computing Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and development of both computer hardware , hardware and software. ...

, a memory address is a reference to a specific

memory Memory is the faculty of the mind by which data or information is Encoding (memory), encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If Foresight (psycholo ...

location used at various levels by

software Software is a set of computer programs and associated software documentation, documentation and data (computing), data. This is in contrast to Computer hardware, hardware, from which the system is built and which actually performs the work. ...

and hardware. Memory addresses are fixed-length sequences of digits conventionally displayed and manipulated as unsigned

integers An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of ...

. Such numerical semantic bases itself upon features of CPU (such as the instruction pointer and incremental address registers), as well upon use of the memory like an array endorsed by various

programming language A programming language is a system of notation for writing computer program, computer programs. Most programming languages are text-based formal languages, but they may also be visual programming language, graphical. They are a kind of computer ...

Types

Physical addresses

digital computer A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as C ...

main memory Computer data storage is a technology consisting of computer components and Data storage, recording media that are used to retain digital data (computing), data. It is a core function and fundamental component of computers. The central pro ...

consists of many memory locations. Each memory location has a physical address which is a code. The CPU (or other device) can use the code to access the corresponding memory location. Generally only

system software System software is software designed to provide a platform for other software. Examples of system software include operating systems (OS) like macOS, Linux, Android and Microsoft Windows, computational science software, game engines, search engin ...

, i.e. the

BIOS In computing, BIOS (, ; Basic Input/Output System, also known as the System BIOS, ROM BIOS, BIOS ROM or PC BIOS) is firmware used to provide runtime services for operating systems and programs and to perform Computer hardware, hardware initializ ...

, operating systems, and some specialized utility programs (e.g., memory testers), address physical memory using machine code

operand In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above exampl ...

s or

processor register A processor register is a quickly accessible location available to a computer's Processor (computing), processor. Registers usually consist of a small amount of fast Computer storage, storage, although some registers have specific hardware functi ...

s, instructing the CPU to direct a hardware device, called the memory controller, to use the

memory bus In computer architecture, a bus (shortened form of the Latin ''wikt:omnibus, omnibus'', and historically also called data highway or databus) is a communication system that transfers Data (computing), data between components inside a computer ...

or system bus, or separate control,

address An address is a collection of information, presented in a mostly fixed format, used to give the location of a building, apartment, or other structure or a plot of land, generally using border, political boundaries and street names as references, ...

and data busses, to execute the program's commands. The memory controllers' bus consists of a number of parallel lines, each represented by a

binary digit Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ...

(bit). The width of the bus, and thus the number of addressable storage units, and the number of bits in each unit, varies among computers.

Logical addresses

computer program A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. Computer programs are one component of software, which also includes software documentation, documentation and oth ...

uses memory addresses to execute

machine code In computer programming Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programm ...

, and to store and retrieve

data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interp ...

. In early computers logical and physical addresses corresponded, but since the introduction of

virtual memory In computing, virtual memory, or virtual storage is a Memory management (operating systems), memory management technique that provides an "idealized abstraction of the storage resources that are actually available on a given machine" which "cr ...

most

application program Application may refer to: Mathematics and computing * Application software, computer software designed to help the user to perform specific tasks ** Application layer, an abstraction layer that specifies protocols and interface methods used in a c ...

s do not have a knowledge of physical addresses. Rather, they address

logical address In computing, a logical address is the address at which an item (Computer data storage, memory cell, storage element, network host) appears to reside from the perspective of an executing application program. A logical address may be different f ...

es, or virtual addresses, using the computer's

memory management unit A memory management unit (MMU), sometimes called paged memory management unit (PMMU), is a computer hardware unit having all computer memory, memory references passed through itself, primarily performing the translation of virtual address, virtua ...

and

operating system An operating system (OS) is system software that manages computer hardware, software resources, and provides common daemon (computing), services for computer programs. Time-sharing operating systems scheduler (computing), schedule tasks for ef ...

memory mapping; see below.

