Binary Numbers Subtraction Using Complement Method |Lesson 17 |Digital Electronics | Learning Monkey

Here we will try to understand Binary Numbers Subtraction Using Complement Method. Here is the discussion on How to find the 1's and 2's Complement and Representation of Negative or Signed Numbers. Binary Numbers Subtraction Using Complement Method is explained step by step. Binary Numbers Subtraction Using 1's Complement: The steps to do 1's complement subtraction. Find the 1's complement of the subtrahend. Add the 1's complement value to the minuend. If there is a carryout, add carry to LSB. Look at the sign bit of the MSB. If it is 0, the result is positive and is in its true binary. If the MSB is 1 ( Whether there is a carry or no carry at all ), the result is negative and is in its complement form. Take the 1's complement to get the magnitude in binary. We will do 1's complement subtraction using the following examples. 1. 00011001 - 00001110. 2. 00001110 - 00011001. Example 1: 00011001 - 00001110. Step 1: Find the 1's complement of the subtrahend ( 00001110 ). 1's complement of subtrahend is 11110001. Step 2: Add the 1's complement value to the minuend ( 00011001 ). We got a carry of 1. Step 3: If there is a carryout, add carry to LSB. Step 4: Look at the sign bit of the MSB. The sign bit of the MSB is 0. Step 5: If it is 0, the result is positive and is in its true binary. The final result is a positive number and is in its true binary form whose decimal equivalent is ( 11 )10. Example 2: 00001110 - 00011001. Step 1: Find the 1's complement of the subtrahend ( 00011001 ). 1's complement of subtrahend is 11100110. Step 2: Add the 1's complement value to the minuend ( 00001110 ). There is no carryout. Step 3: Look at the sign bit of the MSB. The sign bit of the MSB is 1. Step 4: If the MSB is 1 ( Whether there is a carry or no carry at all ), the result is negative and is in its complement form. Step 5: Take the 1's complement to get the magnitude in binary. The result obtained is 11110100. The 1's complement of the result is 00001011 the magnitude is 11 in the decimal. Binary Numbers Subtraction Using 2's Complement: The steps to do 2's complement subtraction. Find the 2's complement of the subtrahend. Add the 2's complement value to the minuend. If there is a carryout, ignore it. Look at the sign bit of the MSB. If it is 0, the result is positive and is in its true binary. If the MSB is 1 ( Whether there is a carry or no carry at all ), the result is negative and is in its complement form. Take the 2's complement to get the magnitude in binary. We will do 2's complement subtraction using the following examples. 1. 00011001 - 00001110. 2. 00001110 - 00011001. Example 1: 00011001 - 00001110. Step 1: Find the 2's complement of the subtrahend ( 00001110 ). 2's complement of subtrahend is 11110010. Step 2: Add the 2's complement value to the minuend ( 00011001 ). We got a carry of 1. Step 3: If there is a carryout, ignore it. After ignoring the carry the value is 00001011 Step 4: Look at the sign bit of the MSB. The sign bit of the MSB is 0. Step 5: If it is 0, the result is positive and is in its true binary. The final result is 00001011 a positive number and is in its true binary form whose decimal equivalent is ( 11 )10. Example 2: 00001110 - 00011001. Step 1: Find the 2's complement of the subtrahend ( 00011001 ). 2's complement of subtrahend is 11100111. Step 2: Add the 2's complement value to the minuend ( 00001110 ). There is no carryout. Step 3: Look at the sign bit of the MSB. The sign bit of the MSB is 1. Step 4: If the MSB is 1 ( Whether there is a carry or no carry at all ), the result is negative and is in its complement form. Step 5: Take the 2's complement to get the magnitude in binary. The result obtained is 11110101. The 2's complement of the result is 00001011 the magnitude is 11 in the decimal. 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]