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Wednesday, October 9, 2019

Virtual machine

From Wikipedia, the free encyclopedia
 
In computing, a virtual machine (VM) is an emulation of a computer system. Virtual machines are based on computer architectures and provide functionality of a physical computer. Their implementations may involve specialized hardware, software, or a combination.

There are different kinds of virtual machines, each with different functions:
  • System virtual machines (also termed full virtualization VMs) provide a substitute for a real machine. They provide functionality needed to execute entire operating systems. A hypervisor uses native execution to share and manage hardware, allowing for multiple environments which are isolated from one another, yet exist on the same physical machine. Modern hypervisors use hardware-assisted virtualization, virtualization-specific hardware, primarily from the host CPUs.
  • Process virtual machines are designed to execute computer programs in a platform-independent environment.
Some virtual machines, such as QEMU, are designed to also emulate different architectures and allow execution of software applications and operating systems written for another CPU or architecture. Operating-system-level virtualization allows the resources of a computer to be partitioned via the kernel. The terms are not universally interchangeable.

Definitions

A "virtual machine" was originally defined by Popek and Goldberg as "an efficient, isolated duplicate of a real computer machine." Current use includes virtual machines that have no direct correspondence to any real hardware. The physical, "real-world" hardware running the VM is generally referred to as the 'host', and the virtual machine emulated on that machine is generally referred to as the 'guest'. A host can emulate several guests, each of which can emulate different operating systems and hardware platforms.

System virtual machines

The desire to run multiple operating systems was the initial motive for virtual machines, so as to allow time-sharing among several single-tasking operating systems. In some respects, a system virtual machine can be considered a generalization of the concept of virtual memory that historically preceded it. IBM's CP/CMS, the first systems to allow full virtualization, implemented time sharing by providing each user with a single-user operating system, the Conversational Monitor System (CMS). Unlike virtual memory, a system virtual machine entitled the user to write privileged instructions in their code. This approach had certain advantages, such as adding input/output devices not allowed by the standard system.

As technology evolves virtual memory for purposes of virtualization, new systems of memory overcommitment may be applied to manage memory sharing among multiple virtual machines on one computer operating system. It may be possible to share memory pages that have identical contents among multiple virtual machines that run on the same physical machine, what may result in mapping them to the same physical page by a technique termed kernel same-page merging (KSM). This is especially useful for read-only pages, such as those holding code segments, which is the case for multiple virtual machines running the same or similar software, software libraries, web servers, middleware components, etc. The guest operating systems do not need to be compliant with the host hardware, thus making it possible to run different operating systems on the same computer (e.g., Windows, Linux, or prior versions of an operating system) to support future software.

The use of virtual machines to support separate guest operating systems is popular in regard to embedded systems. A typical use would be to run a real-time operating system simultaneously with a preferred complex operating system, such as Linux or Windows. Another use would be for novel and unproven software still in the developmental stage, so it runs inside a sandbox. Virtual machines have other advantages for operating system development and may include improved debugging access and faster reboots.

Multiple VMs running their own guest operating system are frequently engaged for server consolidation.

Process virtual machines

A process VM, sometimes called an application virtual machine, or Managed Runtime Environment (MRE), runs as a normal application inside a host OS and supports a single process. It is created when that process is started and destroyed when it exits. Its purpose is to provide a platform-independent programming environment that abstracts away details of the underlying hardware or operating system and allows a program to execute in the same way on any platform. 

A process VM provides a high-level abstraction – that of a high-level programming language (compared to the low-level ISA abstraction of the system VM). Process VMs are implemented using an interpreter; performance comparable to compiled programming languages can be achieved by the use of just-in-time compilation.

This type of VM has become popular with the Java programming language, which is implemented using the Java virtual machine. Other examples include the Parrot virtual machine and the .NET Framework, which runs on a VM called the Common Language Runtime. All of them can serve as an abstraction layer for any computer language.

A special case of process VMs are systems that abstract over the communication mechanisms of a (potentially heterogeneous) computer cluster. Such a VM does not consist of a single process, but one process per physical machine in the cluster. They are designed to ease the task of programming concurrent applications by letting the programmer focus on algorithms rather than the communication mechanisms provided by the interconnect and the OS. They do not hide the fact that communication takes place, and as such do not attempt to present the cluster as a single machine.

