In computing , endianness is the order in which bytes within a word of digital data are transmitted over a data communication medium or addressed (by rising addresses) in computer memory , counting only byte significance compared to earliness. Endianness is primarily expressed as big-endian (BE) or little-endian (LE), terms introduced by Danny Cohen into computer science for data ordering in an Internet Experiment Note published in 1980. The adjective endian has its origin in the writings of 18th century Anglo-Irish writer Jonathan Swift . In the 1726 novel Gulliver's Travels , he portrays the conflict between sects of Lilliputians divided into those breaking the shell of a boiled egg from the big end or from the little end. By analogy, a CPU may read a digital word big end first, or little end first.
84-417: Computers store information in various-sized groups of binary bits. Each group is assigned a number, called its address , that the computer uses to access that data. On most modern computers, the smallest data group with an address is eight bits long and is called a byte. Larger groups comprise two or more bytes, for example, a 32-bit word contains four bytes. There are two possible ways a computer could number
168-517: A hex dump ), little-endian representation of integers has the significance increasing from right to left. In other words, it appears backwards when visualized, which can be counter-intuitive. This behavior arises, for example, in FourCC or similar techniques that involve packing characters into an integer, so that it becomes a sequence of specific characters in memory. For example, take the string "JOHN", stored in hexadecimal ASCII . On big-endian machines,
252-479: A 32-bit address bus , permitting up to 4 GB of RAM to be accessed, far more than previous generations of system architecture allowed. 32-bit designs have been used since the earliest days of electronic computing, in experimental systems and then in large mainframe and minicomputer systems. The first hybrid 16/32-bit microprocessor , the Motorola 68000 , was introduced in the late 1970s and used in systems such as
336-472: A 32-bit base address of the segment stored in little-endian order, but in four nonconsecutive bytes, at relative positions 2, 3, 4 and 7 of the descriptor start. Hardware description languages (HDLs) used to express digital logic often support arbitrary endianness, with arbitrary granularity. For example, in SystemVerilog , a word can be defined as little-endian or big-endian. The recognition of endianness
420-470: A byte being part of a "field" is its "significance". These attributes of the parts of a field play an important role in the sequence the bytes are accessed by the computer hardware, more precisely: by the low-level algorithms contributing to the results of a computer instruction. Positional number systems (mostly base 2, or less often base 10) are the predominant way of representing and particularly of manipulating integer data by computers. In pure form this
504-472: A little-endian should start with FF FE 00 00 . Application binary data formats, such as MATLAB .mat files, or the .bil data format, used in topography, are usually endianness-independent. This is achieved by storing the data always in one fixed endianness or carrying with the data a switch to indicate the endianness. An example of the former is the binary XLS file format that is portable between Windows and Mac systems and always little-endian, requiring
588-486: A mirror surface. HDR imagery allows for the reflection of highlights that can still be seen as bright white areas, instead of dull grey shapes. A 32-bit file format is a binary file format for which each elementary information is defined on 32 bits (or 4 bytes ). An example of such a format is the Enhanced Metafile Format . Arithmetic logic unit In computing , an arithmetic logic unit ( ALU )
672-574: A mixture of both or contain an indicator of which ordering is used throughout the file. Computer memory consists of a sequence of storage cells (smallest addressable units); in machines that support byte addressing , those units are called bytes . Each byte is identified and accessed in hardware and software by its memory address . If the total number of bytes in memory is n , then addresses are enumerated from 0 to n − 1. Computer programs often use data structures or fields that may consist of more data than can be stored in one byte. In
756-546: A number of hardware architectures where floating-point numbers are represented in big-endian form while integers are represented in little-endian form. There are ARM processors that have mixed-endian floating-point representation for double-precision numbers: each of the two 32-bit words is stored as little-endian, but the most significant word is stored first. VAX floating point stores little-endian 16-bit words in big-endian order. Because there have been many floating-point formats with no network standard representation for them,
