| 摘要 |
<p>The invention concerns a method for breaking down and performing with an electronic circuit, a computing operation based on a digital factor (N) expressed in integral base (r) by a series of integers (pn-1, , p2, p1, p0). The invention provides steps which consists in: breaking down the series of integers into elementary multiplets, each elementary multiplet (MJ) comprising part of the series of integers (mji+1, mji, , mj0), wherein each pair of successive numbers (mi, mi-1) has a sum equal in value to the base decreased by one unit (mi+mi1 = r-1); and transforming each elementary multiplet (Mj) into a modified multiplet (Sj) comprising a series of sign digits (sji, sji-1, ,sj1)such that the concatenation of modified multiplets constitute a series of sign digits containing a minimum of non-null digits and representing the value of the digital factor (N) in a relative base ({-(r-1), , -1,0,1, , r-1}). In the preferred embodiment of the invention: for an elementary multiplet containing a minimum number of odd integers, and expressed in the following form: M1 = [b,d,(c,d)k,e] (type I) the transformation follows one of the following conditional formulae: {S1 = [*, (d,c)k, d, *], if b+d<r-1 and e+d<r-1, S1 = [*, (d,c)k, d+1, *], if b+d<r-1 and e+d>r-1, S1 = [*, (-c,-d)k, d-r, *], if b+d>r-1 and e+d<r-1, S1 = [*, (-c,-d)k, -d, *]* if b+d>r-1 and e+d>r-1} (1); for an elementary multiplet containing an even number of integers, and expressed in the following form: M2 = [b,d,(c,d)k,c,e] (type II) the transformation follows one of the following conditional formulae: {S2 = [*, (d,c)k, d, c, *], if b+d<r-1 and e+c<r-1, S2 = [*, (d,c)k, d+1, -d, *], if b+d<r-1 and e+c>r-1, S2 = [*, (-c,-d)k, d-r, c, *], if b+d>r-1 and e+c<r-1, S2 = [*, (-c,-d)k-c,-d, *], if b+d>r-1 and e+c>r-1 (2).</p> |