Unlike other process VMs, these systems do not provide a specific programming language, but are embedded in an existing language; typically such a system provides bindings for several languages (e.g., C and Fortran). Examples are Parallel Virtual Machine (PVM) and Message Passing Interface (MPI). They are not strictly virtual machines because the applications running on top still have access to all OS services and are therefore not confined to the system model.

History

Both system virtual machines and process virtual machines date to the 1960s and continue to be areas of active development. 

System virtual machines grew out of time-sharing, as notably implemented in the Compatible Time-Sharing System (CTSS). Time-sharing allowed multiple users to use a computer concurrently: each program appeared to have full access to the machine, but only one program was executed at the time, with the system switching between programs in time slices, saving and restoring state each time. This evolved into virtual machines, notably via IBM's research systems: the M44/44X, which used partial virtualization, and the CP-40 and SIMMON, which used full virtualization, and were early examples of hypervisors. The first widely available virtual machine architecture was the CP-67/CMS (see History of CP/CMS for details). An important distinction was between using multiple virtual machines on one host system for time-sharing, as in M44/44X and CP-40, and using one virtual machine on a host system for prototyping, as in SIMMON. Emulators, with hardware emulation of earlier systems for compatibility, date back to the IBM System/360 in 1963, while the software emulation (then-called "simulation") predates it. 

Process virtual machines arose originally as abstract platforms for an intermediate language used as the intermediate representation of a program by a compiler; early examples date to around 1966. An early 1966 example was the O-code machine, a virtual machine that executes O-code (object code) emitted by the front end of the BCPL compiler. This abstraction allowed the compiler to be easily ported to a new architecture by implementing a new back end that took the existing O-code and compiled it to machine code for the underlying physical machine. The Euler language used a similar design, with the intermediate language named P (portable).[8] This was popularized around 1970 by Pascal, notably in the Pascal-P system (1973) and Pascal-S compiler (1975), in which it was termed p-code and the resulting machine as a p-code machine. This has been influential, and virtual machines in this sense have been often generally called p-code machines. In addition to being an intermediate language, Pascal p-code was also executed directly by an interpreter implementing the virtual machine, notably in UCSD Pascal (1978); this influenced later interpreters, notably the Java virtual machine (JVM). Another early example was SNOBOL4 (1967), which was written in the SNOBOL Implementation Language (SIL), an assembly language for a virtual machine, which was then targeted to physical machines by transpiling to their native assembler via a macro assembler. Macros have since fallen out of favor, however, so this approach has been less influential. Process virtual machines were a popular approach to implementing early microcomputer software, including Tiny BASIC and adventure games, from one-off implementations such as Pyramid 2000 to a general-purpose engine like Infocom's z-machine, which Graham Nelson argues is "possibly the most portable virtual machine ever created".

Significant advances occurred in the implementation of Smalltalk-80, particularly the Deutsch/Schiffmann implementation which pushed just-in-time (JIT) compilation forward as an implementation approach that uses process virtual machine. Later notable Smalltalk VMs were VisualWorks, the Squeak Virtual Machine, and Strongtalk. A related language that produced a lot of virtual machine innovation was the Self programming language, which pioneered adaptive optimization and generational garbage collection. These techniques proved commercially successful in 1999 in the HotSpot Java virtual machine. Other innovations include having a register-based virtual machine, to better match the underlying hardware, rather than a stack-based virtual machine, which is a closer match for the programming language; in 1995, this was pioneered by the Dis virtual machine for the Limbo language. OpenJ9 is an alternative for HotSpot JVM in OpenJDK and is an open source eclipse project claiming better startup and less resource consumption compared to HotSpot.

Full virtualization

Logical diagram of full virtualization
 
In full virtualization, the virtual machine simulates enough hardware to allow an unmodified "guest" OS (one designed for the same instruction set) to be run in isolation. This approach was pioneered in 1966 with the IBM CP-40 and CP-67, predecessors of the VM family.

Examples outside the mainframe field include Parallels Workstation, Parallels Desktop for Mac, VirtualBox, Virtual Iron, Oracle VM, Virtual PC, Virtual Server, Hyper-V, VMware Workstation, VMware Server (discontinued, formerly called GSX Server), VMware ESXi, QEMU, Adeos, Mac-on-Linux, Win4BSD, Win4Lin Pro, and Egenera vBlade technology.

