An Innovative procedure to minimize Boolean function

R .Mohana Ranga Rao Department of Electronics and communication Engineering KITE college of Professional engineering sciences, JNTUH Shabad,India e-mail: mohana_rangarao@yahoo.co.in

Keywords- Boolean Function, Simplification, M-terms, Quine McCluskey, Face value

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INTRODUCTION

IJ

ISSN: 2230-7818

Boolean function minimization using M-terms is a modiﬁed Quine-McCluskey [4] [6] method; it is a very simple and systematic technique for minimizing Boolean functions. Why do we want to minimize a Boolean expression? By simplifying the logic function we can reduce the original number of digital components (gates) required to implement digital circuits. Therefore by reducing the number of gates, the chip size and the cost will be reduced, and the speed will be increased. Logic minimization uses a variety of techniques to obtain the simplest gate-level implementation of a logic function.

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The heart of digital logic design is the Boolean algebra (Boole, 1954)[2].A few decades later C.E.Shannon showed how the Boolean algebra can be used in the design of digital circuits(Shannon,1938)[7].Using Boolean laws It is possible to minimize digital logic circuits(Huntington,1904).Since minimization with the use of Boolean laws is not systematic nor suitable for computer implementation, a number of algorithms were proposed in order to overcome the implementation issue. Karnaugh [3] proposed a technique for simplifying Boolean expressions using an elegant visual technique, which is actually a modiﬁed truth table intended to allow minimal sum-of-

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Abstract— In this paper a simplification technique is introduced to minimize a Boolean function. Karnaugh map (K-map) and Quine-McCluskey methods are well established methods to simplify a logic function. Using this method the simplification is fast, also the number of gates required to realize a function gets reduced to greater extent with a minimum effort. In present discussion a new method is introduced in which new terms called M-terms obtained in order to improve the performance of conventional methods. The given method can be implemented to any number of variables.

The Quine-McCluskey (Q-M) method is a computerbased technique for simpliﬁcation and has mainly two advantages over the K-Map method. Firstly, it is systematic for producing a minimal function that is less dependent on visual patterns. Secondly, it is available scheme for handling a large number of variables. A number of methods have been developed that can generate optimal solutions directly at the expense of additional computation time. Another algorithm was reported by Petrick(1959)[5]. This algorithm uses an algebraic approach to generate all possible covers of a function. A popular tool for simplifying Boolean expressions is the Espresso, but it is not guaranteed to ﬁnd the best two-level expression (Katz,1994)[1]. The main advantage of proposed method over the conventional methods is the entire simplification is based on the decimal values (E.g. M-terms) which are well known to each and every designer, so in practice it is easy to implement this method to improve the performance. RELATEDWORK The digital gates (Logic gates) are basic electronic components of any digital circuit. A logic gate performs a logical operation based on one or more inputs and produces a single output voltage value (i.e. voltage levels high and low). Logically these voltage values can be referred to as 1s and 0s and are used in designing and analyzing the operations of logic gates. A logic gate represents a Boolean function. A Boolean function is an algebraic expression formed with Boolean variables (having values true or 1 and false or 0) and the logical operators (i.e....