840-483: A processor treats data accesses. Instruction accesses (fetches of instruction words) on a given processor may still assume a fixed endianness, even if data accesses are fully bi-endian, though this is not always the case, such as on Intel's IA-64 -based Itanium CPU, which allows both. Some nominally bi-endian CPUs require motherboard help to fully switch endianness. For instance, the 32-bit desktop-oriented PowerPC processors in little-endian mode act as little-endian from
924-436: A setting which allows for switchable endianness in data fetches and stores, instruction fetches, or both; those instruction set architectures are referred to as bi-endian . Architectures that support switchable endianness include PowerPC / Power ISA , SPARC V9, ARM versions 3 and above, DEC Alpha , MIPS , Intel i860 , PA-RISC , SuperH SH-4 , IA-64 , C-Sky , and RISC-V . This feature can improve performance or simplify
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#17330861981921008-406: A single byte, so the complexity of the hardware is not affected by the byte ordering. Addition, subtraction, and multiplication start at the least significant digit position and propagate the carry to the subsequent more significant position. On most systems, the address of a multi-byte value is the address of its first byte (the byte with the lowest address). The implementation of these operations
1092-521: A single positional element (character) also has a positional value. Lexicographical comparison means almost everywhere: first character ranks highest – as in the telephone book. Almost all machines which can do this using a single instruction are big-endian or at least mixed-endian. Integer numbers written as text are always represented most significant digit first in memory, which is similar to big-endian, independently of text direction . When memory bytes are printed sequentially from left to right (e.g. in
1176-413: A total of 96 bits per pixel. 32-bit-per-channel images are used to represent values brighter than what sRGB color space allows (brighter than white); these values can then be used to more accurately retain bright highlights when either lowering the exposure of the image or when it is seen through a dark filter or dull reflection. For example, a reflection in an oil slick is only a fraction of that seen in
1260-571: A very simple 8-bit ALU: Mathematician John von Neumann proposed the ALU concept in 1945 in a report on the foundations for a new computer called the EDVAC . The cost, size, and power consumption of electronic circuitry was relatively high throughout the infancy of the Information Age . Consequently, all early computers had a serial ALU that operated on one data bit at a time although they often presented
1344-596: A wider word size to programmers. The first computer to have multiple parallel discrete single-bit ALU circuits was the 1951 Whirlwind I , which employed sixteen such "math units" to enable it to operate on 16-bit words. In 1967, Fairchild introduced the first ALU-like device implemented as an integrated circuit, the Fairchild 3800, consisting of an eight-bit arithmetic unit with accumulator. It only supported adds and subtracts but no logic functions. Full integrated-circuit ALUs soon emerged, including four-bit ALUs such as
1428-490: A word in a register to the opposite endianness, that is, they swap the order of the bytes in a 16-, 32- or 64-bit word. Recent Intel x86 and x86-64 architecture CPUs have a MOVBE instruction ( Intel Core since generation 4, after Atom ), which fetches a big-endian format word from memory or writes a word into memory in big-endian format. These processors are otherwise thoroughly little-endian. There are also devices which use different formats in different places. For instance,
1512-427: Is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers . This is in contrast to a floating-point unit (FPU), which operates on floating point numbers. It is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs). The inputs to an ALU are
1596-402: Is a 32-bit machine, with 32-bit registers and instructions that manipulate 32-bit quantities, but the external address bus is 36 bits wide, giving a larger address space than 4 GB, and the external data bus is 64 bits wide, primarily in order to permit a more efficient prefetch of instructions and data. Prominent 32-bit instruction set architectures used in general-purpose computing include
1680-405: Is a group of signals that conveys one binary integer number. Typically, the A, B and Y bus widths (the number of signals comprising each bus) are identical and match the native word size of the external circuitry (e.g., the encapsulating CPU or other processor). The opcode input is a parallel bus that conveys to the ALU an operation selection code, which is an enumerated value that specifies
1764-436: Is an algorithm that operates on integers which are larger than the ALU word size. To do this, the algorithm treats each integer as an ordered collection of ALU-size fragments, arranged from most-significant (MS) to least-significant (LS) or vice versa. For example, in the case of an 8-bit ALU, the 24-bit integer 0x123456 would be treated as a collection of three 8-bit fragments: 0x12 (MS), 0x34 , and 0x56 (LS). Since
