Friday, September 16, 2011

Computer Architecture # 03 :Arithmetic : SIGNED MULTIPLICATION AND DIVISION (9)

3.3.3 SIGNED MULTIPLICATION AND DIVISION
If we apply the multiplication and division methods described in the previous sections to signed integers, then we will run into some trouble. Consider multiplying −1 by +1 using four-bit words, as shown in the left side of Figure 3-16.
The eight-bit equivalent of +15 is produced instead of −1. What went wrong is that the sign bit did not get extended to the left of the result. This is not a problem for a positive result because the high order bits default to 0, producing the correct sign bit 0.
A solution is shown in the right side of Figure 3-16, in which each partial product is extended to the width of the result, and only the rightmost eight bits of the result are retained. If both operands are negative, then the signs are extended for both operands, again retaining only the rightmost eight bits of the result.
Figure 3-15    An example of division using the serial divider.

Figure 3-16    Multiplication of signed integers.
Signed division is more difﬁcult. We will not explore the methods here, but as a general technique, we can convert the operands into their positive forms, perform the division, and then convert the result into its true signed form as a ﬁnal step.