 Hello dear learners, I am Antora Mohanto-Burwa, Assistant Professor, Department of Electronics, HBC School of Science and Technology. Today in this video class we will discuss about the combinational circuits. This unit belongs to the second block of digital techniques paper of first semester BCA program. This unit includes about the introduction of combinational logic circuits. Then we shall discuss some examples of combinational logic circuits like multiplexure and demultiplexure and codar and decoder and then we shall discuss about the adder and subtractor. So, first let us see what is combinational logic circuit. A combinational logic circuits includes inputs, then logic gates and outputs. The output is depend on the present inputs values and it does not have any memory and if there are n numbers of inputs then output will be 2 to the power n. So, if there are n numbers of inputs then the total combinations possible combinations of inputs will be 2 to the power n combinations and suppose n equal to 2 then total possible combinations will be 2 to the power 2 equal to 4. So, 4 numbers of inputs will be there and there will be m outputs. So, output is depends on the present inputs. Then let us see some examples of combinational circuits. Some examples of combinational logic circuits are multiplexure, demultiplexure, then encoder, decoder, then adder and subtractor. So, multiplexure and demultiplexure are the very important combinational circuits and let us first see what is multiplexure. So, multiplexure is a combinational circuit which accepts many inputs and it gives only one output. It is also known as many to one. So, multiplexure is also called as a selector, data selector because it selects only one input out of several input signals to single output. So, what is the relation between input and the control line is n equal to 2 to the power m. That means, if number of input lines is 2 then number of control lines m will be 1 because 2 is equal to 2 to the power 1. So, m will be 1. This control line or we can say selector line it will be 1 when input is 2. Again if we consider input is 4 that means 4 numbers of input signals apply to a multiplexure then number of control lines will be 2 because 2 to the power 2 will be 4. So, similarly the some examples of multiplexures are 2 to 1 multiplexure then 4 to 1 multiplexure then 8 to 1 or 16 to 1 multiplexures here output is always 1. So, in multiplexure the selector inputs determine the outputs. So, in this case we check about the 4 to 1 multiplexure. So, first let us say the 4 to 1 multiplexure here we add a OR gate. So, output is 1 as here the control line will be 2 suppose A and B are the control lines and the inputs are suppose data inputs D0 these are the 4 inputs D0 D1 D2 then D3 and A and B are the control lines suppose A and B here our NOR gate is given. So, how we apply the inputs to these gates let us see it from the truth table suppose A B and output is Y. So, for 2 bits the input combinations will be 0 0 0 1 1 0 then 1 1. So, first A and B is 0 0 that means in the first gate this NOR gate is 0 then B is 0 this will be the input and the second case 0 1 that means A is 0. So, from this line then B is 1. So, this line here both the inputs is 1 1 and we apply a NOR gate to make it a 0 input. Next combination is 1 and 0 that means A is 1. So, here this is the line 1 then B is 0. So, it should be from the NOR gate and the fourth combination is 1 1 with both inputs A and B are 1. So, from this line and this line and output is when the inputs A and B is 0 the D0 output is selected that means the other 3 N gates are disabled and the first N gate is unable. So, in the output of the OR gate it will be data 0 and for the second combination the output will be D1 that means the Y is the value of D1 input line that 1 0 it will be D2 and for 1 1 combination output will be D3. So, this is the truth table of 4 to 1 multiplexure and this is the logic circuit diagram for 4 to 1 multiplexure 4 means there will be 4 data inputs. So, we have to draw 4 N gates and each data input is 4 input is applied to each N gate and the selector line or the control lines will be 2. So, A and B are the control line and we write the combinations for 2 inputs then accordingly we and given the this N gates accepts the input combinations and output is that means it selects only one input line at a time. So, this is about 4 to 1 multiplexure. So, multiplexures are used in various fields where multiple data need to be transmitted using single line. Some applications of multiplexures are communication system in telephone network, computer memory etc. Next we will see the demultiplexure combinational circuit. In demultiplexure it accepts only one input and it gives several outputs. So, demultiplexure is also called one to many. So, similar to the multiplexure, demultiplexures can be 1 to 2, 1 to 4, 1 to 8 or 1 to 16 demultiplexure. So, now let us say the logic circuits and truth table of demultiplexure. This is a block diagram of demultiplexure. It has one input signals and many output lines and M is the number of control lines. If the output line is N then the input control lines will be 2 to the power M. So, in case of 1 to 4 demultiplexure that means output lines will be 4. So, the input control lines or the selection lines it will be 2. So, M is 2. Now, we see the logic diagram and the truth table of demultiplexure 1 to 4. Since output is 4, so there is 4 N gates. Suppose output is y 0, y 1, y 2, y 3 and one input that means suppose this is the D input, D is data input and it applies to all the N gates. Then in case of 1 to 4 demultiplexure