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#17330861981921848-406: Is important when reading a file or filesystem created on a computer with different endianness. Fortran sequential unformatted files created with one endianness usually cannot be read on a system using the other endianness because Fortran usually implements a record (defined as the data written by a single Fortran statement) as data preceded and succeeded by count fields, which are integers equal to
1932-476: Is in principle a 16-bit little-endian system. The instructions to convert between floating-point and integer values in the optional floating-point processor of the PDP-11/45, PDP-11/70, and in some later processors, stored 32-bit "double precision integer long" values with the 16-bit halves swapped from the expected little-endian order. The UNIX C compiler used the same format for 32-bit long integers. This ordering
2016-532: Is known as PDP-endian . UNIX was one of the first systems to allow the same code to be compiled for platforms with different internal representations. One of the first programs converted was supposed to print out Unix , but on the Series/1 it printed nUxi instead. A way to interpret this endianness is that it stores a 32-bit integer as two little-endian 16-bit words, with a big-endian word ordering: Segment descriptors of IA-32 and compatible processors keep
2100-434: Is marginally simpler using little-endian machines where this first byte contains the least significant digit. Comparison and division start at the most significant digit and propagate a possible carry to the subsequent less significant digits. For fixed-length numerical values (typically of length 1,2,4,8,16), the implementation of these operations is marginally simpler on big-endian machines. Some big-endian processors (e.g.
2184-406: Is meant as the extremity where the big resp. little significance is written first , namely where the field starts . The integer data that are directly supported by the computer hardware have a fixed width of a low power of 2, e.g. 8 bits ≙ 1 byte, 16 bits ≙ 2 bytes, 32 bits ≙ 4 bytes, 64 bits ≙ 8 bytes, 128 bits ≙ 16 bytes. The low-level access sequence to the bytes of such a field depends on
2268-442: Is redirected to the corresponding address and unaligned access is not allowed. ARMv6 introduces BE-8 or byte-invariant mode, where access to a single byte works as in little-endian mode, but accessing a 16-bit, 32-bit or (starting with ARMv8) 64-bit word results in a byte swap of the data. This simplifies unaligned memory access as well as memory-mapped access to registers other than 32-bit. Many processors have instructions to convert
2352-410: Is referred to as the "status register" or "condition code register". Depending on the ALU operation being performed, some status register bits may be changed and others may be left unmodified. For example, in bitwise logical operations such as AND and OR, the carry status bit is typically not modified as it is not relevant to such operations. In CPUs, the stored carry-out signal is usually connected to
2436-407: Is repeated for all operand fragments so as to generate a complete collection of partials, which is the result of the multiple-precision operation. In arithmetic operations (e.g., addition, subtraction), the algorithm starts by invoking an ALU operation on the operands' LS fragments, thereby producing both a LS partial and a carry out bit. The algorithm writes the partial to designated storage, whereas
2520-581: Is that a processor with 32-bit memory addresses can directly access at most 4 GiB of byte-addressable memory (though in practice the limit may be lower). The world's first stored-program electronic computer , the Manchester Baby , used a 32-bit architecture in 1948, although it was only a proof of concept and had little practical capacity. It held only 32 32-bit words of RAM on a Williams tube , and had no addition operation, only subtraction. Memory, as well as other digital circuits and wiring,
2604-467: Is the dominant ordering in networking protocols, such as in the Internet protocol suite , where it is referred to as network order , transmitting the most significant byte first. Conversely, little-endianness is the dominant ordering for processor architectures ( x86 , most ARM implementations, base RISC-V implementations) and their associated memory. File formats can use either ordering; some formats use
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2688-412: Is valid for moderate sized non-negative integers, e.g. of C data type unsigned . In such a number system, the value of a digit which it contributes to the whole number is determined not only by its value as a single digit, but also by the position it holds in the complete number, called its significance. These positions can be mapped to memory mainly in two ways: In these expressions, the term "end"
