twoscomplementnotes.txt

Twos complement - HOWTO represent a negative #
Step 1. Write it as positive #
Step 2. Flip all the bits
Step 3. Add 1

Example: Represent -64 using two's complement 
0   1  0  0  0 0 0 0 Step 1
    1  1  1  1 1 1   <== These 1s are the carries from Step 3
1   0  1  1  1 1 1 1 Step 2
                   1 Step 3
--------------------
1   1  0  0  0 0 0 0 Final answer in binary
0xC0 (Final answer in hex)

Another example: Suppose you start with a negative number in two's complement:
11000000 <== You are told this is a two's complement number, so you know it is negative because of the 1 in the first bit position.
Here is how to find the magnitude of the negative number:
    1  1  1  1 1 1 <== These 1s are the carries from Step 2
0   0  1  1  1 1 1 1 Step 1 - Flip all the bits
                   1 Step 2 - Add 1
--------------------
0   1  0  0  0 0 0 0 Final answer in binary 
_   _  _  _  _ _ _ _
128 64 32 16 8 4 2 1

Final answer in decimal: 64 (because there is a 1 in the 64s position).
Therefore the original number must have been -64