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90-428: Geohashes offer properties like arbitrary precision and the possibility of gradually removing characters from the end of the code to reduce its size (and gradually lose precision). Geohashing guarantees that the longer a shared prefix between two geohashes is, the spatially closer they are together. The reverse of this is not guaranteed, as two points can be very close but have a short or no shared prefix. The core part of

180-409: A 32-bit to a 64-bit architecture is a fundamental alteration, as most operating systems must be extensively modified to take advantage of the new architecture, because that software has to manage the actual memory addressing hardware. Other software must also be ported to use the new abilities; older 32-bit software may be supported either by virtue of the 64-bit instruction set being a superset of

270-409: A byte or word , is referred to, it is usually specified by a number from 0 upwards corresponding to its position within the byte or word. However, 0 can refer to either the most or least significant bit depending on the context. Similar to torque and energy in physics; information-theoretic information and data storage size have the same dimensionality of units of measurement , but there

360-509: A unit of information , the bit is also known as a shannon , named after Claude E. Shannon . The symbol for the binary digit is either "bit", per the IEC 80000-13 :2008 standard, or the lowercase character "b", per the IEEE 1541-2002 standard. Use of the latter may create confusion with the capital "B" which is the international standard symbol for the byte. The encoding of data by discrete bits

450-613: A virtual machine of a 16- or 32-bit operating system to run 16-bit applications or use one of the alternatives for NTVDM . Mac OS X 10.4 "Tiger" and Mac OS X 10.5 "Leopard" had only a 32-bit kernel, but they can run 64-bit user-mode code on 64-bit processors. Mac OS X 10.6 "Snow Leopard" had both 32- and 64-bit kernels, and, on most Macs, used the 32-bit kernel even on 64-bit processors. This allowed those Macs to support 64-bit processes while still supporting 32-bit device drivers; although not 64-bit drivers and performance advantages that can come with them. Mac OS X 10.7 "Lion" ran with

540-725: A 16  MiB ( 16 × 1024 bytes ) address space. 32-bit superminicomputers , such as the DEC VAX , became common in the 1970s, and 32-bit microprocessors, such as the Motorola 68000 family and the 32-bit members of the x86 family starting with the Intel 80386 , appeared in the mid-1980s, making 32 bits something of a de facto consensus as a convenient register size. A 32-bit address register meant that 2 addresses, or 4  GB of random-access memory (RAM), could be referenced. When these architectures were devised, 4 GB of memory

630-423: A 32- or 64-bit Java virtual machine with no modification. The lengths and precision of all the built-in types, such as char , short , int , long , float , and double , and the types that can be used as array indices, are specified by the standard and are not dependent on the underlying architecture. Java programs that run on a 64-bit Java virtual machine have access to a larger address space. Speed

720-609: A 64-bit kernel on more Macs, and OS X 10.8 "Mountain Lion" and later macOS releases only have a 64-bit kernel. On systems with 64-bit processors, both the 32- and 64-bit macOS kernels can run 32-bit user-mode code, and all versions of macOS up to macOS Mojave (10.14) include 32-bit versions of libraries that 32-bit applications would use, so 32-bit user-mode software for macOS will run on those systems. The 32-bit versions of libraries have been removed by Apple in macOS Catalina (10.15). Linux and most other Unix-like operating systems, and

810-482: A Bell Labs memo on 9 January 1947 in which he contracted "binary information digit" to simply "bit". A bit can be stored by a digital device or other physical system that exists in either of two possible distinct states . These may be the two stable states of a flip-flop , two positions of an electrical switch , two distinct voltage or current levels allowed by a circuit , two distinct levels of light intensity , two directions of magnetization or polarization ,

900-429: A bit was represented by the polarity of magnetization of a certain area of a ferromagnetic film, or by a change in polarity from one direction to the other. The same principle was later used in the magnetic bubble memory developed in the 1980s, and is still found in various magnetic strip items such as metro tickets and some credit cards . In modern semiconductor memory , such as dynamic random-access memory ,

990-601: A database are Locational codes , which are also called spatial keys and similar to QuadTiles. In some geographical information systems and Big Data spatial databases, a Hilbert curve based indexation can be used as an alternative to Z-order curve , like in the S2 Geometry library . In 2019 a front-end was designed by QA Locate in what they called GeohashPhrase to use phrases to code Geohashes for easier communication via spoken English language. There were plans to make GeohashPhrase open source. The Geohash algorithm

