Formation of optimal Boolean functions for analog-digital conversion

This paper describes a situation in which the function obtained from an analog-to-digital conversion is considered a partially-certain function. In this case it is possible to neglect the least significant bits and therefore redefine them arbitrarily. A realization of proposed method simplifies the further processing of the received signal, and saves hardware consumption at designing and usage of hardware and software systems that include analog-to-digital converters.

I. Introduction

THE extensive development of the idea of “Smart Cities” and “Smart Things” requires increased computing power and reducing the overall dimensions of chips for compact wearable devices and other mobile electronics. At the same time, increasing capacity entails increasing power consumption, which can be a problem especially in devices that use batteries for compact power supply (for example - Smartphones, Smart Watches, unmanned vehicles, GPS trackers, etcetera). Developers are also faced with another problem - the miniaturization of elements in modern electronic devices. Each time another step is taken to reduce the technological size of modern chips to a minimum, it is met with growing difficulties, this is due to the current technological restrictions on production possibilities. There is a number of fundamental obstacles that impede further reduction in the size of individual elements that are found in integrated circuits: –

the greater the amount of elements on a chip per unit volume, the more heat needs to be dissipated from the chip, this greatly increases the power consumption of cooling systems which can be even more than that of the electronic device itself;

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electrodynamic constraints caused by capacitance and inductance inertia in the circuit. This hinders the rapid change of a voltage and a current during transition from one state to another (for example, logic operation keys in the microprocessor or dynamic memory cells);

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while reducing the size of the object to the atomic scale, an atomic and electronic discreteness is visible in the transport phenomena, in the interaction of elementary particles, etc. All these problems lead us to look for new ways of improving the microelectronic structures of computers, which are becoming increasingly important to manufacturers. A one of these ways is an optimisation of using different forms representation of Boolean functions for forming logical circuits at the stage of logical design and for processing of signals which can be presented as Boolean functions.