DIGITAL ARITHMETIC

DIGITAL ARITHMETIC

1.      Represent each of the following  signed decimal numbers I the 2’s-complement system. Use a total of eight bits including the sign bit.

a)      +32

Completion :               00100000 = +32

                     C-I  =>   11011111

                     C-II =>                 1 +

                                    11100000 = -32          

b)      -14

Completion :               00001110= +14

                     C-I  =>   11110001

                     C-II=>                  1  +

                                    11110010= -14

                     C-I =>    00001101

                     C-II =>                 1 +

                                    00001110= +14          

c)      +63

Completion :               00111111= +63

                     C-I =>    11000000

                     C-II =>                1 +

                                    11000010= -63

d)     -104

Completion :               01101000= +104

                     C-I  =>   10010111

                     C-II=>                  1  +

                                    10011000= -104

                     C-I =>    01100111

                     C-II =>                 1 +

                                    01101000= +104

e)      +127

Completion :               01111111= +127

                     C-I =>    10000000

                     C-II =>                1 +

                                    10000001= -127

f)       -127

Completion :               01111111= +127

                     C-I =>    10000000

                     C-II =>                1 +

                                    10000001= -127

                     C-I =>    01111110

                     C-II =>                1 +

                                    01111111= +127

g)      +89

Completion :               01011001= +89

                     C-I =>    10100110

                     C-II =>                1 +

                                    10100111= -89

h)      -55

Completion :               00110111= +55

                     C-I =>    11001000

                     C-II =>                1 +

                                    11001001= -55

                     C-I =>    00110110

                     C-II =>                1 +

                                    00110111= +55

i)        -1

Completion :               00000001= +1

                     C-I =>    11111110

                     C-II =>                1 +

                                    11111111= -1

                     C-I =>    00000000

                     C-II =>                1 +

                                    00000001= +1

j)        -128

Completion :               10000000= +128

                     C-I =>    01111111

                     C-II =>                1 +

                                    10000000= -128

                     C-I =>    01111111

                     C-II =>                1 +

                                    10000000= +127

k)      -169

Completion :               10101000= +169

                     C-I =>    01010111

                     C-II =>                1 +

                                    01011000= -169

                     C-I =>    10100111

                     C-II =>                1 +

                                    10101000= +169

l)        0

Completion :               00000000= 0

                     C-I =>    11111111

                     C-II =>                1 +

                                    00000000= 0

m)    +81

Completion :               01010000= +81

                     C-I =>    10101111

                     C-II =>                1 +

                                    10110000= -81

n)      +3

Completion :               00000011= +3

                     C-I =>    11111100

                     C-II =>                1 +

                                    11111101= -3

o)      -3

Completion :               00000011= +3

                     C-I =>    11111100

                     C-II =>                1 +

                                    11111101= -3

                     C-I =>    00000010

                     C-II =>                1 +

                                    00000011= +3

p)      -190

Completion :               010111110= +190

                     C-I =>    101000001

                     C-II =>                  1 +

                                    101000010= -190

                     C-I =>    010111101

                     C-II =>                  1 +

                                    010111110= +190

2.      Each of the following numbers represent a signed decimal number in the 2’s-complement system. Determine the decimal value in each case. (Hint: use negation to convert negative numbers to positive.)

a)      01101 = 13

b)      11101 = -3

C –I => 00010

C-II =>          1 +

            00011 = 3

c)      01111011= 123

d)     10011001= -103

C-I =>  01100110

C-II =>               1 +

             01100111 = 103

e)      01111111= 127

f)       10000000= +/-128

C-I => 01111111

C-II =>              1+

            10000000 = +/-128

g)      11111111= -1

C-I  => 00000000

C-II =>               1 +

             00000001 =  1

h)      10000001 = -127

C-I  =>  01111110

C-II =>                1 +

              01111111 = 127

i)        01100011 = 99

j)        11011001 = -39

C-I  =>  00100110

C-II  =>               1 +

              00100111 = 39