Optical Flixed-Point Arithmetic

The DMAC (Digital Multiplication by Analog Convolution) algorithm has been shown to be one technique for performing optical matrix-multiplication with improved precision. Past work in this area has addressed fixed-point arithmetic only. Presented in this paper is an extension of the DMAC algorithm for handling floating-point binary numbers as well. However, the technique employed for handling floating-point numbers is based on fixed-point concepts. For this reason we choose to call the arithmetic as being flixed-point, since it is a hybrid combination of both floating and fixed-point arithmetic. In this paper we also describe an acousto-optical time-integrating architecture using binary flixed-point arithmetic to perform matrix-vector multiplication. By employing an array of full-adders in conjunction with the photodetector array at the back-end of this architecture, it is possible to avoid generating mixed binary outputs that normally result through the use of the DMAC algorithm. Hence, we eliminate the need for analog-to-digital converters needed to convert mixed binary to pure binary. Preliminary experimental results are also presented.