Modified signed digit arithmetic using an efficient symbolic substitution

Abstract

We have extended the scheme of Li and Eichmann1 by introducing an additional input bit (referred to as a flag) with each pair of input bits so that the nth additional bit is a characteristic of the (n – 1)th pair of input bits. This modified scheme is found to make the implementation of modified signed digit operations even more practical. A content-addressable memory is used for the optical implementation of the modified scheme. It is shown that only up to nine reference holograms are needed for each output bit. The proposed scheme is, therefore, a significant improvement over that devised by Mirsalehi and Gaylord.2 Furthermore, only 4 bits (3 bits plus a reference bit) are needed in the template, whereas the template used by Li and Eichmann1 requires a total of 5 bits. The resulting improvement of the proposed scheme thus amounts to increasing the page density of the input.