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A. The Binary Number System

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Unicode. Origin and development[edit] Unicode has the explicit aim of transcending the limitations of traditional character encodings, such as those defined by the ISO 8859 standard, which find wide usage in various countries of the world but remain largely incompatible with each other. Many traditional character encodings share a common problem in that they allow bilingual computer processing (usually using Latin characters and the local script), but not multilingual computer processing (computer processing of arbitrary scripts mixed with each other). In text processing, Unicode takes the role of providing a unique code point—a number, not a glyph—for each character. In other words, Unicode represents a character in an abstract way and leaves the visual rendering (size, shape, font, or style) to other software, such as a web browser or word processor.

The first 256 code points were made identical to the content of ISO-8859-1 so as to make it trivial to convert existing western text. Unicode Consortium. Binary Numbers in 60 Seconds. Number Bases: Introduction / Binary Numbers. Number Bases: Introduction / Binary Numbers (page 1 of 3) Sections: Introduction & binary numbers, Base 4 & base 7, Octal & hexadecimal This lesson is not yet availablein Purplemath Plus. Converting between different number bases is actually fairly simple, but the thinking behind it can seem a bit confusing at first. And while the topic of different bases may seem somewhat pointless to you, the rise of computers and computer graphics has increased the need for knowledge of how to work with different (non-decimal) base systems, particularly binary systems (ones and zeroes) and hexadecimal systems (the numbers zero through nine, followed by the letters A through F).

In our customary base-ten system, we have digits for the numbers zero through nine. Instead, when we need to count to one more than nine, we zero out the ones column and add one to the tens column. The only reason base-ten math seems "natural" and the other bases don't is that you've been doing base-ten since you were a child. Binary numeral system. History[edit] The modern binary number system was discovered by Gottfried Leibniz in 1679 and appears in his article Explication de l'Arithmétique Binaire. The full title is translated into English as the "Explanation of the Binary Arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi.[1] (1703). Leibniz's system uses 0 and 1, like the modern binary numeral system.

As a Sinophile, Leibniz was aware of the Yijing (or I-Ching) and noted with fascination how its hexagrams correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.[2] Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. 0 0 0 1 numerical value 20 0 0 1 0 numerical value 21 0 1 0 0 numerical value 22 Fractions[edit]