 Welcome to this session. I am Priyanka Bidla, assistant professor in electronics and telecommunication engineering. Today we will solve the numerical on binary arithmetic using Tooth's complement. This is the learning outcome of this video lecture. At the end of this session students will be able to perform operations, perform arithmetic operations that is addition subtraction on digital numbers on binary numbers. These are the contents of this video lecture. First upon we will see the introduction then the steps for Tooth's complement subtraction and then we will see the example based on that. First upon students must have the basic knowledge of real number system means it includes the integer, then real numbers and its arithmetic operations. Then subtraction of the number from another number can be accomplished by adding the complement of the subtraction hand to the menu end. Subtraction hand to the menu end means what a number from which another number is to be subtracted. So here we will see with the help of example here 9-4 is equal to 5. So which number you want to subtract there this is known as a subtract hand and from which number you have to subtract this is the menu end. So 9 is the menu end, 4 is the subtract hand and result of this is 5. So here this is nothing but it is the output or we can say it is a difference. Then Tooth's complement subtraction. So how to do the Tooth's complement subtraction? So first upon whatever number is given you have to do the one's complement of that binary number, one's complement how to perform. So simply you have to inverting all the ones to the zeros or and all the zeros to the ones. You have to take the complement of that number. Then for getting the result of Tooth's complement you have to add one to its LSB of the ones complement number. LSB is nothing but least significant bit. So whatever we will get the result in that result you have to add one to its LSB and in this way we are getting the Tooth's complement. So Tooth's complement number is nothing but it is the negative equivalent of the original number. Inverting all the bits of the number it produces the same result as subtracting the value one followed by the addition of one. Now before moving towards pause this video for few seconds and you have to recall the steps for the subtraction using Tooth's complement. So you have to recall. Now we will see the steps for the subtraction. So first step is you have to take the Tooth's complement of the subtraction. So whatever the number is given so subtraction means what which number you want to subtract it. So subtracting number which number you want to subtract it that whatever we will get you have to add with the menu end and whatever result will come the in the suppose in that addition suppose there is a caribit then it indicates what this is the positive value right and you have to remove you have to ignore that carry from the obtained result and suppose if there is a no caribit means what it indicates a negative value and for finding the magnitude of that number you have to take Tooth's complement of that result. So there are the two cases if the if there is a carry generated then you have to remove that carry from the result and it shows what positive value ok. If there is a no carry generated means what for finding the magnitude we have to take the Tooth's complement of that result and it indicates what this is the negative value. So there are some steps so you have to clear the idea with the help of examples. Now we will solve the examples now here there are some numbers given some binary numbers are given and we have find out the Tooth's complement for that. So left hand side are nothing but these are the binary numbers and right hand side indicates the Tooth's complement of that particular number. So first case is 000 for this first you have to convert into the one's complement. So one's complement simply you have to complement the numbers means all the ones you have to replace by 0 and all the zeros you have to replace by the 1 ok. So here 000 one's complement for this is what 111 then you have to add 1 to the LSB and here we are getting 000. Similarly for 001 once complement of this number is 110 then add 1 into that and here we are getting 111. Then for 010 Tooth's complement is 110 for 011 Tooth's complement is 101. Then for 100 first you have to convert again once complement. So you have to convert into 011 ok then take the Tooth's complement of that number and we are getting 100 same number. Similarly you have to perform for this then last one is 111. So first you have to convert into one's complement that is 000 then add 1 into that and here we will get 001. So in this way you can find out the Tooth's complement. Now we will solve the examples means you have to do the subtraction using Tooth's complement. So here some examples. So first example you have to evaluate the answer for means this is the example of you have to do the subtraction using Tooth's complement. So this is menu in and this is the subtraction which number you want to subtract that is known as a subtraction. So first you have to take the Tooth's complement of the subtraction ok. So how to get first you have to convert into one's complement that is 11010 then add 1 into that and here we are getting 11011. So this is the Tooth's complement of the subtraction. Now second step is what you have to add this subtraction to the menu in. So here we are getting 11000. So here you can see here there is a carry bit. So it indicates positive number but whenever carry is generated you have to remove that carry and the result is 11000. So here the smaller number is subtracted from the bigger number. So here we will get the positive result. Now here second example 11001-11100. So step one is what you have to take the Tooth's complement of the subtraction. So first upon you have to convert into the one's complement that is 00011 then add 1 into that and we are getting 00100. So this is the Tooth's complement of the subtraction. Now this value you have to add into the menu in. So here we get 11101 ok. So here there is no carry bit right. So if there is no carry bit the meaning is what? Find the magnitude and for that we have to take the Tooth's complement of that result ok. So how to take? So first upon you have to convert into one's complement that is 00010 then add 1 into that and we are getting 00011. So here this is the result 00011. It indicates whenever there is no carry it indicates negative value. So this is the negative equivalent of the original number. So here you can see here bigger number you have to subtract it from the smaller number. So but obviously we are getting the negative value. Now third example 11101-14 times 0. So again step one is you have to take the Tooth's complement of the subtraction. So first upon one's complement is 04 times 1 then add 1 into that and here we are getting 14 times 0. Now this value you have to add with the menu in yes. So here we are getting 011101. Now you can see here there is a carry bit. So if there is a carry bit you have to remove the carry bit from the result and the result is 011101. So in this way you can solve the example. These are the references of this video lecture. Thank you.