q show the rrsquos complementstep1- get the r-1s

Question

Q. Show the r’s Complement?

Step1- get the (r-1)'s complement

Step 2- add 1 to the result ex.

           935₁₀

                                    9 9 9

                                    9 3 5 -

                           0 6 4  (r-1)'s complement

                          0 6 4

                              1 +

                           0 6 5

• When using the r's complement we add usually, and ignore any carry from the most significant digit (MSD)

• If the result is in negative, it will be in r's complement form ex.

            395 - 210

210 is 789 + 1 = 790 in 10's complement form

            395

            790+

            185     

Why Use 2's Complement

• The left-most bit is still a sign bit

            1  for negative

            0  for positive

• One way to write 0

            +0 0000 0000

            -0  0000 0000  (how?)

• With n bits we can represent -2^n-1 to ( 2^n-1 - 1)

Let's now consider the subtraction 22 - 35, again both represented as 7-bit numbers with a sign bit.

                        +22 in binary is:                 00010110
                        +35 in binary is:                 00100011
                        -35 in binary is:                  10100011
                        -35 in 1's complement is:    11011100

The sum to be calculated is now:

                                            00010110
                                         + 11011100
                                            11110010 

This time the addition does not produce a 9th bit, but the sign bit is 1. In this case it again tells us two things:

• the answer is negative
• the answer is represented in 1's complement notation

So to get the final answer we need to turn our answer into binary. If the 1's complement notation is 11110010 then the binary representation is 10001101 (note - the sign bit doesn't change, it's still a negative number!). This is the binary for -13, again, the correct answer.