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Binary Number Subtraction
⇨ Three basic rules of subtraction are:
(i) 0 - 0 = 0
(ii) 1 - 0 = 1
(iii) 10 -1 = 1
⇨ If we take borrow from the left column then every 0 becomes 10 (which means in binary 1+1) and If that 0 which is now becomes 10 donates to the next right it then it becomes 1 and the next one becomes 10 now and continuous in this pattern further.
⇨ Example: Now lets try substracting 13 from 16. Binary for 13 is 1101 which for 16 is 10000.
Binary Decimal
1 0 0 0 0 1 6
- 1 1 0 1 - 1 3
--------------------------
0 0 0 1 1 3
--------------------------
⇨ 0 in the 1st column borrows from 0 in the 2nd column and so on till it get 1.
⇨ Now 4th 0 from right side becomes 10 after borrowing 1 from the 5th number i.e. 1, and 5th becomes 0 after donating 1 to the 4th 0.
⇨ Now 3rd 0 borrows 1 from 4th 0 and becomes 10 now by making 4th 0 as 1 (because 10 means 1+1 in binary, then after donating one 1, it only have one 1 left with it).
⇨ Now 2nd 0 borrows 1 from 3rd 0 and becomes 10 and makes 3rd 0 as 1(because 10 means 1+1 in binary, then after donating one 1, it only have one 1 left with it).
⇨ Now 1st 0 borrows 1 from 2nd zero and becomes 10 and makes 2nd 0 as 1 (because 10 means 1+1 in binary, then after donating one 1, it only have one 1 left with it).
⇨ Now 1st 0 = 10, 2nd 0 = 1, 3rd 0 = 1, 4th 0 = 1 and 5th 1 = 0.
⇨ Now substract 1st:10-1=1, 2nd: 1-0=1, 3rd: 1-1=0, 4th: 1-1=0
and 5th is already a 0.