How Do You Add Binary Numbers And How Do You Subtract Them?

It is so simple that it is confusing.  Let's use 1011 and 0010 as two numbers we are going to add.  We will add right to left just like we would with base 10 numbers:

Step 1

1011

0010

-----

***1 --- 1 + 0 is 1 just like in base 10



Step 2

1011

0010

-----

**01 --- 1 + 1 is 10 in base 2, so we put down a zero and carry the 1



Step 3

1011

0010

-----

*101 --- remember the 1 we carried from the previous step?  We use it here



Step 4

1011

0010

-----

1101 --- 1 + 0 = 1, just like before

Subtraction can be done in the same manner (right to left with borrowing) but in binary there is a more efficient method known as "two's compliment".  Two's compliment is simply reversing all of the bits e.g. 1001 becomes 0110 and then adding 1 to the result: 0111.  Let's use the same numbers as in the previous example:

Step 1

1011 = 11 decimal

0010 = 2 decimal



We preform a two's compliment on the second number and then add it to the first the same way we did above:



1011

1110

----

1001 = 9

If you were following closely you might wonder what happened to the high order bit in the result.  The answer is that it is discarded.

Hope this helps.