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1080-780: A driver for a 32-bit PCI device asking the device to DMA data into upper areas of a 64-bit machine's memory could not satisfy requests from the operating system to load data from the device to memory above the 4 gigabyte barrier, because the pointers for those addresses would not fit into the DMA registers of the device. This problem is solved by having the OS take the memory restrictions of the device into account when generating requests to drivers for DMA, or by using an input–output memory management unit (IOMMU). As of August 2023 , 64-bit architectures for which processors are being manufactured include: Most architectures of 64 bits that are derived from

1170-652: A formal (normative) reference. In the absence of an official specification since the creation of Geohash, the CTA WAVE organization published CTA-5009 to aid in broader adoption and compatibility across implementers in the industry. 64-bit computing 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

1260-449: A generation of computers in which 64-bit processors are the norm. 64 bits is a word size that defines certain classes of computer architecture, buses, memory, and CPUs and, by extension, the software that runs on them. 64-bit CPUs have been used in supercomputers since the 1970s ( Cray-1 , 1975) and in reduced instruction set computers (RISC) based workstations and servers since the early 1990s. In 2003, 64-bit CPUs were introduced to

1350-484: A given process and can have implications for efficient processor cache use. Maintaining a partial 32-bit model is one way to handle this, and is in general reasonably effective. For example, the z/OS operating system takes this approach, requiring program code to reside in 31-bit address spaces (the high order bit is not used in address calculation on the underlying hardware platform) while data objects can optionally reside in 64-bit regions. Not all such applications require

1440-538: A given rectangular area in contiguous slices (the number of slices depends on the precision required and the presence of geohash "fault lines"). This is especially useful in database systems where queries on a single index are much easier or faster than multiple-index queries. Second, this index structure can be used for a quick-and-dirty proximity search: the closest points are often among the closest geohashes. A formal description for Computational and Mathematical views. For exact latitude and longitude translations Geohash

1530-751: A large address space or manipulate 64-bit data items, so these applications do not benefit from these features. x86-based 64-bit systems sometimes lack equivalents of software that is written for 32-bit architectures. The most severe problem in Microsoft Windows is incompatible device drivers for obsolete hardware. Most 32-bit application software can run on a 64-bit operating system in a compatibility mode , also termed an emulation mode, e.g., Microsoft WoW64 Technology for IA-64 and AMD64. The 64-bit Windows Native Mode driver environment runs atop 64-bit NTDLL.DLL , which cannot call 32-bit Win32 subsystem code (often devices whose actual hardware function

1620-521: A problem. 64-bit drivers were not provided for many older devices, which could consequently not be used in 64-bit systems. Driver compatibility was less of a problem with open-source drivers, as 32-bit ones could be modified for 64-bit use. Support for hardware made before early 2007, was problematic for open-source platforms, due to the relatively small number of users. 64-bit versions of Windows cannot run 16-bit software . However, most 32-bit applications will work well. 64-bit users are forced to install

1710-552: 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. The term 64-bit also describes

1800-413: A processor with 64-bit memory addresses can directly access 2 bytes (16 exabytes or EB) of byte-addressable memory. With no further qualification, a 64-bit computer architecture generally has integer and addressing registers that are 64 bits wide, allowing direct support for 64-bit data types and addresses. However, a CPU might have external data buses or address buses with different sizes from

1890-513: A single input box (most commonly used formats for latitude and longitude pairs are accepted), and performs the request. Besides showing the latitude and longitude corresponding to the given Geohash, users who navigate to a Geohash at geohash.org are also presented with an embedded map, and may download a GPX file, or transfer the waypoint directly to certain GPS receivers. Links are also provided to external sites that may provide further details around

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1980-405: A single integer register can store the memory address to any location in the computer's physical or virtual memory . Therefore, the total number of addresses to memory is often determined by the width of these registers. The IBM System/360 of the 1960s was an early 32-bit computer; it had 32-bit integer registers, although it only used the low order 24 bits of a word for addresses, resulting in

2070-404: A time in serial transmission , and by a multiple number of bits in parallel transmission . A bitwise operation optionally processes bits one at a time. Data transfer rates are usually measured in decimal SI multiples of the unit bit per second (bit/s), such as kbit/s. In the earliest non-electronic information processing devices, such as Jacquard's loom or Babbage's Analytical Engine , a bit

