. If n is 3 that is 3 inputs that output will be 2 to the power 3 equal to 8. So 8 outputs it is marked as O0 O1 to O7. So it is a 3 into 8 decoder. Now we see the logic circuit and the truth table. So since there is a 3 inputs so we have given A, B, C, A, B, C these are the 3 inputs and outputs are O0, O1, O2, O3, O4, O5, O6 and O7. So for the 3 inputs what are the combinations first is 0, 0, 0 then 0, 0, 1, 1, 0, 0 and 1, 0, 1, 1, 1, 0 and last is 1, 1, 1. So when all the 3 inputs are 0 then the output O0 is selected. So this is 1 and the rest of the outputs are 0. When the input 001 is selected O1 output is 1, others are 0. For the 3rd case O2 output is selected, for the 4th case output O3 is selected and for the last combinations when all the inputs is high then output I7 is high. So this is the truth table for 3 into 8 decoder. So these are the inputs and these are the outputs. So now we see the logic diagram for 3 into 8 decoder. So now since there are 8 outputs 8 numbers of n gates will be there and the 3 inputs A, B, C are the 3 inputs and it is complemented by using the node queue. So for the first combinations 0, 0, 0 that means when all the 3 inputs A, B, C are 0 that means this one, this one and this one. 0 then output of the first n gate that is O0 is high it is selected. For the second case 001 that means A is 0, A is 0, B is 0, here B is 0 then C is high. So this is the high line. Then for the 3rd case B is high A and C is low. So A is low, B is high and C is low. For the 4th B and C is high A is low. So A is low, B is high, C is high. So this is the C is high. For the next case when output O4 is high then the A is high then the rest B and C is 0. So A is high. So this one is high line and B and C is low. Then A and C is high. So here A is high, B is low and C is high. Then for the 6th output here the combination is A and B is high. So this is high A then B this line is high and C is low. So this is the C low line and for the last n gate that means for O7 output all the 3 inputs are high. So this is A high line then B is high and C is. So this is the logic circuit for 3 into 8 decoder. So 3 means 3 inputs A, B, C and 8 means 8 decoder outputs. So O0 to O7. First you draw the truth table by using these combinations 0, 0, 0, 0, 0, 1. So all these 8 combinations are there and then the 8 outputs O0 to O7 are given here. That means the output only one n gate output is high at a time and the rest of the other output of the n gates is 0. So this is our 3 logic circuit of 3 into 8 decoder. So the function of decoder is just opposite to the encoder. So our 3 to 8 line decoder circuit can be used in binary to octal conversion and the decoder is also used in some code conversion. For example, BCD to 7 segment decoder and another use of a decoder is that it can be used to implement any combinational logic circuit. So we have discussed about the 3 to 8 decoder. Next we see the combinational circuit of Aether and Subjector. So first Aether means there are two types of Aether. One is half Aether and the other is full Aether. And first let us see a half Aether. Half Aether is a combinational circuit that performs the addition of two bits. So in this logic circuit two binary inputs and two binary outputs are required. Now let us see the block diagram of a half Aether. So this is a half Aether. So two inputs, two outputs. Suppose A and B are the inputs and S and C is the output. So here the output S equal to AB bar plus A bar B and C is also known as carry. S is known as sum and C is known as carry. So carry is A into B. Now from this sum equations the proof table will be AB then S and C. So the proof table of the half Aether for the two inputs AB that means 0, 0, 0, 1, 1, 0, 1, 1. So these are Aether so 0 and 0 is added. So when 0 plus 0 we better 0. 0 plus 1 the output sum is 1, 1 plus 0 is 0 sorry 1 and 1 plus 1 is 0 carry 1. So other carries 0. Now the logic circuit of a half Aether is for two inputs that is A and B. Then two end gates and the output of the two end gates are added. So there is a one organ this is the S input sorry S output and the other is C carry output. So here the input is A and A naught B and B naught. So for the first case when 0, 0 that means A0 and B0 for the second 0, 1, 0 when output is high. So sum is when sum is high when the combination is 0, 1. So we have to put 0 and 1. For the next case the sum is high when the input combination is 1, 0. So this is 1 and this is 0. So output is K B bar plus K bar B and in the next case the C carry it is A into B. So A is A high B high carry is 1 here A high and B high. So this is a half Aether logic circuit. So what is a half Aether logic circuit? Half Aether logic circuit is a combinational logic circuit which added two bits and it gives two outputs. Two bits means A and B and S outputs are sum and carry. So sum equations is A B bar plus A bar B and carry it is the output is A into B. So in the truth table for two bits