remember me: binary math

binary_math.md

binary math

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2's complement

101 -> 010 + 1 = 011
11010 -> 00101 + 1 = 00110

binary subtraction

0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 with a borrow of 1

 111
- 10
-----
=101

 1001
- 101
-----
=0100

binary subtraction using the 2's complement

 111
- 10
-----
 111
+110 (2's complement of 010 -> 101 + 1 = 110)
-----
1101
dropping carry-over
=101

If there is a carry-over it is dropped.

Without carry-over the 2's complement is built from the resulting value. This resultis negative then.

 10110 
–11010
-----
 10110 
–00110 (2's complement of 11010 -> 00101 + 1 = 00110)
-----
 11100
no carry-over, build 2's complement (is negative result value)
 11100 -> 00011 + 1 = 00100
= -100

binary addition

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 with a carry-over of 1

  10
+ 11
-----
=101