2160-444: A time, again from the left to the right side. For the latitude value, the interval −90 to +90 is divided by 2, producing two intervals: −90 to 0, and 0 to +90. Since the first bit is 1, the higher interval is chosen, and becomes the current interval. The procedure is repeated for all bits in the code. Finally, the latitude value is the center of the resulting interval. Longitudes are processed in an equivalent way, keeping in mind that

2250-465: Is a spatial index of base 4 , because it transforms the continuous latitude and longitude space coordinates into a hierarchical discrete grid, using a recurrent four-partition of the space. To be a compact code it uses base 32 and represents its values by the following alphabet, that is the "standard textual representation". The "Geohash alphabet" (32ghs) uses all digits 0-9 and all lower case letters except "a", "i", "l" and "o". For example, using

2340-522: Is an abbreviation of "Long, Pointer, 64". Other models are the ILP64 data model in which all three data types are 64 bits wide, and even the SILP64 model where short integers are also 64 bits wide. However, in most cases the modifications required are relatively minor and straightforward, and many well-written programs can simply be recompiled for the new environment with no changes. Another alternative

2430-605: Is correct, rounding to 43 is not. Geohashes can be used to find points in proximity to each other based on a common prefix. However, edge case locations close to each other but on opposite sides of the 180 degree meridian will result in Geohash codes with no common prefix (different longitudes for near physical locations). Points close to the North and South poles will have very different geohashes (different longitudes for near physical locations). Two close locations on either side of

2520-483: Is emulated in user mode software, like Winprinters). Because 64-bit drivers for most devices were unavailable until early 2007 (Vista x64), using a 64-bit version of Windows was considered a challenge. However, the trend has since moved toward 64-bit computing, more so as memory prices dropped and the use of more than 4 GB of RAM increased. Most manufacturers started to provide both 32-bit and 64-bit drivers for new devices, so unavailability of 64-bit drivers ceased to be

2610-486: Is in general no meaning to adding, subtracting or otherwise combining the units mathematically, although one may act as a bound on the other. Units of information used in information theory include the shannon (Sh), the natural unit of information (nat) and the hartley (Hart). One shannon is the maximum amount of information needed to specify the state of one bit of storage. These are related by 1 Sh ≈ 0.693 nat ≈ 0.301 Hart. Some authors also define

2700-554: Is more compressed—the same bucket can hold more. For example, it is estimated that the combined technological capacity of the world to store information provides 1,300 exabytes of hardware digits. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 exabytes of information. When optimally compressed, the resulting carrying capacity approaches Shannon information or information entropy . Certain bitwise computer processor instructions (such as bit set ) operate at

2790-413: Is not the only factor to consider in comparing 32-bit and 64-bit processors. Applications such as multi-tasking, stress testing, and clustering – for high-performance computing (HPC) – may be more suited to a 64-bit architecture when deployed appropriately. For this reason, 64-bit clusters have been widely deployed in large organizations, such as IBM, HP, and Microsoft. Summary: A common misconception

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2880-441: Is often written with implicit assumptions about the widths of data types. C code should prefer ( u ) intptr_t instead of long when casting pointers into integer objects. A programming model is a choice made to suit a given compiler, and several can coexist on the same OS. However, the programming model chosen as the primary model for the OS application programming interface (API) typically dominates. Another consideration

2970-504: Is often, but not always, based on 64-bit units of data. For example, although the x86 / x87 architecture has instructions able to load and store 64-bit (and 32-bit) floating-point values in memory, the internal floating-point data and register format is 80 bits wide, while the general-purpose registers are 32 bits wide. In contrast, the 64-bit Alpha family uses a 64-bit floating-point data and register format, and 64-bit integer registers. Many computer instruction sets are designed so that

3060-418: Is that 64-bit architectures are no better than 32-bit architectures unless the computer has more than 4 GB of random-access memory . This is not entirely true: The main disadvantage of 64-bit architectures is that, relative to 32-bit architectures, the same data occupies more space in memory (due to longer pointers and possibly other types, and alignment padding). This increases the memory requirements of

