Abstract
In this paper, we focus on the M-k-B addition of the form M þ B1 þ B2 þ :::þ Bk based on an optical approach, where M is a modified signed-digit number and Bi's are the binary numbers. We present three trans- forms C, P, and R and an algorithm of carry-free parallel addition of M and B. Based on these transforms, the accumulation computing M-k-B is proposed which indicates that it requires only 2k steps to complete the addition in parallel. Then, the optical structures for C, P, and R transforms as well as the adder realizing M þ B are designed. Moreover, a photoelectric implementation of the ternary optical adder to realize M-1-B structure using the reconfiguration method is presented. Additionally, an optical experiment for 2-bit M-2-B ternary adder is carried out to demonstrate the feasibility of M-k-B adder. The work indicates that the parallel carry-free addition in form M0 þ B1 þ B2 þ :::þ Bk is easily completed. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. (DOI: 10.1117/1.OE.53.9.095108)
Highlights
Bocker et al applied the modified signed-digit representation (MSD) to optical computing,[5] which is easier to be implemented in hardware and leads to the applications in optical computer
Jin et al proposed a principle of ternary optical computer (TOC), the decrease-radix design principle, and the reconfiguration principle and structure,[19,20,21] which laid a solid foundation to the system design of the application-oriented TOC
We present the process of n-bit M-k-B addition of the form M þ B1 þ B2 þ : : : þ Bk as follows
Summary
Proposed a two-step MSD addition and subtraction algorithm based on binary logic arithmetic using electron-trapping device, and presented one-step digit-set-restricted modified signed-digit adder.[17,18] Jin et al proposed a principle of ternary optical computer (TOC), the decrease-radix design principle, and the reconfiguration principle and structure,[19,20,21] which laid a solid foundation to the system design of the application-oriented TOC. The process of M-1-B addition of n bits is described as follows: Denote the MSD number mnmn−1: : : m1 by M and the binary number bnbn−1: : : b1 by B. From the above computing processes, only two steps are required to perform n-bit M-1-B addition using C, P, and R transforms in parallel.
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