Show work and explain the flags please Complete the followin

Complete the following arithmetic operations in two\'s complement representation. What are the value of the carry flag and the overflow flag? (Assume a six-bit system) -7 +(-29) 31 + 11 15-19 -7 times (-3) -7 times (3) 21 3 21 (-3) Show work and explain the flags please.

Solution

a. -7 +(-29)

7 = 000111

-7 = complement of 7 +1= 2\'s complement = 111000 + 1= 111001

29 = 011101

-29 = 2\'s complement of 29 = 100010 + 1 = 100011

carry-> 10000

-7        111001

+(-29)100011

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

Overflow->1     011100 = -36

b.

31 +11

Both are positive numbers so there is no need of 2\'s complement(representation of negative numbers)

carry->11111

31 = 011111

11 = 001011

+

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

Overflow->0 101010 = 42

c. 15-19

= 15+(-19)

15 = 001111

19 = 010011

-19 = 2\'s complement of 19 = 101100 + 1 = 101101

carry->01111

15      001111

+(-19) 101101

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

overflow-> 0 111100 = -4

d. -7 *(-3)

7 = 000111

-7 = 111000+1 = 111001

3 = 000011

-3 = 2\'s complement of 3 = 111100+1 = 111101

-7 *(-3)

->111001

* 111101

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

10111001

000000*

111001**

111001***

111001****

111001*****

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

010101---->last 6 bits = 21 (-7)*(-3)

e. -7 * 3

same as above except answer is negative -21

21 = 010101

its 2\'s complement = 101011 = -21

f

21/3

21 = 10101

3 = 11

11 | 10101 | 111

        11

        ----

         100

           11

         ------

           11

           11

          ---

          0

= 111 = 7

g

21 /(-3)

same as above except answer is negative = -7

-7 = 111001