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Principles of Computer Hardware_Part199.doc - 4.10...

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4.10 Multiplication and division191(Two’s complementform)First partialproductSecond partialproductThird partialproductFourth partialproductFifth partialproductUncorrectedresultCorrection factorCorrected resultdouble-length product. In order to get the correct two’scom-plement result we have to add a correction factor of22n-2nX=2n(2n-X)This correction factor is the two’s complement ofXscaledby 2n. As a further illustration consider theproduct ofX=15andY= -13in 5 bits.The final result in 10 bits, 11001111012=-19510, is cor-rect. Similarly, whenXis negative andYis positive, acorrec-tion factor of 2n(2n-Y) must be added to the result.When both multiplier and multiplicand are negative thefollowing situation exists.(2n-X)(2n-Y)=22n-2nX-2nY+XYIn this case correction factors of 2nXand 2nYmust beadded to the result. The 22nterm represents a carry-out bitfrom the most-significant position and can be neglected.
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