Two's Complement Arithmetic

1. Determine the largest and smallest integers that can be represented in 10-bit two's complement.

    

2. For each of the following sums find the base 10 value of each of the 10-bit two's complement integers being added (note that several of the problems use the same numbers so you only need to do a few conversions), compute the two's complement sum, and find its base 10 value. Determine if overflow occurred.

    
   (a)    0 1 0 1 0 1 1 0 1 0 
       +  1 0 0 1 0 0 0 1 0 1
         --------------------
   
   
   
   
   (b)    0 1 0 1 0 1 1 0 1 0
       +  0 0 1 1 0 0 0 1 1 0
         --------------------
   
   
   
   
   
   (c)    1 0 0 1 0 0 0 1 0 1
       +  1 1 1 1 0 1 1 1 1 0
         --------------------
   
   
   
   
   
   (d)    1 0 0 1 0 0 0 1 0 1
        + 1 1 0 1 1 0 0 0 0 0
         --------------------
   
   
   
   
   (e)    0 1 0 1 0 1 1 0 1 0
        + 1 1 1 1 0 1 1 1 1 0
         --------------------
   
   
   
   

3. TRUE or FALSE: If a 1 is carried out of the leftmost position (and hence lost), did overflow occur? Explain.

4. Can the sum of two numbers with opposite signs (one positive and one negative) cause overflow? Explain.