the four combinations are there and the output sum is high when any of the input is high. And when both the inputs are equal that means either it is 0 or it is 1 then the sum output is 0. And for the carry output when both the inputs are 1 then the output is high. So this is the logic circuit for half Aether. Next we will see a full Aether combinational circuit. So now we will discuss about the full Aether combinational circuit. Our full Aether combinational circuit is a circuit which added three bits binary signals or binary inputs. And there are two outputs sum and carry. The three inputs consist A and B which we have already seen in case of half Aether. And the third input is the carry which is coming from the lower order bits when multi-bit addition is performed. So in case of a full Aether two of the input variables suppose A and B represents the two significant bits to be added. And the third variable that is C which is represent to carry from the previous lower significant position. And the output variables that is S which gives the value of the least significant bit of the sum and the output variable C which gives the output carry. Now let us see the truth table and the logic circuit of a full Aether. So here full Aether this is the block diagram three inputs A, B and C and two outputs S and C sum and carry. The output sum it is represent as the relation by this A bar B bar C plus A bar B C bar plus A B bar C bar plus A B C. And the equation of the carry that is C is A B plus B C plus C A. And here the truth table here is three inputs A B C and the combinations it is written like this. And for the sum when A 0 0 that means 0 plus 0 is 0 again 0 plus 0 it is 0. Then for the next 0 plus 0 is 0 and 0 plus 1 it is 1. Then 0 plus 1 1 1 plus 0 it is 1. Then 0 plus 1 it is 1 and 1 plus 1 is 0 carry 1. So here carry is 0. And for the fifth combination 1 plus 0 is 1 and 1 plus 0 is 1. And 1 plus 0 is 1 1 plus 1 is 0 carry 1. Then 1 plus 1 is 0 carry 1 0 plus 0 is 0. Then 1 plus 1 is 0 carry 1 0 plus 1 is 1. So this is the outputs of the full adder. What we have seen here that when any of the input is high that is 1 the output sum is high. And when any of the two inputs are equal that means here 1 1 the output is low. Now we draw the logic circuits here for the first is sum S. First we have given 4 n gates then because 4 terms is there and 1 or gate. So for the first combination 0 0 0 sum is 0. For the next when sum is high for the combination 0 0 1 that means A is 0 0 and C is high. For the next case when 1 is high A is 0 B is high C is 0. A is 0 B is high and C is 0. For the next this combination A is 1 B and C is 0. A is 1 and B and C is 0. Then for the last combinations all A B C are 1. So here this is A high B high and C high. So this is the logic diagram for the S output. And for the C output that is scary when it is 1 when the combination is. So this A B plus B C plus C A these are the A B C. So first case when it is high that is B C. So B C next it is high that means A C. So A C then it is high A C then B C A B. So A B. So this is the circuit for the output scary C and this is the circuit for the output sum. So now dear learners in today's class what we have discussed it till now. First we have discussed the combinational logic circuit. What is a combinational logic circuit? It is a circuit which consists of some interconnected set of logic gates with some input variables and output variables. And some examples of combinational circuits we have discussed. First we have discussed a multiplexure. So a multiplexure is a combinational circuit where the binary information is selected from one of the 2 to the power n input lines and it is transmitted to a single output line. If the n is a number of selection lines then that 2 to the power n combinations will be there. So multiplexure is also called many to one. Next we have discussed the demultiplexure. So in the multiplexure we have discussed the one to four demultiplexure. It is a one to many. And after that we have gone through a encoder which is a combinational circuit which generates the binary code for the 2 n input variables. That means 2 to the power n into n encoder. Next we have seen a decoder combinational circuit which receives codes information on n input lines and transmit them to maximum of 2 to the power n unique output lines after conversion. And next we have discussed the adder. So there are 2 adders. One is half adder and the full adder. In the half adder it is a combinational circuit that adds 2 bits and next is the full adder which is used to add 3 bits. So in the next class we will discuss about the substractor and then we go to our next unit that is sequential logic circuit. So in sequential logic circuit the output depends on the input as well as the past outputs. So in sequential circuit our memory is used. So that's all for today's class. In the next class we will continue the next part and thank you learners.