there is 2 selection lines. Suppose A and B here a N gate is applied. So, let us first see the output truth table that is A, B and 4 outputs. So, 4 outputs is y 0, y 1, y 2 and y 3. First combination is 0, 0, then 0, 1, 1, 0 and 1, 1. So, when the input is 0, 0 that means this is 0, 0. Then the output this D is selected at the output of the first N gate. So, y 0 will be D here. So, what is the value is applied to the input that is reflected on the output of the first N gate and the other N gate are disabled and the rest of the output of the N gate are 0, 0. For the second combination that is 0, 1. Here it is 0, then next is 1. Then the output of y 1 takes the data input. So, D is here. If D is 1 we can write here 1, 1 and rest of the outputs are 0, 0. For the third combination 1, 0 that means A is 1 and B is 0. For this combination the output is reflected on the y 2 that is the output of the third N gate and the for last combination that is 1, 1, 1, 1. The other three outputs is 0, here it is 0 and it is 1. So, this is the logic proof table of 1, 2, 4 D multiplexure. So, what is the value of input it reflects on the outputs. For other cases it is 0. Similarly, same concept we can draw the 8, 1, 2, 8 D multiplexure or 1, 2, 16 D multiplexure or we can draw the 1, 2, 2 D multiplexure. So, I have shown the 1, 2, 4 D multiplexure. So, now D multiplexure is used to connect a single source to multiple destinations. Some of the applications of D multiplexure are the communication system, arithmetic logic unit, serial to parallel converter. In the multiplexure receiver the output signals of multiplexure and converts them back to the original form of the data at the receiver end. Multiplexure and demultiplexure work together to carry out the process of transmission and reception of data in communication system. Next we shall see the encoder and decoder combinational circuit. Here the encoder is octal to binary encoder logic circuits we will see. Here if 2, 2D power n is the inputs then output will be n, n outputs. So, in the block diagram the block diagram of the encoder is like this. So, this is our encoder if 2, 2D power n inputs then n numbers of outputs. So, this 2, 2D power n into n encoder and here if this 2, 2D n is equal to 3 then 2, 2D power n is 8. So, this encoder will be 8 into 3 encoder, 3 output lines, 8 numbers of input lines. So, encoder is generally used to encode the inputs, encode the informations. Now, let us see the logic circuits and the truth table of 8 into 3 encoder. This encoder is just a opposite of decoder. First we will see the logic truth table, first we will see the truth table that is the inputs are 8 inputs. So, i 0, i 1, i 2, i 3, i 4, i 5, i 6, i 7 and outputs are given as 0, 0, 1, 0, 2. So, where is 0, 0, 1, 0, 2. So, first suppose a first input is high that means 1 is applied to the first input and the rest of the inputs are 0. So, in case of encoder at a time only one input is high. Then what will be the outputs? This output will be 0, 0, 0. Then for the next input 1, rest of the inputs are 0. Now, this is the truth table of 8 into 3 encoder. Here what it is given that means at a time only one input signal is high and for the outputs will be similarly this are the outputs of the encoder. So, what we have seen the output o 0 that means first output is 1 when the i 4, i 5, i 6 and i 7 is 1. Then output o 0 that means first output is high and for the other cases the output is 0. Again the output second output that means o 1 what it is saying this output is high when the input i 1 then i 3 and i 6 and i 7 is high. So, the output equations can be written as o 0 equal to when o 0 is high when i 4, i 4 plus i 5 then i 6 and i 7. Then for the next output o 1 when this output is high first i 2 plus next is i 3 plus here for this combination i 6 and for the last combination it is i 7 and for o 2 it is 1 when i 1 is high next is 1 when i 3 is high plus next 1 i 5 is high and it is 1 when i 7 is high. So, this is the equations of output 3 outputs o 0 o 1 and o 2. Now, this is the truth table. Now, we will draw the logic diagram of the 8 into 3 and go down. Here 3 outputs so these are the combinations. So, here they all are last to the inputs. So, we used 3 organs and in the 3 organs output is o 0 o 1 and o 2 and here 1 unable input that means to enable the cheap, cheap unable input is applied and this unable input is applied to all the 4 all the 3 organs. Now, for o 0 what are the inputs i 4, i 5, i 6 and i 7. So, here as i 0 is not when i 0 is high no one output is high. So, I have not given here i 0 I have started from i 1. So, for output o 0 this i 4, i 4 then i 5 and i 6 i 7. So, these are the inputs for o 0 then for the second output o 1 what are the inputs i 1, i 3, i 6 and i 7, i 2 first is i 2. So, here it is i 2 then i 3, i 3, i 6 given then i 7. So, these are the i 7. So, 3 4 inputs then for o 2 combinations the input combinations are i 1 this is the i 1, i 1 then i 3 there already this drawn i 3, i 3, i 5, i 5 and i 7. So, i 7. So, this is the logic circuit for 8 into 3 encoder. So, I think this clear now again I am repeating first you draw the truth table for 8 into 3 encoder there are 8 inputs. So, I have marked here i 1, i 0, 2, i 7 and 3 outputs o 0, o 1 and o 2 and at a time it is assumed that at a time only 1 input is high. So, accordingly this truth table has been drawn here and when the output is 1 we have checked the inputs. So, when output o 0 is high the business inputs are high. So, we have combine it and then we get the 3 outputs. So, this is the logic diagram of 8 into 3 encoder. Next we will see the decoder circuit.