Boolean Algebra and digital logic Books PDF -INTRODUCTION

George Boole was a mathematician and logician who invented ways of expressing logical processes using algebraic symbols, thus creating a branch of mathematics known as Boolean algebra. It was later that Boolean algebra was applied to computing by John Vincent Atanasoff. He attempted to build a machine based on the same technology used by Pascal and Babbage, and wanted to use this machine to solve linear algebraic equations. After struggling with repeated failures, Atanasoff was so frustrated he decided to take a drive. Exercising his physics and mathematics backgrounds and focused on the failures of his previous computing machine, he made four critical breakthroughs necessary in the machine’s new design. He will be using electricity instead of mechanical movements (vacuum tubes would allow him to do this). Because he was using electricity, he would use base 2 numbers instead of base 10 (this correlated directly with switches that were either “on” or “off”), resulting in a digital, rather than an analog, machine.

He would use capacitors (condensers) for memory because they store electrical charges with a regenerative process to avoid power leakage.

He was unaware that in 1938, Claude Shannon proved that two-valued Boolean algebra could describe the operation of two-valued electrical switching circuits. Computations will be done by what Atanasoff termed “direct logical action” (which is essentially equivalent to Boolean algebra) and not by enumeration of all previous computing machines had done.As a computer scientist, you may never have to design digital circuits or other physical components—in fact, this chapter will not prepare you to design such items It provides minimal coverage of Boolean algebra and this algebra’s relationship to logic gates and basic digital circuits.It is for this reason that we include a chapter on Boolean logic and its relationship to digital computers. This chapter contains a brief introduction to the basics of logic design. It should be noted that at the time, Atanasoff did not recognize the application of Boolean algebra to his problem and that he devised his own direct logical action by trial and error. Today, we see the significance of Boolean algebra’s application in the design of modern computing systems. It is for this reason that we include a chapter on Boolean logic and its relationship to digital computers. This chapter contains a brief introduction to the basics of logic design. It provides minimal coverage of Boolean algebra and this algebra’s relationship to logic gates and basic digital circuits. You may already be familiar with the basic Boolean operators from a previous programming class. It is a fair question, then, to ask why you must study this material in more detail. The relationship between Boolean logic and the actual physical components of any computer system is very strong, As a computer scientist, you may never have to design digital circuits or other physical components—in fact, this chapter will not prepare you to design such items.For the interested reader, there are many resources listed at the end of the chapter to allow further investigation into these topics. Rather, it provides sufficient background for you to understand the basic motivation underlying computer design and implementation. Understanding how Boolean logic affects the design of various computer system components will allow you to use, from a programming perspective, any computer system more effectively. For the interested reader, there are many resources listed at the end of the chapter to allow further investigation into these topics.