Decimal/rf_.sidue/decimal Optical Converters
نویسندگان
چکیده
Residue arithmetic [1-3] appears to be an attractive scheme for realizing a high speed numerical processor. Huang [4,5 ] was one of the first to suggest fabrication of an optical residue arithmetic processor. One recent optical approach [6] to such a system uses ~he phase or polarization of a spatial point as the cyclic variable. Another approach [7] uses pulse-position modulation to represent numbers and achieves the ne. cessary cyclic permutation by use of maps. Many possible realizations of optical residue arithmetic systems using integrated optical switches, planar waveguides, etc. have been suggested [7]. In this paper we address the design of a decimal/residue and residue/decimal converter. We present a correlation formulation of the required operations rather than expressing them by maps [7]. This approach leads directly to 2-D optical processor designs that can utilize the large available space bandwidth product of optical systems. In residue notation, we represent a decimal number X by its N residues Rmi moduli m i (where i = 1, . . . . N). All computations in residue arithmetic can thus be divided into sub-computations in each of N moduli. Since there are no carries in residue addition, subtraction and multiplication, all subcomputations can be performed in parallel. Such systems are thus directly implementable in a parallel multichannel optical processor. Furthermore, the maximum decimal number that can be represented in residue notation equals the product of the moduli. However, since a given computation is divided into sub-computations in the N moduli mi, the dynamic range of each sub-computation is greatly reduced with an associated reduction in the accuracy required. Since the accuracy and dynamic range of an optical processor are often questioned, an optical residue arithmetic system is an attractive way to reduce the required dynamic range and improve the accuracy of the overall system. In residue arithmetic, this is achieved at an increased system space bandwidth (SBW). However, since the available SBW of an optical processor can rarely be fully utilized, this represents no limitation in practice. For these many reasons optical residue arithmetic systems have recently received considerable attention [4-7] .
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