2772-524: The 6809 and the 68000 series of processors use the big-endian format. Solely big-endian architectures include the IBM z/Architecture and OpenRISC . The PDP-11 minicomputer, however, uses little-endian byte order, as does its VAX successor. The Datapoint 2200 used simple bit-serial logic with little-endian to facilitate carry propagation . When Intel developed the 8008 microprocessor for Datapoint, they used little-endian for compatibility. However, as Intel
2856-606: The 8088/8086 or 80286 , 16-bit microprocessors with a segmented address space where programs had to switch between segments to reach more than 64 kilobytes of code or data. As this is quite time-consuming in comparison to other machine operations, the performance may suffer. Furthermore, programming with segments tend to become complicated; special far and near keywords or memory models had to be used (with care), not only in assembly language but also in high level languages such as Pascal , compiled BASIC , Fortran , C , etc. The 80386 and its successors fully support
2940-651: The Altera Nios II , the Atmel AVR , the Andes Technology NDS32, the Qualcomm Hexagon , and many other processors and processor families are also little-endian. The Intel 8051 , unlike other Intel processors, expects 16-bit addresses for LJMP and LCALL in big-endian format; however, xCALL instructions store the return address onto the stack in little-endian format. Some instruction set architectures feature
3024-462: The Am2901 and 74181 . These devices were typically " bit slice " capable, meaning they had "carry look ahead" signals that facilitated the use of multiple interconnected ALU chips to create an ALU with a wider word size. These devices quickly became popular and were widely used in bit-slice minicomputers. Microprocessors began to appear in the early 1970s. Even though transistors had become smaller, there
3108-643: The Cray T3E ). IBM AIX and IBM i run in big-endian mode on bi-endian Power ISA; Linux originally ran in big-endian mode, but by 2019, IBM had transitioned to little-endian mode for Linux to ease the porting of Linux software from x86 to Power. SPARC has no relevant little-endian deployment, as both Oracle Solaris and Linux run in big-endian mode on bi-endian SPARC systems, and can be considered big-endian in practice. ARM, C-Sky, and RISC-V have no relevant big-endian deployments, and can be considered little-endian in practice. The term bi-endian refers primarily to how
3192-743: The IBM System/360 , IBM System/370 (which had 24-bit addressing), System/370-XA , ESA/370 , and ESA/390 (which had 31-bit addressing), the DEC VAX , the NS320xx , the Motorola 68000 family (the first two models of which had 24-bit addressing), the Intel IA-32 32-bit version of the x86 architecture, and the 32-bit versions of the ARM , SPARC , MIPS , PowerPC and PA-RISC architectures. 32-bit instruction set architectures used for embedded computing include
3276-536: The IBM System/360 Model 30 had an 8-bit ALU, 8-bit internal data paths, and an 8-bit path to memory, and the original Motorola 68000 had a 16-bit data ALU and a 16-bit external data bus, but had 32-bit registers and a 32-bit oriented instruction set. The 68000 design was sometimes referred to as 16/32-bit . However, the opposite is often true for newer 32-bit designs. For example, the Pentium Pro processor
3360-456: The Intel Fortran compiler supports the non-standard CONVERT specifier when opening a file, e.g.: OPEN ( unit , CONVERT = 'BIG_ENDIAN' ,...) . Other compilers have options for generating code that globally enables the conversion for all file IO operations. This permits the reuse of code on a system with the opposite endianness without code modification. On most systems,
3444-450: The XDR standard uses big-endian IEEE 754 as its representation. It may therefore appear strange that the widespread IEEE 754 floating-point standard does not specify endianness. Theoretically, this means that even standard IEEE floating-point data written by one machine might not be readable by another. However, on modern standard computers (i.e., implementing IEEE 754), one may safely assume that
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3528-406: The electrical conductors used to convey digital signals between the ALU and external circuitry. When an ALU is operating, external circuits apply signals to the ALU inputs and, in response, the ALU produces and conveys signals to external circuitry via its outputs. A basic ALU has three parallel data buses consisting of two input operands ( A and B ) and a result output ( Y ). Each data bus
3612-533: The 16-bit segments of the 80286 but also segments for 32-bit address offsets (using the new 32-bit width of the main registers). If the base address of all 32-bit segments is set to 0, and segment registers are not used explicitly, the segmentation can be forgotten and the processor appears as having a simple linear 32-bit address space. Operating systems like Windows or OS/2 provide the possibility to run 16-bit (segmented) programs as well as 32-bit programs. The former possibility exists for backward compatibility and
