Arithmetic is a branch of mathematics that consists of the study of numbers, especially concerning the properties of the traditional operations on them—addition, subtraction, multiplication, division, exponentiation and extraction of roots. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory, and are sometimes still used to refer to a wider part of number theory.
The duodecimal system is a positional notation numeral system using twelve as its base. The number twelve is instead written as "10" in duodecimal, whereas the digit string "12" means "1 dozen and 2 units". Similarly, in duodecimal "100" means "1 gross", "1000" means "1 great gross", and "0.1" means "1 twelfth".
In mathematics and computing, the hexadecimal numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the common way of representing numbers using 10 symbols, hexadecimal uses 16 distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" to represent values 10 to 15.
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7, that is to say 10 represents 8 in decimal and 100 represents 64 in decimal. However, English uses a base-10 number language system and so a true octal system might use different language to avoid confusion with the decimal system.
A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable computers and calculators. Numerical values are stored as groupings of bits, such as bytes and words. The encoding between numerical values and bit patterns is chosen for convenience of the operation of the computer; the encoding used by the computer's instruction set generally requires conversion for external use, such as for printing and display. Different types of processors may have different internal representations of numerical values and different conventions are used for integer and real numbers. Most calculations are carried out with number formats that fit into a processor register, but some software systems allow representation of arbitrarily large numbers using multiple words of memory.
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the UK. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators it is usually known as "SCI" display mode.
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one).
A numerical digit is a single symbol used alone or in combinations, to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits.
A quaternary numeral system is base-4. It uses the digits 0, 1, 2 and 3 to represent any real number. Conversion from binary is straightforward.
Positional notation usually denotes the extension to any base of the Hindu–Arabic numeral system. More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred. In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string.
Hexadecimal floating point is a format for encoding floating-point numbers first introduced on the IBM System/360 computers, and supported on subsequent machines based on that architecture, as well as machines which were intended to be application-compatible with System/360.
Base32 is the base-32 numeral system. It uses a set of 32 digits, each of which can be represented by 5 bits (25). One way to represent Base32 numbers in a human-readable way is by using a standard 32-character set, such as the twenty-two upper-case letters A–V and the digits 0-9. However, many other variations are used in different contexts.
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system the radix is ten, because it uses the ten digits from 0 through 9.
Hexadecimal time is the representation of the time of day as a hexadecimal number in the interval [0,1).
John Williams Nystrom (1825–1885) was a Swedish born, American civil engineer, inventor, and author. He served as an assistant Secretary and Chief Engineer of the United States Navy during the American Civil War.
The earliest recorded systems of weights and measures originate in the 3rd or 4th millennium BC. Even the very earliest civilizations needed measurement for purposes of agriculture, construction and trade. Early standard units might only have applied to a single community or small region, with every area developing its own standards for lengths, areas, volumes and masses. Often such systems were closely tied to one field of use, so that volume measures used, for example, for dry grains were unrelated to those for liquids, with neither bearing any particular relationship to units of length used for measuring cloth or land. With development of manufacturing technologies, and the growing importance of trade between communities and ultimately across the Earth, standardized weights and measures became critical. Starting in the 18th century, modernized, simplified and uniform systems of weights and measures were developed, with the fundamental units defined by ever more precise methods in the science of metrology. The discovery and application of electricity was one factor motivating the development of standardized internationally applicable units.
Non-standard positional numeral systems here designates numeral systems that may loosely be described as positional systems, but that do not entirely comply with the following description of standard positional systems:
The Bibi-binary system for numeric notation is a hexadecimal numeral system first described in 1968 by singer/mathematician Robert "Boby" Lapointe (1922–1972). At the time, it attracted the attention of André Lichnerowicz, then engaged in studies at the University of Lyon. It found some use in a variety of unforeseen applications: stochastic poetry, stochastic art, colour classification, aleatory music, architectural symbolism, etc.
