Novel method to simplify Boolean functions
Journal Title: Automatyka - Year 2018, Vol 22, Issue 2
Abstract
Most methods for determining the prime implicants of a Boolean function depend on the minterms of the function. Deviating from this philosophy, this paper presents a method that depends on maxterms (the minterms of the complement of the function) for this purpose. Normally, maxterms are used to get prime implicates and not prime implicants. It is shown that all prime implicants of a Boolean function can be obtained by expanding and simplifying any product of sums form of the function appropriately. No special form of the product of the sums is required. What is more, prime implicants can generally be generated from any form of the function by converting it into a POS using well-known techniques. The prime implicants of a product of Boolean functions can be obtained from the prime implicants of individual Boolean functions. This allows us to handle big functions by breaking them into the products of smaller functions. A simple method is presented to obtain one minimal set of prime implicants from all prime implicants without using minterms. Similar statements also hold for prime implicates. In particular, all prime implicates can be obtained from any sum of a product’s form. Twelve variable examples are solved to illustrate the methods.
Authors and Affiliations
V. C. Prasad
Keywords
Related Articles
- EP ID EP531458
- DOI 10.7494/automat.2018.22.2.29
- Views 69
- Downloads 0
A sufficient condition for existence of constantly nondominated trajectories in linear time-invariant systems
This paper considers the multi-criteria optimal control problem in linear time-invariant systems with a single bounded input. It has been proven that, under certain assumptions, a state trajectory is non-dominated throug...
New approach in modelling of the patients behavior in Primary Health Care (PHC)
The purpose of this paper is to show the concept of simulation of Primary Health Care (PHC) patients behavior. There are two reasons for interest in this area. The first of them is the need for support in decision making...
Shape optimization of a flywheel
The article presents the problem of the use of flywheels as an energy storage. More specifically focused on the issue of the optimal shape for isotropic materials and shapes, for which you can analytically determine the...
A thermal model of the building for the design of temperature control algorithms
This paper presents an efficient and effective method for modeling the temperature dynamics in buildings. The method relies on the simultaneous application of heat transfer and engineering thermodynamics principles. The...
The use of EMG signal in human-machine interface
In this paper, the analysis and processing algorithms of EMG signals have been presented. The main purpose of the research was to verify the usefulness of EMG signals in controlling a bionic prosthesis or exoskeleton. Th...