3696-423: The 68000 family and ColdFire , x86, ARM, MIPS, PowerPC, and Infineon TriCore architectures. On the x86 architecture , a 32-bit application normally means software that typically (not necessarily) uses the 32-bit linear address space (or flat memory model ) possible with the 80386 and later chips. In this context, the term came about because DOS , Microsoft Windows and OS/2 were originally written for
3780-451: The ALU circuitry before sampling the ALU outputs. In general, external circuitry controls an ALU by applying signals to the ALU inputs. Typically, the external circuitry employs sequential logic to generate the signals that control ALU operation. The external sequential logic is paced by a clock signal of sufficiently low frequency to ensure enough time for the ALU outputs to settle under worst-case conditions (i.e., conditions resulting in
3864-403: The ALU inputs and, when enough time (known as the " propagation delay ") has passed for the signals to propagate through the ALU circuitry, the result of the ALU operation appears at the ALU outputs. The external circuitry connected to the ALU is responsible for ensuring the stability of ALU input signals throughout the operation, and for allowing sufficient time for the signals to propagate through
3948-400: The ALU's carry-in net. This facilitates efficient propagation of carries (which may represent addition carries, subtraction borrows, or shift overflows) when performing multiple-precision operations, as it eliminates the need for software-management of carry propagation (via conditional branching, based on the carry status bit). In integer arithmetic computations, multiple-precision arithmetic
4032-524: The Add instruction of the IBM 1401 addresses variable-length fields at their low-order (highest-addressed) position with their lengths being defined by a word mark set at their high-order (lowest-addressed) position. When an operation such as addition is performed, the processor begins at the low-order positions at the high addresses of the two fields and works its way down to the high-order. Another important attribute of
4116-659: The BQ27421 Texas Instruments battery gauge uses the little-endian format for its registers and the big-endian format for its random-access memory . SPARC historically used big-endian until version 9, which is bi-endian. Similarly early IBM POWER processors were big-endian, but the PowerPC and Power ISA descendants are now bi-endian. The ARM architecture was little-endian before version 3 when it became bi-endian. Although many processors use little-endian storage for all types of data (integer, floating point), there are
4200-489: The C11 standard and commonly used in code interacting with hardware. Some operations in positional number systems have a natural or preferred order in which the elementary steps are to be executed. This order may affect their performance on small-scale byte-addressable processors and microcontrollers . However, high-performance processors usually fetch multi-byte operands from memory in the same amount of time they would have fetched
4284-713: The IBM System/360 and its successors) contain hardware instructions for lexicographically comparing varying length character strings . The normal data transport by an assignment statement is in principle independent of the endianness of the processor. Many historical and extant processors use a big-endian memory representation, either exclusively or as a design option. The IBM System/360 uses big-endian byte order, as do its successors System/370 , ESA/390 , and z/Architecture . The PDP-10 uses big-endian addressing for byte-oriented instructions. The IBM Series/1 minicomputer uses big-endian byte order. The Motorola 6800 / 6801,
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#17330861981924368-512: The LS bit of each partial—which is conveyed via the stored carry bit—must be obtained from the MS bit of the previously left-shifted, less-significant operand. Conversely, operands are processed MS first in right-shift operations because the MS bit of each partial must be obtained from the LS bit of the previously right-shifted, more-significant operand. In bitwise logical operations (e.g., logical AND, logical OR),
4452-545: The Mac application to swap the bytes on load and save when running on a big-endian Motorola 68K or PowerPC processor. 32-bit In computer architecture , 32-bit computing refers to computer systems with a processor , memory , and other major system components that operate on data in 32- bit units. Compared to smaller bit widths, 32-bit computers can perform large calculations more efficiently and process more data per clock cycle. Typical 32-bit personal computers also have
