Binary subtraction using borrowing
The following is a systematic, if somewhat light hearted, approach to borrowing.
A ‘1’ in any column is worth two ‘1’s in the column to its right.
Step 1.
The first borrow. We can add two ‘1’s to the least significant bit column by borrowing the ‘1’ from the next to least significant bit column.
Step 2.
Borrow again like there were no debt collectors.
Step 3
so no borrowing is required.
Step 4
This time borrowing looks more like taking out a mortgage than a short term loan.
The first ‘1’ that can be borrowed is in the next to most significant bit column.
When we borrow a ‘1’ from 1000 what is left is 0111
No further borrowing is required.
+1
Borrow 10 and get 1 since 10 = 01 + 01
+1
Borrow 100 and get 11 since 100 = 011 + 001
+1
Borrow 1000 and get 111 since 1000 = 0111 +0001
On not borrowing unless you need to
This time the borrows create enough ones to make further borrowing unnecessary.
Have fun and let me know how easy this is to read.
This page should download easily to Windows, Mac and Linux based browsers. If it doesn’t please email the Webmaster