Unit of address resolution

Most modern computers are '' byte-addressable''. Each address identifies a single

byte The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable un ...

( eight bits) of storage. Data larger than a single byte may be stored in a sequence of consecutive addresses. There exist '' word-addressable'' computers, where the minimal addressable storage unit is exactly the processor's

word A word is a basic element of language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, ...

. For example, the

Data General Nova The Data General Nova is a series of 16-bit computing, 16-bit minicomputers released by the American company Data General. The Nova family was very popular in the 1970s and ultimately sold tens of thousands of units. The first model, known sim ...

minicomputer A minicomputer, or colloquially mini, is a class of smaller general purpose computers that developed in the mid-1960s and sold at a much lower price than Mainframe computer, mainframe and mid-size computers from IBM and BUNCH, its direct competi ...

, and the

Texas Instruments TMS9900 Introduced in June 1976, the TMS9900 was one of the first commercially available, single-chip 16-bit microprocessors. It implemented Texas Instruments' TI-990 minicomputer architecture in a single-chip format, and was initially used for low-end m ...

and National Semiconductor IMP-16

microcomputer A microcomputer is a small, relatively inexpensive computer having a central processing unit (CPU) made out of a microprocessor. The computer also includes Computer memory, memory and input/output (I/O) circuitry together mounted on a printed ...

s used 16 bit

s, and there were many 36-bit

mainframe computer A mainframe computer, informally called a mainframe or big iron, is a computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital ele ...

s (e.g.,

PDP-10 Digital Equipment Corporation (DEC)'s PDP-10, later marketed as the DECsystem-10, is a mainframe computer family manufactured beginning in 1966 and discontinued in 1983. 1970s models and beyond were marketed under the DECsystem-10 name, especi ...

) which used 18-bit word addressing, not

byte addressing Byte addressing in hardware architectures supports accessing individual bytes. Computers with byte addressing are sometimes called ''byte machines,'' in contrast to ''word-addressable'' architectures, ''word machines'', that access data by word ...

, giving an address space of 2¹⁸ 36-bit words, approximately 1 megabyte of storage. The efficiency of addressing of memory depends on the bit size of the bus used for addresses – the more bits used, the more addresses are available to the computer. For example, an 8-bit-byte-addressable machine with a 20-bit

address bus In computer architecture, a bus (shortened form of the Latin ''wikt:omnibus, omnibus'', and historically also called data highway or databus) is a communication system that transfers Data (computing), data between components inside a computer ...

(e.g.

Intel 8086 The 8086 (also called iAPX 86) is a 16-bit computing, 16-bit microprocessor chip designed by Intel between early 1976 and June 8, 1978, when it was released. The Intel 8088, released July 1, 1979, is a slightly modified chip with an external 8-bit ...

) can address 2²⁰ (1,048,576) memory locations, or one MiB of memory, while a 32-bit bus (e.g.

Intel 80386 The Intel 386, originally released as 80386 and later renamed i386, is a 32-bit microprocessor introduced in 1985. The first versions had 275,000 transistorsGiB address space. In contrast, a 36-bit word-addressable machine with an 18-bit address bus addresses only 2¹⁸ (262,144) 36-bit locations (9,437,184 bits), equivalent to 1,179,648 8-bit bytes, or 1152 KiB, or 1.125 MiB — slightly more than the 8086. Some older computers ( decimal computers), were ''

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

digit-addressable''. For example, each address in the

IBM 1620 The IBM 1620 was announced by IBM on October 21, 1959, and marketed as an inexpensive scientific computer. After a total production of about two thousand machines, it was withdrawn on November 19, 1970. Modified versions of the 1620 were used as ...

's magnetic-core memory identified a single six bit binary-coded decimal digit, consisting of a

parity bit A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of Error detection and correction, error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, ...

, flag bit and four numerical bits. The 1620 used 5-digit decimal addresses, so in theory the highest possible address was 99,999. In practice, the CPU supported 20,000 memory locations, and up to two optional external memory units could be added, each supporting 20,000 addresses, for a total of 60,000 (00000–59999).