3150-495: Is the IBM AS/400 , software for which is compiled into a virtual instruction set architecture (ISA) called Technology Independent Machine Interface (TIMI); TIMI code is then translated to native machine code by low-level software before being executed. The translation software is all that must be rewritten to move the full OS and all software to a new platform, as when IBM transitioned the native instruction set for AS/400 from

3240-507: Is the LLP64 model, which maintains compatibility with 32-bit code by leaving both int and long as 32-bit. LL refers to the long long integer type, which is at least 64 bits on all platforms, including 32-bit environments. There are also systems with 64-bit processors using an ILP32 data model, with the addition of 64-bit long long integers; this is also used on many platforms with 32-bit processors. This model reduces code size and

3330-400: Is the data model used for device drivers . Drivers make up the majority of the operating system code in most modern operating systems (although many may not be loaded when the operating system is running). Many drivers use pointers heavily to manipulate data, and in some cases have to load pointers of a certain size into the hardware they support for direct memory access (DMA). As an example,

3420-649: The Apple Watch Series 4 and 5. Many 64-bit platforms today use an LP64 model (including Solaris, AIX , HP-UX , Linux, macOS, BSD, and IBM z/OS). Microsoft Windows uses an LLP64 model. The disadvantage of the LP64 model is that storing a long into an int truncates. On the other hand, converting a pointer to a long will "work" in LP64. In the LLP64 model, the reverse is true. These are not problems which affect fully standard-compliant code, but code

3510-513: The C and C++ toolchains for them, have supported 64-bit processors for many years. Many applications and libraries for those platforms are open-source software , written in C and C++, so that if they are 64-bit-safe, they can be compiled into 64-bit versions. This source-based distribution model, with an emphasis on frequent releases, makes availability of application software for those operating systems less of an issue. In 32-bit programs, pointers and data types such as integers generally have

3600-464: The Cray-1 , used registers up to 64 bits wide, and supported 64-bit integer arithmetic, although they did not support 64-bit addressing. In the mid-1980s, Intel i860 development began culminating in a 1989 release; the i860 had 32-bit integer registers and 32-bit addressing, so it was not a fully 64-bit processor, although its graphics unit supported 64-bit integer arithmetic. However, 32 bits remained

3690-468: The Earth , so that referencing them in emails , forums , and websites is more convenient. Many variations have been developed, including OpenStreetMap 's short link (using base64 instead of base32) in 2009, the 64-bit Geohash in 2014, the exotic Hilbert-Geohash in 2016, and others. To obtain the Geohash, the user provides an address to be geocoded , or latitude and longitude coordinates, in

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3780-963: The Nintendo 64 and the PlayStation 2 had 64-bit microprocessors before their introduction in personal computers. High-end printers, network equipment, and industrial computers also used 64-bit microprocessors, such as the Quantum Effect Devices R5000 . 64-bit computing started to trickle down to the personal computer desktop from 2003 onward, when some models in Apple 's Macintosh lines switched to PowerPC 970 processors (termed G5 by Apple), and Advanced Micro Devices (AMD) released its first 64-bit x86-64 processor. Physical memory eventually caught up with 32 bit limits. In 2023, laptop computers were commonly equipped with 16GB and servers up to 64 GB of memory, greatly exceeding

3870-410: The yottabit (Ybit). When the information capacity of a storage system or a communication channel is presented in bits or bits per second , this often refers to binary digits, which is a computer hardware capacity to store binary data ( 0 or 1 , up or down, current or not, etc.). Information capacity of a storage system is only an upper bound to the quantity of information stored therein. If

3960-449: The 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down a mercury delay line , charges stored on the inside surface of a cathode-ray tube , or opaque spots printed on glass discs by photolithographic techniques. In the 1950s and 1960s, these methods were largely supplanted by magnetic storage devices such as magnetic-core memory , magnetic tapes , drums , and disks , where

4050-521: The 32-bit instruction set, so that processors that support the 64-bit instruction set can also run code for the 32-bit instruction set, or through software emulation , or by the actual implementation of a 32-bit processor core within the 64-bit processor, as with some Itanium processors from Intel, which included an IA-32 processor core to run 32-bit x86 applications. The operating systems for those 64-bit architectures generally support both 32-bit and 64-bit applications. One significant exception to this