4536-717: The addition operation) upon operation completion. The ALU's input signals, which are held stable until the next clock, are allowed to propagate through the ALU and to the destination register while the CPU waits for the next clock. When the next clock arrives, the destination register stores the ALU result and, since the ALU operation has completed, the ALU inputs may be set up for the next ALU operation. A number of basic arithmetic and bitwise logic functions are commonly supported by ALUs. Basic, general purpose ALUs typically include these operations in their repertoires: ALU shift operations cause operand A (or B) to shift left or right (depending on
4620-421: The address of a multi-byte value is the address of its first byte (the byte with the lowest address); little-endian systems of that type have the property that, for sufficiently low data values, the same value can be read from memory at different lengths without using different addresses (even when alignment restrictions are imposed). For example, a 32-bit memory location with content 4A 00 00 00 can be read at
4704-439: The context of this article where its type cannot be arbitrarily complicated, a "field" consists of a consecutive sequence of bytes and represents a "simple data value" which – at least potentially – can be manipulated by one single hardware instruction . On most systems, the address of a multi-byte simple data value is the address of its first byte (the byte with the lowest address). There are exceptions to this rule – for example,
4788-429: The data to be operated on, called operands , and a code indicating the operation to be performed; the ALU's output is the result of the performed operation. In many designs, the ALU also has status inputs or outputs, or both, which convey information about a previous operation or the current operation, respectively, between the ALU and external status registers . An ALU has a variety of input and output nets , which are
4872-520: The desired arithmetic or logic operation to be performed by the ALU. The opcode size (its bus width) determines the maximum number of distinct operations the ALU can perform; for example, a four-bit opcode can specify up to sixteen different ALU operations. Generally, an ALU opcode is not the same as a machine language instruction , though in some cases it may be directly encoded as a bit field within such instructions. The status outputs are various individual signals that convey supplemental information about
4956-446: The endianness is the same for floating-point numbers as for integers, making the conversion straightforward regardless of data type. Small embedded systems using special floating-point formats may be another matter, however. Most instructions considered so far contain the size (lengths) of their operands within the operation code . Frequently available operand lengths are 1, 2, 4, 8, or 16 bytes. But there are also architectures where
5040-400: The individual bytes in a larger group, starting at either end. Both types of endianness are in widespread use in digital electronic engineering. The initial choice of endianness of a new design is often arbitrary, but later technology revisions and updates perpetuate the existing endianness to maintain backward compatibility . A big-endian system stores the most significant byte of a word at
5124-405: The late 1990s (SPARC v9 compliant processors) allow data endianness to be chosen with each individual instruction that loads from or stores to memory. The ARM architecture supports two big-endian modes, called BE-8 and BE-32 . CPUs up to ARMv5 only support BE-32 or word-invariant mode. Here any naturally aligned 32-bit access works like in little-endian mode, but access to a byte or 16-bit word
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#17330861981925208-412: The latter is usually meant to be used for new software development . In digital images/pictures, 32-bit usually refers to RGBA color space ; that is, 24-bit truecolor images with an additional 8-bit alpha channel . Other image formats also specify 32 bits per pixel, such as RGBE . In digital images, 32-bit sometimes refers to high-dynamic-range imaging (HDR) formats that use 32 bits per channel,
5292-588: The length of an operand may be held in a separate field of the instruction or with the operand itself, e.g. by means of a word mark . Such an approach allows operand lengths up to 256 bytes or larger. The data types of such operands are character strings or BCD . Machines able to manipulate such data with one instruction (e.g. compare, add) include the IBM 1401 , 1410 , 1620 , System/360 , System/370 , ESA/390 , and z/Architecture , all of them of type big-endian. Numerous other orderings, generically called middle-endian or mixed-endian , are possible. The PDP-11
5376-497: The logic of networking devices and software. The word bi-endian , when said of hardware, denotes the capability of the machine to compute or pass data in either endian format. Many of these architectures can be switched via software to default to a specific endian format (usually done when the computer starts up); however, on some systems, the default endianness is selected by hardware on the motherboard and cannot be changed via software (e.g. Alpha, which runs only in big-endian mode on
