Fast Memoryless,over 64 bits, residue-to-binary convertor

This paper describes an algorithm and its hardware implementation which converts the 3 moduli (2^{n} - 1,2^{n}, 2^{n} + 1) residue numbers into their binary representation. The given technique requires only binary adders, and no look-up tables. antages of this approach are two-fold: 1) It enables an extremely wide, fixed-point dynamic range, since its upper bound is not limited by a memory size. 2) The Integrated Circuit area required for its realization can be directly traded off with conversion speed. As a result, a 66-bit convertor with a conversion time of 120 ns, or a 36-bit one with 40 ns, may be implemented as single CMOS chips with 3 \mu m geometries.