q show the r-1s complement subtract every digit

Question

Q. Show the r-1s Complement?

• Subtract every digit of the number from r-1 (the radix of the system - 1)ex.

            952₁₀                                    

                                                9 9 9

                                                9 5 2 -

                                               0 4 7 (9's complement)

• To represent the negative number using the one's complement, write out the value (absolute value) of the number. then subtract each digit from r-1 ex.

5                    0000 0101

to represent -5

            1 1 1 1 1 1 1 1

            0 0 0 0 0 1 0 1 -

           1 1 1 1 1 0 1 0     (this is -5 in one's complement)

• Notice that a sign bit is correct (it became 1) which indicates a negative number.

• The Problems with using r-1's complement

            - zero has two representations

                        +0                    0000 0000

                        -0                     1111 1111

               but +0 and -0 are equal (so the machine has to know this)

            - Addition is harder