5460-420: The maximum possible propagation delay). For example, a CPU starts an addition operation by routing the operands from their sources (typically processor registers ) to the ALU's operand inputs, while simultaneously applying a value to the ALU's opcode input that configures it to perform an addition operation. At the same time, the CPU enables the destination register to store the ALU output (the resulting sum from
5544-612: The mid-2000s with installed memory often exceeding the 32-bit 4G RAM address limits on entry level computers. The latest generation of smartphones have also switched to 64 bits. A 32-bit register can store 2 different values. The range of integer values that can be stored in 32 bits depends on the integer representation used. With the two most common representations, the range is 0 through 4,294,967,295 (2 − 1) for representation as an ( unsigned ) binary number , and −2,147,483,648 (−2 ) through 2,147,483,647 (2 − 1) for representation as two's complement . One important consequence
5628-403: The number of bytes in the data. An attempt to read such a file using Fortran on a system of the other endianness results in a run-time error, because the count fields are incorrect. Unicode text can optionally start with a byte order mark (BOM) to signal the endianness of the file or stream. Its code point is U+FEFF. In UTF-32 for example, a big-endian file should start with 00 00 FE FF ;
5712-406: The opcode) and the shifted operand appears at Y. Simple ALUs typically can shift the operand by only one bit position, whereas more complex ALUs employ barrel shifters that allow them to shift the operand by an arbitrary number of bits in one operation. In all single-bit shift operations, the bit shifted out of the operand appears on carry-out; the value of the bit shifted into the operand depends on
5796-588: The operand fragments may be processed in any arbitrary order because each partial depends only on the corresponding operand fragments (the stored carry bit from the previous ALU operation is ignored). Although it is possible to design ALUs that can perform complex functions, this is usually impractical due to the resulting increases in circuit complexity, power consumption, propagation delay, cost and size. Consequently, ALUs are typically limited to simple functions that can be executed at very high speeds (i.e., very short propagation delays), with more complex functions being
5880-416: The operation to be performed. The least-significant byte is accessed first for addition , subtraction and multiplication . The most-significant byte is accessed first for division and comparison . See § Calculation order . When character (text) strings are to be compared with one another, e.g. in order to support some mechanism like sorting , this is very frequently done lexicographically where
5964-640: The original Apple Macintosh . Fully 32-bit microprocessors such as the HP FOCUS , Motorola 68020 and Intel 80386 were launched in the early to mid 1980s and became dominant by the early 1990s. This generation of personal computers coincided with and enabled the first mass-adoption of the World Wide Web . While 32-bit architectures are still widely-used in specific applications, the PC and server market has moved on to 64 bits with x86-64 and other 64-bit architectures since
6048-410: The partial is written to designated storage. This process repeats until all operand fragments have been processed, resulting in a complete collection of partials in storage, which comprise the multi-precision arithmetic result. In multiple-precision shift operations, the order of operand fragment processing depends on the shift direction. In left-shift operations, fragments are processed LS first because
6132-559: The point of view of the executing programs, but they require the motherboard to perform a 64-bit swap across all 8 byte lanes to ensure that the little-endian view of things will apply to I/O devices. In the absence of this unusual motherboard hardware, device driver software must write to different addresses to undo the incomplete transformation and also must perform a normal byte swap. Some CPUs, such as many PowerPC processors intended for embedded use and almost all SPARC processors, allow per-page choice of endianness. SPARC processors since
6216-415: The processor's state machine typically stores the carry out bit to an ALU status register. The algorithm then advances to the next fragment of each operand's collection and invokes an ALU operation on these fragments along with the stored carry bit from the previous ALU operation, thus producing another (more significant) partial and a carry out bit. As before, the carry bit is stored to the status register and
