 Hello dear learners, I am Antora Mohantra Borua, Assistant Professor, Discipline of Electronics. In this video class, we shall discuss about some sequential logic circuits, which is included in the digital technique paper of first semester PCA program. In our previous video class, we have discussed about the combinational logic circuits. We came to know that all the digital circuits are categorized into two types. One is combinational logic circuits and the other is sequential logic circuits. In combinational logic circuits, the output at any instance depends on the input at that instance. We have already discussed about the encoder, decoder, multiplexer, demultiplexer, adder, all these combinational logic circuits. Today, we shall also discuss about the subtractor before going to the details of the combinational logic circuits. So, the subtractor, similar to the adder, the subtractor also classified as two types. One is half a subtractor and other is a full subtractor. Now, let us first discuss about half subtractor. We know the rules of binary subtraction as 0 minus 0, it is a 0. Then 0 minus 1, it is 1, that means 1 borough. Then 1 minus 0 is 1, then 1 minus 1 is 1. So, this is the subtraction rule in binary subtraction rule. So, in case of half adder, first let us see the block diagram of half adder. It has two inputs, suppose a and b and two outputs, that is di and b0. So, this is the half subtractor. So, what is di? Di is the difference output and b0 it is the borough output. And if we see the truth table, suppose these are the inputs a and b and outputs are di and b0. This is the difference and this b0 is the borough. So, for the two inputs, the four possible combinations are 0 0, 0 1, 1 0, then 1 1. So, from this difference binary subtraction rule, so difference for 0 0, 0 0 is 0. So, there is no borough, so borough is 0. For the second case, 0 minus 1, so 0 minus 1, the difference is 1 and there is a 1 borough. So, it is 1. For the third case, 1 minus 0, that means 1 minus 0, difference is 1. So, it is 1, no borough, so 0. And for the fourth combination, 1 minus 1, the difference is 1 and the borough is 0. So, this is the truth table for half subtractor. So, next we shall see the logic circuit for the half subtractor. So, two gates are used. So, this output is di and this is the b0. So, two inputs a and b, so these are the two inputs a and b and the inputs of the n gate, that is where the output is b0, the inputs are a bar. That means, a north gate is applied and another is b. So, what are the Boolean expression for the half subtractor? For difference output, the Boolean expression is similar to the half adder that we have discussed already discussed. So, this is the expression for di, that means difference output. And for the other output b0, a bar dot b equal to b0. So, this is the Boolean expression for the borough output. So, till now what we have seen, first we have see the half adder, half subtractor. So, in half subtractor there are two inputs, suppose a and b and two outputs, one is difference and other is the borough. So, this is the truth table for the half subtractor and this is the logic circuit diagram for the half subtractor. So, now, so this is the block diagram of full subtractor and this is the logic circuit diagram for full subtractor. In case of full subtractor, there are three input bits and two output bits similar to the full adder. And here the two input bits, that is a and b, means one input is subtracted from the other inputs and the third input is a borough of the previous stage. That means borough from the previous stage, that is the third input for full subtractor. And there are two outputs, one is difference and other is the borough output. So, let us see the truth table for full subtractor. There are three inputs that is a, b and other is the borough input. That means it is the borough of the previous stage and the two outputs, that is di difference and the borough output. So, for the three inputs, the eight possible combinations are 0 0 0, 0 0 1, 0 1 0, 0 1 1, 1 0 0, 1 0 1, 1 1 0 and 1 1 1. So, now let us see the difference in output. So, first all are 0, so difference is 0. There is no borough, so borough is 0. Next 0 minus 0 is 0, then 0 minus 1. So, here difference is 1, borough is 1. Next 0 minus 1, from the law of binary subtraction 0 minus 1 is 1, then 1 minus 0 is 1. So, here 0 minus 1 there is borough 1, so b output is 1. Next 0 minus 1 that is difference is 1, borough is 1, so borough 1, then 1 minus 1 that is 0, so difference is 0. Next 1 minus 0 that is 1, again 1 minus 0 that is 1, so borough is 0. Next 1 minus 0 that is 1, again 1 minus 1 is 0, so borough is 0. Then 1 minus 1 that is 0 and 0 minus 0 is 0, so borough is 0. And the last case that is 1 minus 1 is 0, then 0 minus 1 is 1 and borough 1. So, this is the truth table for full subtractor. Now, we have discussed about the subtractor combinational circuit. Here the full adder there are in the logic circuit there are two half adder circuits are there. So, this is one half adder circuit and this is the another half adder circuits. As there are three inputs one is A, B and other is borough input that is from the previous borough. And the for the first half subtractor the output difference output is applied to the input and the borough output these are added by using a OR gate to get a final borough output. So, these are all about combinational circuits now we shall discuss about sequential logic circuit.