4140-833: The 32-bit limit of 4 GB ( 4 × 1024 bytes ), allowing room for later expansion and incurring no overhead of translating full 64-bit addresses. The Power ISA v3.0 allows 64 bits for an effective address, mapped to a segmented address with between 65 and 78 bits allowed, for virtual memory, and, for any given processor, up to 60 bits for physical memory. The Oracle SPARC Architecture 2015 allows 64 bits for virtual memory and, for any given processor, between 40 and 56 bits for physical memory. The ARM AArch64 Virtual Memory System Architecture allows 48 bits for virtual memory and, for any given processor, from 32 to 48 bits for physical memory. The DEC Alpha specification requires minimum of 43 bits of virtual memory address space (8 TB) to be supported, and hardware need to check and trap if

4230-655: The 4 GB address capacity of 32 bits. In principle, a 64-bit microprocessor can address 16 EB ( 16 × 1024 = 2 = 18,446,744,073,709,551,616 bytes ) of memory. However, not all instruction sets, and not all processors implementing those instruction sets, support a full 64-bit virtual or physical address space. The x86-64 architecture (as of 2016 ) allows 48 bits for virtual memory and, for any given processor, up to 52 bits for physical memory. These limits allow memory sizes of 256  TB ( 256 × 1024 bytes ) and 4  PB ( 4 × 1024 bytes ), respectively. A PC cannot currently contain 4  petabytes of memory (due to

4320-563: The Equator (or Greenwich meridian) will not have a long common prefix since they belong to different 'halves' of the world. Put simply, one location's binary latitude (or longitude) will be 011111... and the other 100000...., so they will not have a common prefix and most bits will be flipped. This can also be seen as a consequence of relying on the Z-order curve (which could more appropriately be called an N-order visit in this case) for ordering

4410-470: The Geohash algorithm and the first initiative to similar solution was documented in a report of G.M. Morton in 1966, "A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing". The Morton work was used for efficient implementations of Z-order curve , like in this modern (2014) Geohash-integer version (based on directly interleaving 64-bit integers ), but his geocode proposal

4500-409: The ambiguity of relying on the underlying hardware design, the unit octet was defined to explicitly denote a sequence of eight bits. Computers usually manipulate bits in groups of a fixed size, conventionally named " words ". Like the byte, the number of bits in a word also varies with the hardware design, and is typically between 8 and 80 bits, or even more in some specialized computers. In

4590-424: The average. This principle is the basis of data compression technology. Using an analogy, the hardware binary digits refer to the amount of storage space available (like the number of buckets available to store things), and the information content the filling, which comes in different levels of granularity (fine or coarse, that is, compressed or uncompressed information). When the granularity is finer—when information

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4680-433: The binary representation: This operation results in the bits 01101 11111 11000 00100 00010 . Starting to count from the left side with the digit 0 in the first position, the digits in the even positions form the longitude code ( 0111110000000 ), while the digits in the odd positions form the latitude code ( 101111001001 ). Each binary code is then used in a series of divisions, considering one bit at

4770-445: The difficulty of mapping coordinates on a sphere (non linear and with wrapping of values, similar to modulo arithmetic) to two dimensional coordinates and the difficulty of exploring a two dimensional space uniformly. The first is related to Geographical coordinate system and Map projection , and the other to Hilbert curve and z-order curve . Once a coordinate system is found that represents points linearly in distance and wraps up at

4860-415: The early 21st century, retail personal or server computers have a word size of 32 or 64 bits. The International System of Units defines a series of decimal prefixes for multiples of standardized units which are commonly also used with the bit and the byte. The prefixes kilo (10 ) through yotta (10 ) increment by multiples of one thousand, and the corresponding units are the kilobit (kbit) through

4950-597: The edges, and can be explored uniformly, applying geohashing to those coordinates will not suffer from the limitations above. While it is possible to apply geohashing to an area with a Cartesian coordinate system , it would then only apply to the area where the coordinate system applies. Despite those issues, there are possible workarounds, and the algorithm has been successfully used in Elasticsearch, MongoDB, HBase, Redis, and Accumulo to implement proximity searches. An alternative to storing Geohashes as strings in

5040-460: The function j = ⌊ i 2 ⌋ {\displaystyle j=\left\lfloor {\frac {i}{2}}\right\rfloor } . The illustration shows how to obtain the grid of 32 rectangular cells from the grid of 64 square cells. The most important property of Geohash for humans is that it preserves spatial hierarchy in the code prefixes . For example, in the "1 Geohash digit grid" illustration of 32 rectangles, above,

