Logic Behind 9's and 10's Complement Subtraction || Lesson 4 || Digital Logic || Learning Monkey ||

Here we will try to understand the Logic Behind 9's and 10's Complement Subtraction. The discussion about how to subtract decimal numbers by using the 9's and 10's complement click here. The steps involved in decimal number subtraction using 9's complement are Obtain the 9's complement of the subtrahend and add it to the minuend. This is a result, not the final answer. If there is a carry the result is the final answer and the answer is a positive number. Add carry to the Least Significant Digit. If there is no carry it indicates that the result is not the final answer and the final answer is a negative number. To get the final answer find the 9's complement of the result. Add a minus sign to the final answer. The steps involved in decimal number subtraction using 10's complement are Obtain the 10's complement of the subtrahend and add it to the minuend. This is a result, not the final answer. If there is a carry the result is the final answer and the answer is a positive number. Ignore carry. If there is no carry it indicates that the result is not the final answer and the final answer is a negative number. To get the final answer find the 10's complement of the result. Add a minus sign to the final answer. In our discussion on how to subtract decimal number by using 9's and 10's complement only the above steps were discussed but we haven't discussed the logic behind those steps. In order to understand the logic behind the subtraction, we will use all the above steps. We will consider the following examples to understand the logic behind the subtraction using 10's complement method. The logic is applied for 9's complement subtraction also. Example 1: 94 - 23. To do the 10's complement subtraction the first step is to find the 10's complement and we have to add it to the minuend. 9's complement of subtrahend. Adding 1 to the result. From the above steps, how did we obtained the 77? How is that happening? First, we have subtracted 23 from 99 and to the result, we have added 1. Which is 100 - 23. What is our next step? We have to add 10's complement to the minuend. What is our next step? We have to check for carry if the result is having carry we have to ignore the carry and the result is the final answer. Ignoring the carry means we have to remove the 1 in the 100's position. Which means we are removing 100. So the final answer is 71. Consider the above calculation how did we obtain 77. In the place of 77, we have substituted (100 - 23) which we have discussed above. 94  + 100 -23  = 171. Ignoring 1 means we have to remove 100. Removing 100 from the above calculation means 94 - 23 = 71. What is the use of the above calculation? With the 9's or 10's complement subtraction, we have avoided the borrowing aspect of the subtraction. Even though we are using subtraction in the 9's complement we will never ger the problem of borrow because we are subtracting a two-digit number from the highest 2 digit number possible which is 99. So we will never come across with the borrowing problem. Example 2: 23 - 94. To do the 10's complement subtraction the first step is to find the 10's complement and we have to add it to the minuend. 9's complement of subtrahend. Adding 1 to the result. From the above steps, how did we obtained the 06? How is that happening? First, we have subtracted 94 from 99 and to the result, we have added 1. Which is 100 - 94. What is our next step? We have to add 10's complement to the minuend. What is our next step? We have to check for carry if there is no carry we have to find the 10's complement of the result which is 29 ad we have to add a minus sign to the result. To find the 10's complement we have to find the 9's complement of 29 and we have to add 1. Adding 1 and a minus sign to the result. From the above calculation, how did we obtained 71? From the above calculation, how did we obtained 29? Expand he above 100 - 100 + 94 - 23 = 71. The given question is 23 - 94 but we are doing 94 - 23, that is the reason why we add a minus sign. This concept of 9's or 10's complement subtraction can be generalized to any type of number system as (b - 1)'s and (b)'s complement. This means if we consider binary number system we can have 1's or 2's complement subtraction. The logic behind any (b - 1)'s and (b)'s complement is the same as the above. Link for playlists: https://www.youtube.com/channel/UCl8x4Pn9Mnh_C1fue-Yndig/playlists Link for our website: https://learningmonkey.in Follow us on Facebook @ https://www.facebook.com/learningmonkey Follow us on Instagram @ https://www.instagram.com/learningmonkey1/ Follow us on Twitter @ https://twitter.com/_learningmonkey Mail us @ [email protected]