Word size versus address size

Word A word is a basic element of language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, ...

size is a characteristic of

computer architecture In computer engineering, computer architecture is a description of the structure of a computer system made from component parts. It can sometimes be a high-level description that ignores details of the implementation. At a more detailed level, the ...

denoting the number of bits that a CPU can process at one time. Modern processors, including

embedded systems An embedded system is a computer system—a combination of a computer processor, computer memory, and input/output peripheral devices—that has a dedicated function within a larger mechanical or Electronics, electronic system. It is '' ...

, usually have a word size of 8, 16, 24, 32 or 64 bits; most current general-purpose computers use 32 or 64 bits. Many different sizes have been used historically, including 8, 9, 10, 12, 18, 24, 36, 39, 40, 48 and 60 bits. Very often, when referring to the ''word size'' of a modern computer, one is also describing the size of address space on that computer. For instance, a computer said to be "

32-bit In computer architecture In computer engineering, computer architecture is a description of the structure of a computer system made from component parts. It can sometimes be a high-level description that ignores details of the implementation. A ...

" also usually allows 32-bit memory addresses; a byte-addressable 32-bit computer can address 2³² = 4,294,967,296 bytes of memory, or 4 gibibytes (GiB). This allows one memory address to be efficiently stored in one word. However, this does not always hold true. Computers can have memory addresses larger or smaller than their word size. For instance, many

8-bit In computer architecture, 8-bit Integer (computer science), integers or other Data (computing), data units are those that are 8 bits wide (1 octet (computing), octet). Also, 8-bit central processing unit (CPU) and arithmetic logic unit (ALU) arc ...

processors, such as the

MOS Technology 6502 The MOS Technology 6502 (typically pronounced "sixty-five-oh-two" or "six-five-oh-two") William Mensch and the moderator both pronounce the 6502 microprocessor as ''"sixty-five-oh-two"''. is an 8-bit computing, 8-bit microprocessor that was desig ...

, supported 16-bit addresses— if not, they would have been limited to a mere 256

s of memory addressing. The 16-bit

Intel 8088 The Intel 8088 ("''eighty-eighty-eight''", also called iAPX 88) microprocessor is a variant of the Intel 8086. Introduced on June 1, 1979, the 8088 has an eight-bit external data bus instead of the 16-bit bus of the 8086. The 16-bit registers ...

and

supported 20-bit addressing via segmentation, allowing them to access 1 MiB rather than 64 KiB of memory. All Intel

Pentium Pentium is a brand used for a series of x86 architecture-compatible microprocessors produced by Intel. The Pentium (original), original Pentium processor from which the brand took its name was first released on March 22, 1993. After that, th ...

processors since the

Pentium Pro The Pentium Pro is a sixth-generation x86 microprocessor developed and manufactured by Intel and introduced on November 1, 1995. It introduced the P6 (microarchitecture), P6 microarchitecture (sometimes termed i686) and was originally intended t ...

include

Physical Address Extension In computing, Physical Address Extension (PAE), sometimes referred to as Page Address Extension, is a memory management feature for the x86 architecture. PAE was first introduced by Intel in the Pentium Pro, and later by AMD in the Athlon process ...

s (PAE) which support mapping 36-bit physical addresses to 32-bit virtual addresses. Many early processors held 2 addresses per word , such as 36-bit processors. In theory, modern byte-addressable

64-bit In computer architecture, 64-bit Integer (computer science), integers, memory addresses, or other Data (computing), data units are those that are 64 bits wide. Also, 64-bit central processing unit, CPUs and arithmetic logic unit, ALUs are those ...

computers can address 2⁶⁴ bytes (16 exbibytes), but in practice the amount of memory is limited by the CPU, the memory controller, or the

printed circuit board A printed circuit board (PCB; also printed wiring board or PWB) is a medium used in Electrical engineering, electrical and electronic engineering to connect electronic components to one another in a controlled manner. It takes the form of a L ...

design (e.g., number of physical memory connectors or amount of soldered-on memory).