5130-413: The initial interval is −180 to +180. For example, in the latitude code 101111001001 , the first bit is 1, so we know our latitude is somewhere between 0 and 90. Without any more bits, we'd guess the latitude was 45, giving us an error of ±45. Since more bits are available, we can continue with the next bit, and each subsequent bit halves this error. This table shows the effect of each bit. At each stage,

5220-409: The level of manipulating bits rather than manipulating data interpreted as an aggregate of bits. In the 1980s, when bitmapped computer displays became popular, some computers provided specialized bit block transfer instructions to set or copy the bits that corresponded to a given rectangular area on the screen. In most computers and programming languages, when a bit within a group of bits, such as

5310-631: The mainstream PC market in the form of x86-64 processors and the PowerPC G5 . A 64-bit register can hold any of 2 (over 18 quintillion or 1.8×10 ) different values. The range of integer values that can be stored in 64 bits depends on the integer representation used. With the two most common representations, the range is 0 through 18,446,744,073,709,551,615 (equal to 2 − 1) for representation as an ( unsigned ) binary number , and −9,223,372,036,854,775,808 (−2 ) through 9,223,372,036,854,775,807 (2 − 1) for representation as two's complement . Hence,

5400-542: The mid-1990s, HAL Computer Systems , Sun Microsystems , IBM , Silicon Graphics , and Hewlett-Packard had developed 64-bit architectures for their workstation and server systems. A notable exception to this trend were mainframes from IBM, which then used 32-bit data and 31-bit address sizes; the IBM mainframes did not include 64-bit processors until 2000. During the 1990s, several low-cost 64-bit microprocessors were used in consumer electronics and embedded applications. Notably,

5490-409: The norm until the early 1990s, when the continual reductions in the cost of memory led to installations with amounts of RAM approaching 4 GB, and the use of virtual memory spaces exceeding the 4 GB ceiling became desirable for handling certain types of problems. In response, MIPS and DEC developed 64-bit microprocessor architectures, initially for high-end workstation and server machines. By

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5580-763: The older 32/48-bit IMPI to the newer 64-bit PowerPC-AS , codenamed Amazon . The IMPI instruction set was quite different from even 32-bit PowerPC, so this transition was even bigger than moving a given instruction set from 32 to 64 bits. On 64-bit hardware with x86-64 architecture (AMD64), most 32-bit operating systems and applications can run with no compatibility issues. While the larger address space of 64-bit architectures makes working with large data sets in applications such as digital video , scientific computing, and large databases easier, there has been considerable debate on whether they or their 32-bit compatibility modes will be faster than comparably priced 32-bit systems for other tasks. A compiled Java program can run on

5670-408: The orientation of reversible double stranded DNA , etc. Bits can be implemented in several forms. In most modern computing devices, a bit is usually represented by an electrical voltage or current pulse, or by the electrical state of a flip-flop circuit. For devices using positive logic , a digit value of 1 (or a logical value of true) is represented by a more positive voltage relative to

5760-428: The other types of registers cannot. The size of these registers therefore normally limits the amount of directly addressable memory, even if there are registers, such as floating-point registers, that are wider. Most high performance 32-bit and 64-bit processors (some notable exceptions are older or embedded ARM architecture (ARM) and 32-bit MIPS architecture (MIPS) CPUs) have integrated floating point hardware, which

5850-420: The physical size of the memory chips), but AMD envisioned large servers, shared memory clusters, and other uses of physical address space that might approach this in the foreseeable future. Thus the 52-bit physical address provides ample room for expansion while not incurring the cost of implementing full 64-bit physical addresses. Similarly, the 48-bit virtual address space was designed to provide 65,536 (2 ) times

5940-443: The physical states of the underlying storage or device is a matter of convention, and different assignments may be used even within the same device or program . It may be physically implemented with a two-state device. A contiguous group of binary digits is commonly called a bit string , a bit vector, or a single-dimensional (or multi-dimensional) bit array . A group of eight bits is called one  byte , but historically

6030-433: The points, as two points close by might be visited at very different times. However, two points with a long common prefix will be close by. In order to do a proximity search, one could compute the southwest corner (low geohash with low latitude and longitude) and northeast corner (high geohash with high latitude and longitude) of a bounding box and search for geohashes between those two. This search will retrieve all points in

