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A binary code represents text , computer processor instructions , or other data using any two-symbol system, but often the binary number system 's 0 and 1. The binary code assigns a pattern of binary digits bits to each character, instruction, etc. For example, a binary string of eight bits can represent any of possible values and can therefore represent a variety of different items. In computing and telecommunications, binary codes are used for various methods of encoding data, such as character strings , into bit strings.

Those methods may use fixed-width or variable-width strings. In a fixed-width binary code, each letter, digit, or other character is represented by a bit string of the same length; that bit string, interpreted as a binary number , is usually displayed in code tables in octal , decimal or hexadecimal notation.

There are many character sets and many character encodings for them. A bit string, interpreted as a binary number, can be translated into a decimal number. For example, the lower case a , if represented by the bit string as it is in the standard ASCII code , can also be represented as the decimal number 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.

Leibniz's system uses 0 and 1, like the modern binary numeral system. Leibniz encountered the I Ching through French Jesuit Joachim Bouvet and noted with fascination how its hexagrams correspond to the binary numbers from 0 to , and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.

Binary numerals were central to Leibniz's theology. He believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. The book had confirmed his theory that life could be simplified or reduced down to a series of straightforward propositions. He created a system consisting of rows of zeros and ones. During this time period, Leibniz had not yet found a use for this system. Binary systems predating Leibniz also existed in the ancient world.

The residents of the island of Mangareva in French Polynesia were using a hybrid binary- decimal system before The ordering is also the lexicographical order on sextuples of elements chosen from a two-element set. In Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text.

Another mathematician and philosopher by the name of George Boole published a paper in called 'The Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as Boolean algebra. Shannon wrote his thesis in , which implemented his findings. Shannon's thesis became a starting point for the use of the binary code in practical applications such as computers, electric circuits, and more.

The bit string is not the only type of binary code. A binary system in general is any system that allows only two choices such as a switch in an electronic system or a simple true or false test.

Braille is a type of binary code that is widely used by blind people to read and write by touch, named for its creator, Louis Braille. This system consists of grids of six dots each, three per column, in which each dot has two states: The different combinations of raised and flattened dots are capable of representing all letters, numbers, and punctuation signs.

The bagua are diagrams used in feng shui , Taoist cosmology and I Ching studies. The relationships between the trigrams are represented in two arrangements, the primordial, "Earlier Heaven" or "Fuxi" bagua , and the manifested, "Later Heaven,"or "King Wen" bagua. In Yoruba religion , the rite provides a means of communication with spiritual divinity.

In wood powder, these are recorded as single and double lines. The American Standard Code for Information Interchange ASCII , uses a 7-bit binary code to represent text and other characters within computers, communications equipment, and other devices. Each letter or symbol is assigned a number from 0 to For example, lowercase "a" is represented by as a bit string which is 97 in decimal.

Binary-coded decimal , or BCD, is a binary encoded representation of integer values that uses a 4-bit nibble to encode decimal digits. Four binary bits can encode up to 16 distinct values; but, in BCD-encoded numbers, only the first ten values in each nibble are legal, and encode the decimal digits zero, through nine.

The remaining six values are illegal, and may cause either a machine exception or unspecified behavior, depending on the computer implementation of BCD arithmetic.

BCD arithmetic is sometimes preferred to floating-point numeric formats in commercial and financial applications where the complex rounding behaviors of floating-point numbers is inappropriate. Most modern computers use binary encoding for instructions and data. Telephone calls are carried digitally on long-distance and mobile phone networks using pulse-code modulation , and on voice over IP networks. The weight of a binary code, as defined in the table of constant-weight codes , [18] is the Hamming weight of the binary words coding for the represented words or sequences.

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Leibniz, Mysticism and Religion. Proceedings of the National Academy of Sciences. Philosophy East and West. University of Hawaii Press. The I Ching or Book of Changes. Baynes, forward by C. Jung, preface to 3rd ed. Retrieved from " https: Views Read Edit View history.

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