Perform the following computations involving 8bit numbers in

Perform the following computations involving 8-bit numbers in 2\'s complement representations and indicate whether an arithmetic overflow occurs. 01110110 + 11000101 01010101 + 11111110 00110110-00101011 11010110 - 11101100 01110100 - 11010111

Solution

i)    [1]  1       1        Carry  

            0111 0110

        +  1100 0101

-------------------------

            0011 1011
-------------------------

Above has arthmetic overflow represented as [1]

so we will find the 2\'s compliment of the result (0011 1011).

Step 1: 1\'s complement of 0011 1011 is (replace 0 with 1 and 1 with 0) = 1100 0100

Step 2 : add 1 to step 1 result

final result: 11000101

ii) [1]   1111 1        Carry  

            0101 0101

        +  1111 1110

-------------------------

            0101 0011
-------------------------

Above has arthmetic overflow represented as [1].

so we will find the 2\'s compliment of the result (1010 1100).

Step 1: 1\'s complement of 0011 1011 is (replace 0 with 1 and 1 with 0) = 1010 1100

Step 2 : add 1 to step 1 result

final result: 10101101