Abstract. In this paper, we focus on the M-k -B addition of the form M þ B 1 þ B 2 þ : : : þ B k based on an optical approach, where M is a modified signed-digit number and B i 's are the binary numbers. We present three transforms 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 M 0 þ B 1 þ B 2 þ : : : þ B k is easily completed.

On the basis of the research in MSD adder of Ternary Optical Computer (TOC), further work is carried out in one-step MSD adder with restricted input symbols. In this paper, the principle of general one-step MSD adder is introduced briefly. The core part of the principle can be reduced to the new conceptions of mid-bit transform, mid-bit transform table (MTT) and mid-bit transform unit (MTU). By restricting the input symbols, a simplified mid-bit transform table is obtained. Through the deep analysis to the simplified MTT, the subtransforms V and U as well as the main transform of the mid-bit transform are obtained, and the corresponding optical graphs are designed. Based on these, the structure of one-step MSD adder with restricted input symbols is proposed and its structure is designed. The software simulation and experiment to the mid-bit transform and the one-step adder show that the designed one-step MSD adder is effective. The adder will be one of the basic components of the ternary optical computer.

In this paper, the fast algorithm to Walsh-Hadamard transform (WHT) is studied from the point of view of the optical computation. Firstly, MSD addition and butterfly calculation in discrete WHT are presented in detail. Then the design and implementation scheme of fast algorithm of WHT is proposed and the software simulations to fast WHT are carried out optically. Meanwhile, the computational complexity of the algorithms in time and space are analyzed. The analysis shows that the problem of WHT with large-scale data can be solved in a few of clock cycles with optical computational method. The scheme also provides a good way for the design of fast optical Walsh-Hadamard transformer and an application in ternary optical computer.