Modified Ternary Optical Logic Gates and their Applications in Optical Computation
01 Jan 2008-pp 87-92
TL;DR: In this article, the trinary optical logic gates with optical implementations and a few applications of it to the half adder and full adder circuits, this may also be extended to multiplexers and de-multiplexers, flip-flops, registers, counters, etc.
Abstract: Optical logic gates are most important factors for the parallel operations and utilizations in VLSI circuits for the very high speed data processing and communications. This calls for multivalued logic implementation. In this paper we have communicated the trinary optical logic gates with optical implementations and a few applications of it to the half adder and full adder circuits, this may also be extended to multiplexers and de-multiplexers, flip-flops, registers, counters, etc.
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TL;DR: An architecture and implementation method of modified signed-digit (MSD) optical adder from the point of applicability and shows, the MSD adder not only has a reasonable and correct design, but also has high throughput rate, can work efficiently and steadily.
Abstract: How to fully apply the characteristics and advantages of light in numerical computation is an important issue that attracts many scholars. Though much research has been done in this field, how to design and realize specific applications or devices is still an issue to be solved. Based on this, we present an architecture and implementation method of modified signed-digit (MSD) optical adder from the point of applicability. In the implementation, we fully consider the different procedures of the MSD addition which including optical logical operation, results decoding, special storage area design, data feedback, control of light path, etc. Meanwhile, we also introduce pipeline mechanism which guarantees that the addition operation is an automatic and continuous process. This is a carry free adder design method which guarantees the addition has high data throughput. It is very suitable to fulfill the large-scale numerical computation. The experiment shows, the MSD adder not only has a reasonable and correct design, but also has high throughput rate, can work efficiently and steadily.
34 citations
Additional excerpts
...designed the half-adder and full adder circuits to complete the optoelectronics system [5]....
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TL;DR: This paper has communicated the conversion from Binary to MTN and vice-versa including the mixed MTN with details of optoelectronic circuit implementation.
Abstract: With the demand of the super fast processing and handling of huge volume of data the scientific workers in the field of computer and optics felt the importance of optical computation with multivalued logic. One of the most important number system suitable for optical computation with multivalued logic is the modified trinary number (MTN) system because of its carry and borrow-free operations. At this juncture to avail the advantages of both the Binary and MTN system the conversion from one system to another is most important. In this paper we have communicated the conversion from Binary to MTN and vice-versa including the mixed MTN with details of optoelectronic circuit implementation.
15 citations
TL;DR: This paper has communicated the quadruple valued logic system using di-bit concept and their implementations to meet up the tremendous needs of speeds by exploiting the advantages of savart plates and spatial light modulators (SLM) in the optical tree architecture (OTA).
Abstract: With the demanding scenario of communication and optical computing technology the trinary and quadruple valued logic systems are the most important ones in the many valued logic system. Different techniques are being proposed day-by-day to implement the multi-valued logics (MVL). In our previous papers we have proposed the modified trinary number (MTN) systems using savart plates and spatial light modulators (SLM). In this paper we have communicated the quadruple valued logic system using di-bit concept and their implementations to meet up the tremendous needs of speeds by exploiting the advantages of savart plates and spatial light modulators (SLM) in the optical tree architecture (OTA).
12 citations
TL;DR: The work indicates that the parallel carry-free addition in form M0+B1+B2+…+Bk is easily completed and requires only 2k steps to complete the addition in parallel.
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)
9 citations
TL;DR: A new set of designs for existing logic gates in the Modified Trinary Number system with more efficiency and less complexity is proposed, enabling direct cascading of multiple gates and require lesser number of SLMs and Savart plates for realization, hence greatly reducing the circuit complexity of larger circuits.
Abstract: Multivalued optical logic shows immense promise in modern computing systems with several advantages like ultrahigh computational speed, large amount of data handling capability and high data density. The logic gates are building blocks of computational systems, and all the logic circuits can be realized by cascading different logic gates. This paper proposes a new set of designs for existing logic gates in the Modified Trinary Number system with more efficiency and less complexity. The newly designed gates enable direct cascading of multiple gates and require lesser number of SLMs and Savart plates for realization, hence greatly reducing the circuit complexity of larger circuits. The Optical Tree Architecture of these new logic gates is realized using Spatial Light Modulators (SLM) and Savart plates. Moreover, a comparative study between the newly designed gates and existing gates is also incorporated to demonstrate the reduction in SLMs and Savart plates in the newly developed designs.
6 citations
References
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TL;DR: Sign-digit representations limit carry-propagation to one position to the left during the operations of addition and subtraction in digital computers and arithmetic operations with signed-digit numbers: addition, subtraction, multiplication, division and roundoff are discussed.
Abstract: This paper describes a class of number representations which are called signed-digit representations. Signed-digit representations limit carry-propagation to one position to the left during the operations of addition and subtraction in digital computers. Carry-propagation chains are eliminated by the use of redundant representations for the operands. Redundancy in the number representation allows a method of fast addition and subtraction in which each sum (or difference) digit is the function only of the digits in two adjacent digital positions of the operands. The addition time for signed-digit numbers of any length is equal to the addition time for two digits. The paper discusses the properties of signed-digit representations and arithmetic operations with signed-digit numbers: addition, subtraction, multiplication, division and roundoff. A brief discussion of logical design problems for a signed-digit adder concludes the presentation.
1,232 citations
01 Jul 1984
TL;DR: The paper begins with a review of analog, discrete, and binary methods of representing information in a computer, followed by a survey of many techniques for implementing binary combinatorial and sequential logic functions with individual optical devices and arrays of devices.
Abstract: This paper concerns binary digital computing systems in which the information-carrying medium consists entirely or primarily of photons. The paper begins with a review of analog, discrete, and binary methods of representing information in a computer, followed by a survey of many techniques for implementing binary combinatorial and sequential logic functions with individual optical devices and arrays of devices. Next is a discussion of communication, interconnection, and input-output problems of digital electronic and optical computers at the gate, chip, and processor level. A particular architecture for implementing general sequential optical logic systems including digital optical processors is described. This architecture avoids some of the interconnection problems of electronic integrated circuits and VLSI systems, and offers the potential of non von Neumann parallel digital processors. Finally, the current limitations and future needs of optical logic devices and digital optical computing systems are outlined.
315 citations
TL;DR: Using residue arithmetic it is possible to perform additions, subtractions, multiplications, and polynomial evaluation without the necessity for carry operations.
Abstract: Using residue arithmetic it is possible to perform additions, subtractions, multiplications, and polynomial evaluation without the necessity for carry operations. Calculations can, therefore, be performed in a fully parallel manner. Several different optical methods for performing residue arithmetic operations are described. A possible combination of such methods to form a matrix vector multiplier is considered. The potential advantages of optics in performing these kinds of operations are discussed.
168 citations
116 citations
TL;DR: A detailed analysis of the relative advantages of both direct and associative truth table processing is presented, and the respective merits from the point of view of the number of computations per second and the energy required per computation are outlined.
Abstract: The operating characteristics of digital optical computers utilizing spatial light modulator based shadow casting are reviewed. The geometric and physical limitations of this method are examined. Because of the highly parallel nature of this approach, such systems are capable of truth-table processing. A detailed analysis of the relative advantages of both direct and associative truth table processing is presented. For each case, the use of binary or of multiple-valued logic is considered. The respective merits from the point of view of the number of computations per second and the energy required per computation are outlined. Switching energy considerations based on the use of multiple wavelengths in these systems are also discussed. The characteristic features of this type of optical logic are compared to those of electronic logic.
45 citations