Research Interests
Computer Arithmetic
In computer arithmetic, the choice of the number system can have a profound influence on the execution time and on the size of implementation of arithmetic algorithms. A redundant number system where a number can be represented by several strings can be used to reduce the complexity of algorithm. The signed digit number representation of Avizienis is a classical example. By using positive and negative digits, a redundant system is obtained. Generalized signed digit number systems have been studied by Parhami. Redundant representations are proved to be useful for arithmetic operation. For example, the division algorithm implemented in the Pentium processor gives a result in base 4 on alphabet { -2, -1, 0, 1, 2 }.By using positive and negative digits, it is possible to perform addition with carry propagation chains that are limited to a few digit positions. Computation using the signed digit representation and the most significant digit first (MSDF) serial arithmetic has come to be known as on-line arithmetic (first introduced by Ercegovac and Trivedi). On-line arithmetic is used for special circuits, such as signal processing, and for very long precision arithmetic. Some theoretical aspects of on-line computation have been examined. My research consists of an on-line computational fashion in computer arithmetic
Algorithm & Automata
We are concerned instead with the theory of computers, which means that we shall form several mathematical models that will describe with varying degrees of accuracy parts of computers, types of computers, and similar machines. The "mathematical" in this phrase does not necessarily mean that classical mathematical tools such as Euclidean geometry or calculus will be employed. What is mathematical about the models we shall be creating and analyzing is that the only conclusions that we shall be allowed to draw are claims that can be supported by pure deductive reasoning; in other words, we are obliged to prove the truth about whatever we discover. Our main conclusions will be of the form, "this can be done" or "this can never be done"