Number Systems

Number Systems in Switching theory and logic design uploaded at Engineering Study material

Number Systems in Switching theory and logic design at Engineering Study material uploaded by suryam m in lecturenotes.net

We all use numbers to communicate and perform several tasks in our daily lives. Our present day world is characterized by measurements and numbers associated with everything. In fact, many consider if we cannot express something in terms of numbers is not worth knowing. While this is an extreme view that is difficult to justify, there is no doubt that quantification and measurement, and consequently usage of numbers, are desirable whenever possible. Manipulation of numbers is one of the early skills that the present day child is trained to acquire. The present day technology and the way of life require the usage of several number systems. Usage of decimal numbers starts very early in one’s life. Therefore, when one is confronted with number systems other than decimal, some time during the high-school years, it calls for a fundamental change in one’s framework of thinking. There have been two types of numbering systems in use through out the world. One type is symbolic in nature. Most important example of this symbolic numbering system is the one based on Roman numerals I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000 IIMVII - 2007 While this system was in use for several centuries in Europe it is completely superseded by the weighted-position system based on Indian numerals. The Roman number system is still used in some places like watches and release dates of movies. The weighted-positional system based on the use of radix 10 is the most commonly used numbering system in most of the transactions and activities of today’s world. However, the advent of computers and the convenience of using devices that have two well defined states brought the binary system, using the radix 2, into extensive use. The use of binary number system in the field of computers and electronics also lead to the use of octal (based on radix 8) and hex-decimal system (based on radix 16). The usage of binary numbers at various levels has become so essential that it is also necessary to have a good understanding of all the binary arithmetic operations. Here we explore the weighted-position number systems and conversion from one system to the other.

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Title:

Number Systems

Subject:

Switching theory and logic design

Institute:

Engineering Study material