6300-451: The responsibility of external circuitry. For example: An ALU is usually implemented either as a stand-alone integrated circuit (IC), such as the 74181 , or as part of a more complex IC. In the latter case, an ALU is typically instantiated by synthesizing it from a description written in VHDL , Verilog or some other hardware description language . For example, the following VHDL code describes
6384-498: The result of the current ALU operation. General-purpose ALUs commonly have status signals such as: The status inputs allow additional information to be made available to the ALU when performing an operation. Typically, this is a single "carry-in" bit that is the stored carry-out from a previous ALU operation. An ALU is a combinational logic circuit, meaning that its outputs will change asynchronously in response to input changes. In normal operation, stable signals are applied to all of
6468-427: The same address as either 8-bit (value = 4A), 16-bit (004A), 24-bit (00004A), or 32-bit (0000004A), all of which retain the same numeric value. Although this little-endian property is rarely used directly by high-level programmers, it is occasionally employed by code optimizers as well as by assembly language programmers. While not allowed by C++, such type punning code is allowed as "implementation-defined" by
6552-432: The size of a fragment exactly matches the ALU word size, the ALU can directly operate on this "piece" of operand. The algorithm uses the ALU to directly operate on particular operand fragments and thus generate a corresponding fragment (a "partial") of the multi-precision result. Each partial, when generated, is written to an associated region of storage that has been designated for the multiple-precision result. This process
6636-615: The smallest memory address and the least significant byte at the largest. A little-endian system, in contrast, stores the least-significant byte at the smallest address. Of the two, big-endian is thus closer to the way the digits of numbers are written left-to-right in English, comparing digits to bytes. Bi-endianness is a feature supported by numerous computer architectures that feature switchable endianness in data fetches and stores or for instruction fetches. Other orderings are generically called middle-endian or mixed-endian . Big-endianness
6720-404: The type of shift. Upon completion of each ALU operation, the ALU's status output signals are usually stored in external registers to make them available for future ALU operations (e.g., to implement multiple-precision arithmetic ) and for controlling conditional branching . The bit registers that store the status output signals are often collectively treated as a single, multi-bit register, which
6804-989: The value appears left-to-right, coinciding with the correct string order for reading the result ("J O H N"). But on a little-endian machine, one would see "N H O J". Middle-endian machines complicate this even further; for example, on the PDP-11 , the 32-bit value is stored as two 16-bit words "JO" "HN" in big-endian, with the characters in the 16-bit words being stored in little-endian, resulting in "O J N H". Byte-swapping consists of rearranging bytes to change endianness. Many compilers provide built-ins that are likely to be compiled into native processor instructions ( bswap / movbe ), such as __builtin_bswap32 . Software interfaces for swapping include: Some CPU instruction sets provide native support for endian byte swapping, such as bswap ( x86 — 486 and later, i960 — i960Jx and later), and rev ( ARMv6 and later). Some compilers have built-in facilities for byte swapping. For example,
6888-595: Was expensive during the first decades of 32-bit architectures (the 1960s to the 1980s). Older 32-bit processor families (or simpler, cheaper variants thereof) could therefore have many compromises and limitations in order to cut costs. This could be a 16-bit ALU , for instance, or external (or internal) buses narrower than 32 bits, limiting memory size or demanding more cycles for instruction fetch, execution or write back. Despite this, such processors could be labeled 32-bit , since they still had 32-bit registers and instructions able to manipulate 32-bit quantities. For example,
6972-530: Was sometimes insufficient die space for a full-word-width ALU and, as a result, some early microprocessors employed a narrow ALU that required multiple cycles per machine language instruction. Examples of this includes the popular Zilog Z80 , which performed eight-bit additions with a four-bit ALU. Over time, transistor geometries shrank further, following Moore's law , and it became feasible to build wider ALUs on microprocessors. Modern integrated circuit (IC) transistors are orders of magnitude smaller than those of
7056-502: Was unable to deliver the 8008 in time, Datapoint used a medium-scale integration equivalent, but the little-endianness was retained in most Intel designs, including the MCS-48 and the 8086 and its x86 successors, including IA-32 and x86-64 processors. The MOS Technology 6502 family (including Western Design Center 65802 and 65C816 ), the Zilog Z80 (including Z180 and eZ80 ),
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