Hexadecimal in the context of Computer hardware

A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1"), or in combinations (such as "15"), to represent numbers in positional notation, such as the common base 10. The name "digit" originates from the Latin digiti meaning fingers.

For any numeral system with an integer base, the number of different digits required is the absolute value of the base. For example, decimal (base 10) requires ten digits (0 to 9), and binary (base 2) requires only two digits (0 and 1). Bases greater than 10 require more than 10 digits, for instance hexadecimal (base 16) requires 16 digits (usually 0 to 9 and A to F).

In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠${\displaystyle {\tfrac {p}{q}}}$⁠ of two integers, a numerator p and a non-zero denominator q. For example, ⁠${\displaystyle {\tfrac {3}{7}}}$⁠ is a rational number, as is every integer (for example, ${\displaystyle -5={\tfrac {-5}{1}}}$). The set of all rational numbers is often referred to as "the rationals", and is closed under addition, subtraction, multiplication, and division by a nonzero rational number. It is a field under these operations and therefore also calledthe field of rationals or the field of rational numbers. It is usually denoted by boldface Q, or blackboard bold ⁠${\displaystyle \mathbb {Q} .}$⁠

A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: 3/4 = 0.75), or eventually begins to repeat the same finite sequence of digits over and over (example: 9/44 = 0.20454545...). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see Repeating decimal § Extension to other bases).

0 (zero) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently dividing by 0 is generally considered to be undefined in arithmetic.

As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya.

Chinese units of measurement, known in Chinese as the shìzhì ("market system"), are the traditional units of measurement of the Han Chinese. Although Chinese numerals have been decimal (base-10) since the Shang, several Chinese measures use hexadecimal (base-16). Local applications have varied, but the Chinese dynasties usually proclaimed standard measurements and recorded their predecessor's systems in their histories.

In the present day, the People's Republic of China maintains some customary units based upon the market units but standardized to round values in the metric system, for example the common jin or catty of exactly 500 g. The Chinese name for most metric units is based on that of the closest traditional unit; when confusion might arise, the word "market" (市, shì) is used to specify the traditional unit and "common" or "public" (公, gōng) is used for the metric value. Taiwan, like Korea, saw its traditional units standardized to Japanese values and their conversion to a metric basis, such as the Taiwanese ping of about 3.306 m based on the square ken. The Hong Kong SAR continues to use its traditional units, now legally defined based on a local equation with metric units. For instance, the Hong Kong catty is precisely 604.78982 g.

A binary code is the value of a data-encoding convention represented in a binary notation that usually is a sequence of 0s and 1s; sometimes called a bit string. For example, ASCII is an 8-bit text encoding that in addition to the human readable form (letters) can be represented as binary. Binary code can also refer to the mass noun code that is not human readable in nature such as machine code and bytecode.

Even though all modern computer data is binary in nature, and therefore can be represented as binary, other numerical bases may be used. Power of 2 bases (including hex and octal) are sometimes considered binary code since their power-of-2 nature makes them inherently linked to binary. Decimal is, of course, a commonly used representation. For example, ASCII characters are often represented as either decimal or hex. Some types of data such as image data is sometimes represented as hex, but rarely as decimal.

In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by at least one array index or key, a collection of which may be a tuple, known as an index tuple. In general, an array is a mutable and linear collection of elements with the same data type. An array is stored such that the position (memory address) of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called a one-dimensional array.

For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, ..., 0x7F4) so that the element with index i has the address 2000 + (i × 4).The memory address of the first element of an array is called first address, foundation address, or base address.

In computing, a nibble, also spelled nybble to match byte, is a unit of information that is an aggregation of four-bits; half of a byte/octet. The unit is alternatively called nyble, nybl, half-byte or tetrade. In networking or telecommunications, the unit is often called a semi-octet, quadbit, or quartet.

As a nibble can represent sixteen (2) possible values, a nibble value is often shown as a hexadecimal digit (hex digit). A byte is two nibbles, and therefore, a value can be shown as two hex digits.

In computing, an executable is a resource that a computer can use to control its behavior. As with all information in computing, it is data, but distinct from data that does not imply a flow of control. Terms such as executable code, executable file, executable program, and executable image describe forms in which the information is represented and stored. A native executable is machine code and is directly executable at the instruction level of a CPU. A script is also executable although indirectly via an interpreter. Intermediate executable code (such as bytecode) may be interpreted or converted to native code at runtime via just-in-time compilation.

Web colors are colors used in displaying web pages on the World Wide Web; they can be described by way of three methods: a color may be specified as an RGB triplet, in hexadecimal format (a hex triplet) or according to its common English name in some cases. A color tool or other graphics software is often used to generate color values. In some uses, hexadecimal color codes are specified with notation using a leading number sign (#). A color is specified according to the intensity of its red, green and blue components, each represented by eight bits. Thus, there are 24 bits used to specify a web color within the sRGB gamut, and 16,777,216 colors that may be so specified. In hexadecimal, these are specified with two hexidecimal digits per colour, leading to a total of six hexadecimal digits.

Colors outside the sRGB gamut can be specified in Cascading Style Sheets by making one or more of the red, green and blue components negative or greater than 100%, so the color space is theoretically an unbounded extrapolation of sRGB similar to scRGB. Specifying a non-sRGB color this way requires the RGB() function call. It is impossible with the hexadecimal syntax (and thus impossible in legacy HTML documents that do not use CSS).

Hexadecimal floating point (now called HFP by IBM) 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.

In comparison to IEEE 754 floating point, the HFP format has a longer significand, and a shorter exponent. All HFP formats have 7 bits of exponent with a bias of 64. The normalized range of representable numbers is from 16 to 16 (approx. 5.39761 × 10 to 7.237005 × 10).

The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve squared (144), "1,000" means twelve cubed (1,728), and "0.1" means a twelfth (0.08333...).

Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses A and B, as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and finally 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published material: 2 (a turned 2) for ten (dek, pronounced /dɛk/) and 3 (a turned 3) for eleven (el, pronounced /ɛl/).

In computer architecture, 64-bit integers, memory addresses, or other data units are those that are 64 bits wide. Also, 64-bit central processing units (CPU) and arithmetic logic units (ALU) are those that are based on processor registers, address buses, or data buses of that size. A computer that uses such a processor is a 64-bit computer.

From the software perspective, 64-bit computing means the use of machine code with 64-bit virtual memory addresses. However, not all 64-bit instruction sets support full 64-bit virtual memory addresses; x86-64 and AArch64, for example, support only 48 bits of virtual address, with the remaining 16 bits of the virtual address required to be all zeros (000...) or all ones (111...), and several 64-bit instruction sets support fewer than 64 bits of physical memory address.