Signed Integers

Signed binary integers can be either positive or negative. The most significant bit (MSB) indicates the number's sign. A value of 0 indicates that the integer is positive, and 1 indicates that it is negative. For example,

 Negative Integer:   (-26)10 = 1 1 1 0 0 1 1 0
 Positive Integer:   (38)10 = 0 0 1 0 0 1 1 0

Two's Complement Notation
Negative integers are represented by using two's complement representation, which is the integer's additive inverse. Adding an integer's additive inverse to the integer itself gives a value zero. Its definition is
The two's complement of a positive number N in base r with n digits is rn - N for N <> 0 and 0 for N = 0.
Two's complement representation is useful to processor designers because a single digital circuit can handle both addition and subtraction. The following two steps can also be used to find the two's complement of a binary integer. The two's complement operation is reversible.

 Starting value:   (44)10 = (00101100)2   0 0 1 0 1 1 0 0
 Step 1: Reverse the bits  
 Step 2: Add 1 to the value from Step 1   + 0 0 0 0 0 0 0 1
 Sum  
 2's complement notation of (-44)10 is   ( )2        

 Starting value:   (-26)10 = (11100110)2   1 1 1 0 0 1 1 0
 Step 1: Reverse the bits  
 Step 2: Add 1 to the value from Step 1   + 0 0 0 0 0 0 0 1
 Sum  
 2's complement of (-26)10 is   ( )2