6120-578: The registers, even larger (the 32-bit Pentium had a 64-bit data bus, for instance). Processor registers are typically divided into several groups: integer , floating-point , single instruction, multiple data (SIMD), control , and often special registers for address arithmetic which may have various uses and names such as address , index , or base registers . However, in modern designs, these functions are often performed by more general purpose integer registers. In most processors, only integer or address-registers can be used to address data in memory;

6210-444: The relevant half of the range is highlighted in green; a low bit selects the lower range, a high bit selects the upper range. The column "mean value" shows the latitude, simply the mean value of the range. Each subsequent bit makes this value more precise. (The numbers in the above table have been rounded to 3 decimal places for clarity) Final rounding should be done carefully in a way that So while rounding 42.605 to 42.61 or 42.6

6300-547: The remaining unsupported bits are zero (to support compatibility on future processors). Alpha 21064 supported 43 bits of virtual memory address space (8 TB) and 34 bits of physical memory address space (16 GB). Alpha 21164 supported 43 bits of virtual memory address space (8 TB) and 40 bits of physical memory address space (1 TB). Alpha 21264 supported user-configurable 43 or 48 bits of virtual memory address space (8 TB or 256 TB) and 44 bits of physical memory address space (16 TB). A change from

6390-517: The representation of 0 . Different logic families require different voltages, and variations are allowed to account for component aging and noise immunity. For example, in transistor–transistor logic (TTL) and compatible circuits, digit values 0 and 1 at the output of a device are represented by no higher than 0.4 V and no lower than 2.6 V, respectively; while TTL inputs are specified to recognize 0.8 V or below as 0 and 2.2 V or above as 1 . Bits are transmitted one at

6480-672: The same architecture of 32 bits can execute code written for the 32-bit versions natively, with no performance penalty. This kind of support is commonly called bi-arch support or more generally multi-arch support . Bit The bit is the most basic unit of information in computing and digital communication . The name is a portmanteau of binary digit . The bit represents a logical state with one of two possible values . These values are most commonly represented as either " 1 " or " 0 " , but other representations such as true / false , yes / no , on / off , or + / − are also widely used. The relation between these values and

6570-486: The same length. This is not necessarily true on 64-bit machines. Mixing data types in programming languages such as C and its descendants such as C++ and Objective-C may thus work on 32-bit implementations but not on 64-bit implementations. In many programming environments for C and C-derived languages on 64-bit machines, int variables are still 32 bits wide, but long integers and pointers are 64 bits wide. These are described as having an LP64 data model , which

6660-448: The size of data structures containing pointers, at the cost of a much smaller address space, a good choice for some embedded systems. For instruction sets such as x86 and ARM in which the 64-bit version of the instruction set has more registers than does the 32-bit version, it provides access to the additional registers without the space penalty. It is common in 64-bit RISC machines, explored in x86 as x32 ABI , and has recently been used in

6750-424: The size of the byte is not strictly defined. Frequently, half, full, double and quadruple words consist of a number of bytes which is a low power of two. A string of four bits is usually a nibble . In information theory , one bit is the information entropy of a random binary variable that is 0 or 1 with equal probability, or the information that is gained when the value of such a variable becomes known. As

6840-418: The spatial region of the code e (rectangle of greyish blue circle at position 4,3) is preserved with prefix e in the "2 digit grid" of 1024 rectangles (scale showing em and greyish green to blue circles at grid). Using the hash ezs42 as an example, here is how it is decoded into a decimal latitude and longitude. The first step is decoding it from textual " base 32ghs ", as showed above, to obtain

6930-425: The specified location. For example, the coordinate pair 57.64911,10.40744 (near the tip of the peninsula of Jutland, Denmark ) produces a slightly shorter hash of u4pruydqqvj . The main usages of Geohashes are: Geohashes have also been proposed to be used for geotagging . When used in a database, the structure of geohashed data has two advantages. First, data indexed by geohash will have all points for

7020-461: The table above and the constant B = 32 {\displaystyle B=32} , the Geohash ezs42 can be converted to a decimal representation by ordinary positional notation : The geometry of the Geohash has a mixed spatial representation: It is possible to build the "И-order curve" from the Z-order curve by merging neighboring cells and indexing the resulting rectangular grid by

