Introducing binary

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We all know what decimal numbers are: However, many other numeral systems exist and you might have heard about or seen others, like hexadecimal numbers for example: These hexadecimal or binary numbers can easily be converted to the well-known decimal numbers. Other numeral systems exist because there are specific uses where a certain numeral system is easier to use and offers advantages over another. Binary and hexadecimal numbers are widely used in computer science. Binary numbers can be considered the very basic representation of a number in an electronic device.

This binary signals and coding in computing the mean of a sample help to explain why binary numbers are so important. The very first computers used binary numbers, and they are still used today. Every computer is made up of many electronic components. That is why a basic knowledge of electronics is needed to understand how and why binary numbers are used in computers. A computer is built with many connections and components, which are used to transfer and store data, as well as communicate with other components.

Most of that storing, transferring, and communicating happens with digital electronics. In electronics, a voltage level or current flow is a way to represent a value.

For example, 5V volts or 0. The makers of electronic devices could, of course, assign any meaning that they want to different voltage values. You would end up with 0. This means that when building an electronic device, it is most often desired to have the energy consumption as low as possible and to have a low voltage. Furthermore, electronic signals are not always very steady and can vary because of surrounding influences, like nearby internal circuits for other electronic devices.

This might then lead to voltage levels where it gets difficult to distinguish which value it represents. As a result, we cannot divide the 5V into 10 steps. The values could be misinterpreted. A binary signals and coding in computing the mean of a sample might suddenly make wrong calculations because of random interference. This example of voltage ranges shows that it is necessary to have a safe range between two voltage levels in order to read the correct value with percent probability.

There are additional methods on the software level to verify that data is read correctly, but this is out of the scope of this article.

Binary comes from the Latin language and means that something is composed of two things. Binary electronics are usually called digital electronics. Another major reason is because a lot more circuitry is needed to distinguish between more than two voltage levels. Each additional state needs about the same amount of additional circuitry.

Quantum computing, however, binary signals and coding in computing the mean of a sample one day replace the binary system. It might be the next big step in how our computers work! What does a Binary Number Mean?

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A binary code represents text , computer processor instructions , or any other data using a two-symbol system. The two-symbol system used is often the binary number system 's 0 and 1.

The binary code assigns a pattern of binary digits, also known as 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 wide 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. From Wikipedia, the free encyclopedia.

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March Learn how and when to remove this template message. List of binary codes. Gerhardt, Berlin , vol. What Kind of Rationalist?: What Kind of Rationalist? 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. In other projects Wikimedia Commons. This page was last edited on 7 April , at By using this site, you agree to the Terms of Use and Privacy Policy.