Carry—borrow free sequential quotient generation with segmented signed-digit operands†

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Abstract
A theoretical analysis is carried out and division schemes are described for sequential (or digit-by-digit) generation of carry—borrow free quotient digits with segmented signed-digit operands. These schemes permit storing each one of these quotient digits permanently, in the vacant storage created by liquidating the leading digit of each one of the partial remainders. This analysis has also given rise to a division scheme suitable for conventional number systems which could generate reduced-magnitude quotient digits. Although this scheme has the same objective as Robertson's scheme, it has two additional advantages—it does not involve the use of different fractional comparison constants for quotient determination and there is no borrow propagation through a sequence of zeros while expressing the quotient in the conventional form. A comparative study of these schemes with the earlier schemes of Avizienis, Tung and Atkins is presented.

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