Trinary registers and counters using savart plate and spatial light modulator for optical computation in multivalued logic

Abstract

Registers and counters are the most important devices in any system of computations. In this paper we have communicated the trinary registers and counters in modified trinary number (MTN) system. It is suitable for the optical computing and other applications in multivalued logic system. Here the savart plate and spatial light modulator (SLM) based optoelectronic circuits have been used to exploit the optical tree architecture (OTA) in optical interconnection network.The carry and borrow-free mathematical operations are possible with modified trinary number (MTN) system [1][2][3] . The basic logic gates and the flip-flops are also reported [4][5][6][7][8][9][10] in MTN system using spatial light modulators (SLM) and savart plates. The flip-flops are the basic building block of sequential logic system. Any sequential logic system can be designed by using the flip-flops and the combinational logic units. One of the most important sequential circuits used in computing system is the register. A register consists of a group of flipflops that can store information. Since a trinary flip-flop [10] can store 1 trit of information, a n-trit word register requires n number of flip-flops connected in cascaded, i.e. the output of one flip-flop is connected to the input of another.In this paper we have communicated the implementation of trinary valued different shift registers and counters by using the clocked D-trinary flip-flops. The basic optical logic gates in MTN system have been used to implement the same. The basic clock pulse in trinary system is also used here. A mode control selector (MCS) is used to convert the D-trinary flip-flop into clocked D-trinary flip-flop. To implement the shift registers the MCS is used to implement the parallel and serial shift. The circuit implementations and the truth tables for the shift counter, ring counter and the ripple counters are discussed in details.Before going into the details a short introduction to the basic logical system of trinary along with the process of implementation is given. The three states of the trinary representation are classified as the true, false and contradiction as shown in Tab.1. The truth states for the trinary logic gates required to implement the trinary flip-flops, registers and counters are mentioned in Tab.2. The basic logic gates and their output functions have been defined earlier [5] . The required gates as mentioned may be implemented [5] by using the basic building block discussed hereunder.For the implementation of the logical operations as mentioned we have used a basic building block given in Fig.1. A light from a laser source L through a polarizer P is incident on the first savart plate S 1 . The basic property of a savart plate is that if a light polarized at a direction of 45 0 with the vertical axis as shown in the Fig.1, is incident on it, the output will be two parallel beams shifted between themselves. The state of polarization of the output beams is orthogonal to each other as shown. The output beams may be controlled (the presence o...