Please show all the steps to subtracting the following problem with binary numbers:   00000110 - 11110011 ____________   Thank you!

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Please show all the steps to subtracting the following problem with binary numbers:

  00000110

- 11110011

____________

 

Thank you! 

 

Expert Solution
Step 1: Steps to substrate the given problem
  • We start by aligning the two binary numbers with the least significant bits (rightmost bits) in the same column.

  • In each column, we perform binary subtraction just like in decimal subtraction, where we consider borrow if needed.

  • In the first column, 0 - 1 results in 1, with a borrow of 1.

  • In the second column, 1 - 1 results in 0, with no borrow.

  • In the third column, 1 - 0 results in 1, with no borrow.

  • In the fourth column, 0 - 0 results in 0, with no borrow.

  • Finally, in the leftmost column, 0 - 1 results in 1, with no borrow.

  • We write down the results of each subtraction step, which gives us the final result 10101.

So, the binary subtraction of 00000110 from 11110011 yields the binary result 10101.

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