Multiplication circuit block design using reversible logic gates

Abstract

There has been an ever-increasing demand for electronic devices and computers since the day they were first produced. This request can be examined under three main headings; faster, cheaper and smaller. Over the years, there has always been upgradings on the smaller production technologies. This upgrades create chances to produce smaller applications to meet the demand on this area. Also, for a microchip, being smaller means having shorter lines between circuits, smaller serial resistances on circuits, closer transistors inside the chip etc. These features create a positive momentum for being faster. Because, smaller chip means that more resources can fit inside it which leads to parallel computing and shorthens logic operation delays. Also, smaller designs require less power to operate and loss less energy during computing. So being smaller affect both speed and energy in a positive way. However, Moore's law [1] says that smaller chip technologies will saturate eventually. This is because technology and physical limits. Even if smaller technologies would be produced, there is a physical barrier which is the diameter of electrons. In today's computing devices, electrons move from higher potentials to lower potentials to change states of bits. These bit changes occur in a small transistors. Even if incredibly small transistors would be produces, at one point, channel widths of transistor will be a limit for enough electron flow. If electron flow gets slower, state changes become slower so this directly affects the speed demand. In such cases, there can be alternative solutions such as using multi-core applications. Neverthless, once the core sizes and numbers are increased, delays and power consumptions are negatively affected. One other way to overcome faster applications without these limits is using and developing quantum computing devices. These devices work different than today's computers. They use quantum bits in other words qubit which can be 0 and 1 at the same time where classical computing devices uses 0 or 1 as a state. Since the possibility of states increase, the faster applications can be designed. This infastructure is based on quantum physics. Thus, quantum computers can solve more complex problems and run complex simulations faster than classical computing devices. There are some requirements to develop such devices, for example, these devices need to be isolated from enviromental affects or noises. They are difficult to built. They are developed for special tasks rather than being multi task computers. Also, they need to be build reversible since the creation of quantum states can not be erased. On the other hand, reversible design create less power loss opportunity because in reversible computing there is no need to erase or overwrite a bit. Every erase and write operations creates energy loss by heat around 3 x 10−21 Joule at room temperature. In this situation, using reversible gates can create optimizations for the designs. This study is mainly focused on this research area. So, reversible logic gates mean that n to n mapped, universal gates which leads finding it's unique inputs using it's outputs. Here, universal word means that using the same gate can help to find it's own unique inputs. So, learning universal gates, their application areas, advantages/disadvantages are studied along this thesis and one example is performed to realize their usage in an application. This application is chosen to be a multiplication circuit block example because, multiplication circuit blocks are one of the most resource and time demanding blocks in digital systems. So, using reversible logic gates in a multiplication circuit block example would be helpful to both understand the gates and having a design approach for a widely used application in the literature. The main motivation during the design is to use one single gate type to perform less circuit complexity and fast development opportunity.