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Addition and subtraction in fixed point numbers

Addition

Rules of binary addition

0 + 0 = 0 
0 + 1 = 1 
1 + 0 = 1 
1 + 1 = 10

Example unsigned binary integer

Example 01

0000
0101
----
0101

Example 02

1000
0101
----
1101

Example 03

11011000
01010110
--------
100101110

Subtraction

Subtraction rules:

0 - 0 = 0
0 - 1 =-1
1 - 0 = 1
1 - 1 = 0

Examples of signed binary subtractions

Example 01

 0101
-0000
-----
 0101

Example 02

 0111
-0101
----
 0010

Example 03

 01010110
-11011000
--------
 10000010

Interpreting number is negative or positive

  • Observe the sign bit (MSB)
  • If ‘0’, the number is positive
  • If ‘1’, the number is negative