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Book details
• Genre:MATHEMATICS
• SubGenre:Probability & Statistics / General
• Language:English
• Pages:179
• Paperback ISBN:9781098328719

E1THER, 0R

Exploring the Binary World

by Reza Noubary

Overview
Numbers and numeration systems have played a key role in human development. Throughout history, our understanding of numbers has gone through a dramatic change and has reached a high level of sophistication. A number is an abstract concept used to describe a quantity. A numeration system is a set of basic symbols called numerals—such as 0, 1, and 2—and some rules—such as addition and multiplication—for making other symbols from them. The invention of a precise, workable numeration system is one of the greatest accomplishments of humanity. The numerical digits that we use today are based on the Hindu-Arabic numeral system developed over a thousand years ago. Other than decimal system/base 10 system that uses the ten symbols (0, 1 … 9), a most popular system is the binary or base 2 system, which uses only the two symbols 0 and 1. Because computers use a sequence of switches that can be only on or off (bit), base 2 works well there. This book is an attempt to explore certain aspects of the binary system that relates to everyday life and mathematical sciences in particular. It focuses on the role of such systems and tries to analyze and visualize the world where decimal system is replaced by binary. It, whenever appropriate, uses what is known as Boolean logic.
Description
As humanity has progressed throughout its tenure on earth, so too has a numerical system. The decimal system motivated by our ten fingers, is the beating heart behind the mathematical processes essential to current human understanding and impressive technological advancement. As expected, human curiosity has naturally led one to contemplate the idea of other number systems, and as it turned out, the possibilities were unlimited. One of the most prominent is the numeric basis of logic and computer systems, the binary. Today the binary system plays an important role in our life. Several technologies used on a daily basis including communication, data transfer and storage, Web, and smart systems all work with the help of binary codes. It is a system that provides the most basic and fastest approach in any programming language as it is the most singular representation of an electrical impulse. As the binary system is now a part of the human life, it is natural to imagine a world much like ours but with the decimal numbers is replaced by the two digits of the binary system. In other words, imagine that people started counting using the binary numbering system based on (0,1) in place of the decimal system based on (0,1,2,3,4,5,6,7,8,9). If so, what would be the major differences between these two worlds? What would be more/less advanced, easier/harder, faster/slower, and more/less efficient and practical? For example, as a kid we may appreciate the fact that in a binary world there would be no need for a multiplication table. What logical or social similarities/differences would that civilization have with ours? These and many other puzzling but interesting questions may come to one's curious mind. This book is an attempt to explore certain aspects of the binary system. Its goal is not to answer the questions posed above in its entirety but to provide some helpful discussions and clues. To begin with we note that binary thinking feels safe and understandable as it always puts things in terms of two mutually exclusive options. It creates a world where things are mostly "black, white", "either, or", "right, wrong", and "good, bad", ignoring any subtleties or consideration of third or more alternatives. It seems that the largest and most powerful part of our brain loves to think that this is how the world works. It craves the clarity of a world that unfolds in a straight line. It's happy that there's a plan and it takes comfort that if we stick to it, everything will be ok.