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Draw the data path of 2’s compliment multiplier. Give the Robertson multiplication algorithm for 2’s compliment fractions.Also illustrate the algorithm for 2’s compliment fraction by a suitable example.

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By Dipali Umre

The algorithm for 2’s complement multiplication is as follows :

Step 1 : Load multiplicand in B, multiplier in Q. For negative numbers, 2’s complement format to be used.
Step 2 : Initialize the down counter CR by the number of bits involved.
Step 3 : Clean locations A (n-bits) and Qn + 1 (1-bit).
Step 4 : Check LS bit of Qn and Qn + 1 jointly. If the pattern is 00 or 11 then go to Step 5. If 10, then A = A – B. If 01, then A = A + B.
Step 5 : Perform arithmetic right-shift with A, Qn and Qn + 1. LS of A goes to MS of Qn and LS of Q goes to Qn + 1. Old content of Qn + 1 is discarded.
Step 6 : Decrement CR by one. If CR is not zero then go to Step 4.
Step 7 : Final result (or the product) is available in A (higher part) and Qn(lower part).

Robertson algorithm :

  1. A ← 0, B← Multiplicand Q← Multiplier and count ← n.
  2. If Q0= 1 then perform A←A + B.
  3. Shift right register F.A.Q by 1 bit F ←B [n – 1] AND Q[0] OR F and count← count – 1.
  4. If count > 1 Repeat steps 2 and 3, otherwise if Q0= 1 then perform A ←A – B and set Q [0] = 0.
    For example : We perform the multiplication of fraction as :
    Multiplicand = 0.625
    Multiplier = 0.5
    Equivalent binary representation 0.625 = 0101
    2’s complement representation – 0.625 = 1010 + 1 (– 0.625) = 1011
    Equivalent binary representation + 0.5 = 0100
    2 complement representation – 0.5 = 1011 + 1 – 0.5 = 1100
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