Contents of each memory location

Each memory location in a

stored-program computer A stored-program computer is a computer that stores Instruction (computer science), program instructions in electronically or optically accessible memory. This contrasts with systems that stored the program instructions with plugboards or simila ...

holds a

binary number 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). The base-2 numeral system is a positional notation ...

or decimal number ''of some sort''. Its interpretation, as data of some

data type In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or Interpreter (computing), interpreter how the programmer intends to u ...

or as an instruction, and use are determined by the instructions which retrieve and manipulate it. Some early programmers combined instructions and data in words as a way to save memory, when it was expensive: The Manchester Mark 1 had space in its 40-bit words to store little bits of data – its processor ignored a small section in the middle of a word – and that was often exploited as extra data storage. Self-replicating programs such as

viruses A virus is a wikt:submicroscopic, submicroscopic infectious agent that replicates only inside the living Cell (biology), cells of an organism. Viruses infect all life forms, from animals and plants to microorganisms, including bacteria and ...

treat themselves sometimes as data and sometimes as instructions. Self-modifying code is generally

deprecated In several fields, especially computing Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and development of both ...

nowadays, as it makes testing and maintenance disproportionally difficult to the saving of a few bytes, and can also give incorrect results because of the compiler or processor's assumptions about the machine's state, but is still sometimes used deliberately, with great care.

Address space in application programming

In modern multitasking environment, an application process usually has in its address space (or spaces) chunks of memory of following types: *

Machine code In computer programming Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programm ...

, including: ** program's own code (historically known as '' code segment'' or ''text segment''); ** shared libraries. *

Data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interp ...

, including: ** initialized data ( data segment); ** uninitialized (but allocated) variables; ** run-time stack; ** heap; ** shared memory and memory mapped files. Some parts of address space may be not mapped at all. Some systems have a "split" memory architecture where machine code, constants, and data are in different locations, and may have different address sizes. For example, PIC18 microcontrollers have a 21-bit program counter to address machine code and constants in Flash memory, and 12-bit address registers to address data in SRAM.

Addressing schemes

A computer program can access an address given explicitly – in low-level programming this is usually called an , or sometimes a specific address, and is known as pointer data type in higher-level languages. But a program can also use relative address which specifies a location in relation to somewhere else (the '' base address''). There are many more

addressing mode Addressing modes are an aspect of the instruction set architecture in most central processing unit (CPU) designs. The various addressing modes that are defined in a given instruction set architecture define how the machine language instruction ...

s. Mapping logical addresses to physical and virtual memory also adds several levels of indirection; see below.

Memory models

Many programmers prefer to address memory such that there is no distinction between code space and data space (see above), as well as from physical and virtual memory (see above) — in other words, numerically identical pointers refer to exactly the same byte of RAM. However, many early computers did not support such a ''flat memory model'' — in particular, Harvard architecture machines force program storage to be completely separate from data storage. Many modern DSPs (such as the Motorola 56000) have three separate storage areas — program storage, coefficient storage, and data storage. Some commonly used instructions fetch from all three areas simultaneously — fewer storage areas (even if there were the same total bytes of storage) would make those instructions run slower.

Memory models in x86 architecture

Early x86 computers use the segmented memory model addresses based on a combination of two numbers: a memory segment, and an offset within that segment. Some segments are implicitly treated as ''code segments'', dedicated for instructions, '' stack segments'', or normal ''

segments''. Although the usages are different, the segments do not have different

memory protection Memory protection is a way to control memory access rights on a computer, and is a part of most modern instruction set architectures and operating systems. The main purpose of memory protection is to prevent a process (computing), process from acc ...

s reflecting this. In the flat memory model all segments (segment registers) are generally set to zero, and only offsets are variable.

References

{{Data types Computer memory