7110-577: The thickness of alternating black and white lines. The bit is not defined in the International System of Units (SI). However, the International Electrotechnical Commission issued standard IEC 60027 , which specifies that the symbol for binary digit should be 'bit', and this should be used in all multiples, such as 'kbit', for kilobit. However, the lower-case letter 'b' is widely used as well and

7200-556: The two possible values of one bit of storage are not equally likely, that bit of storage contains less than one bit of information. If the value is completely predictable, then the reading of that value provides no information at all (zero entropic bits, because no resolution of uncertainty occurs and therefore no information is available). If a computer file that uses n  bits of storage contains only m  <  n  bits of information, then that information can in principle be encoded in about m  bits, at least on

7290-444: The two values of a bit may be represented by two levels of electric charge stored in a capacitor . In certain types of programmable logic arrays and read-only memory , a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. In optical discs , a bit is encoded as the presence or absence of a microscopic pit on a reflective surface. In one-dimensional bar codes , bits are encoded as

7380-704: The z-order curve between the two corners, which can be far too many points. This method also breaks down at the 180 meridians and the poles. Solr uses a filter list of prefixes, by computing the prefixes of the nearest squares close to the geohash [1] . Since a geohash (in this implementation) is based on coordinates of longitude and latitude the distance between two geohashes reflects the distance in latitude/longitude coordinates between two points, which does not translate to actual distance, see Haversine formula . Example of non-linearity for latitude-longitude system: Note that these limitations are not due to geohashing, and not due to latitude-longitude coordinates, but due to

7470-451: Was also used in Morse code (1844) and early digital communications machines such as teletypes and stock ticker machines (1870). Ralph Hartley suggested the use of a logarithmic measure of information in 1928. Claude E. Shannon first used the word "bit" in his seminal 1948 paper " A Mathematical Theory of Communication ". He attributed its origin to John W. Tukey , who had written

7560-412: Was not human-readable and was not popular. Apparently, in the late 2000s, G. Niemeyer still didn't know about Morton's work, and reinvented it, adding the use of base32 representation. In February 2008, together with the announcement of the system, he launched the website http://geohash.org , which allows users to convert geographic coordinates to short URLs which uniquely identify positions on

7650-460: Was often stored as the position of a mechanical lever or gear, or the presence or absence of a hole at a specific point of a paper card or tape . The first electrical devices for discrete logic (such as elevator and traffic light control circuits , telephone switches , and Konrad Zuse's computer) represented bits as the states of electrical relays which could be either "open" or "closed". When relays were replaced by vacuum tubes , starting in

7740-456: Was put in the public domain by its inventor in a public announcement on February 26, 2008. While comparable algorithms have been successfully patented and had copyright claimed upon, GeoHash is based on an entirely different algorithm and approach. Geohash is standardized as CTA-5009.  This standard follows the Misplaced Pages article as of the 2023 version but provides additional detail in

7830-507: Was recommended by the IEEE 1541 Standard (2002) . In contrast, the upper case letter 'B' is the standard and customary symbol for byte. Multiple bits may be expressed and represented in several ways. For convenience of representing commonly reoccurring groups of bits in information technology, several units of information have traditionally been used. The most common is the unit byte , coined by Werner Buchholz in June 1956, which historically

7920-416: Was so far beyond the typical amounts (4 MiB) in installations, that this was considered to be enough headroom for addressing. 4.29 billion addresses were considered an appropriate size to work with for another important reason: 4.29 billion integers are enough to assign unique references to most entities in applications like databases . Some supercomputer architectures of the 1970s and 1980s, such as

8010-541: Was used in the punched cards invented by Basile Bouchon and Jean-Baptiste Falcon (1732), developed by Joseph Marie Jacquard (1804), and later adopted by Semyon Korsakov , Charles Babbage , Herman Hollerith , and early computer manufacturers like IBM . A variant of that idea was the perforated paper tape . In all those systems, the medium (card or tape) conceptually carried an array of hole positions; each position could be either punched through or not, thus carrying one bit of information. The encoding of text by bits

8100-405: Was used to represent the group of bits used to encode a single character of text (until UTF-8 multibyte encoding took over) in a computer and for this reason it was used as the basic addressable element in many computer architectures . The trend in hardware design converged on the most common implementation of using eight bits per byte, as it is widely used today. However, because of

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