Assume 4 bit register are used Evaluate 0xB 0x3 using twos

Assume 4 bit register are used. Evaluate 0xB - 0x3 using twos complement arithmetic.

What is the final value in decimal.

Solution

      ASCII code      8 4 2 1
      0xB in binary   1 0 1 1
      0x3 in binary    0 0 1 1
  
need to find complement for -0x3
so by changing 1\'s to 0\'s and 0\'s to 1\'s
                            1 1 0 0
Now adding 0xB and 0x3
          0xB         1 0 1 1
          0x3     +   1 1 0 0
       -----------------------------
      overflow -->1 0 1 1 1
overflow occurs sum of the most significant produce the carry forward. it will cancel out.   

now convert 1\'s complement into real number
              carry 1 1 1
                    0 1 1 1
                         + 1
                   -------------
                    1 0 0 0  
Result is 1000 == 8 (decimal)                 
          
           verfiy 11 - 3 = 8