NEW SVOBODA-TUNG DIVISION

This paper presents a general theory for developing new Svoboda-Tung ( or simply NST) division algorithms not suffering the drawbacks of the ''classical'' Svoboda lung (or simply ST) method. NST avoids the drawb acks of ST by proper recoding of the two most significant digits of th e residual before selecting the most significant digit of this recoded residual as the quotient-digit. NST relies on the divisor being in th e range [1, 1 + delta), where delta is a positive fraction depending u pon: 1) the radix, 2) the signed-digit set used to represent the resid ual, and 3) the recoding conditions of the two most significant digits of the residual. if the operands belong to the IEEE-Std range [1, 2), they have to be conveniently prescaled. In that case, NST produces th e correct quotient but the final residual is scaled by the same factor as the operands, therefore, NST is not useful in applications where t he unsealed residual is necessary. An analysis of NST shows that previ ously published algorithms can be derived from the general theory prop osed in this paper. Moreover, NST reveals a spectrum of new possibilit ies for the design of alternative division units. For a given radix-b, the number of different algorithms of this kind is b(2)/4.