Hardware-assisted virtualization

In hardware-assisted virtualization, the hardware provides architectural support that facilitates building a virtual machine monitor and allows guest OSes to be run in isolation. Hardware-assisted virtualization was first introduced on the IBM System/370 in 1972, for use with VM/370, the first virtual machine operating system offered by IBM as an official product.

In 2005 and 2006, Intel and AMD provided additional hardware to support virtualization. Sun Microsystems (now Oracle Corporation) added similar features in their UltraSPARC T-Series processors in 2005. Examples of virtualization platforms adapted to such hardware include KVM, VMware Workstation, VMware Fusion, Hyper-V, Windows Virtual PC, Xen, Parallels Desktop for Mac, Oracle VM Server for SPARC, VirtualBox and Parallels Workstation.

In 2006, first-generation 32- and 64-bit x86 hardware support was found to rarely offer performance advantages over software virtualization.

Operating-system-level virtualization

In operating-system-level virtualization, a physical server is virtualized at the operating system level, enabling multiple isolated and secure virtualized servers to run on a single physical server. The "guest" operating system environments share the same running instance of the operating system as the host system. Thus, the same operating system kernel is also used to implement the "guest" environments, and applications running in a given "guest" environment view it as a stand-alone system. The pioneer implementation was FreeBSD jails; other examples include Docker, Solaris Containers, OpenVZ, Linux-VServer, LXC, AIX Workload Partitions, Parallels Virtuozzo Containers, and iCore Virtual Accounts.

Machine code

From Wikipedia, the free encyclopedia
 
Machine language monitor in a W65C816S single-board computer, displaying code disassembly, as well as processor register and memory dumps.
 
Machine code is a computer program written in machine language instructions that can be executed directly by a computer's central processing unit (CPU). Each instruction causes the CPU to perform a very specific task, such as a load, a store, a jump, or an ALU operation on one or more units of data in CPU registers or memory. 

Machine code is a strictly numerical language which is intended to run as fast as possible, and may be regarded as the lowest-level representation of a compiled or assembled computer program or as a primitive and hardware-dependent programming language. While it is possible to write programs directly in machine code, it is tedious and error prone to manage individual bits and calculate numerical addresses and constants manually. For this reason, programs are very rarely written directly in machine code in modern contexts, but may be done for low level debugging, program patching (especially when assembler source is not available) and assembly language disassembly

The overwhelming majority of practical programs today are written in higher-level languages or assembly language. The source code is then translated to executable machine code by utilities such as compilers, assemblers, and linkers, with the important exception of interpreted programs, which are not translated into machine code. However, the interpreter itself, which may be seen as an executor or processor, performing the instructions of the source code, typically consists of directly executable machine code (generated from assembly or high-level language source code). 

Machine code is by definition the lowest level of programming detail visible to the programmer, but internally many processors use microcode or optimise and transform machine code instructions into sequences of micro-ops. This is not generally considered to be a machine code.

Instruction set

Every processor or processor family has its own instruction set. Instructions are patterns of bits that by physical design correspond to different commands to the machine. Thus, the instruction set is specific to a class of processors using (mostly) the same architecture. Successor or derivative processor designs often include all the instructions of a predecessor and may add additional instructions. Occasionally, a successor design will discontinue or alter the meaning of some instruction code (typically because it is needed for new purposes), affecting code compatibility to some extent; even nearly completely compatible processors may show slightly different behavior for some instructions, but this is rarely a problem. Systems may also differ in other details, such as memory arrangement, operating systems, or peripheral devices. Because a program normally relies on such factors, different systems will typically not run the same machine code, even when the same type of processor is used. 

A processor's instruction set may have all instructions of the same length, or it may have variable-length instructions. How the patterns are organized varies strongly with the particular architecture and often also with the type of instruction. Most instructions have one or more opcode fields which specifies the basic instruction type (such as arithmetic, logical, jump, etc.) and the actual operation (such as add or compare) and other fields that may give the type of the operand(s), the addressing mode(s), the addressing offset(s) or index, or the actual value itself (such constant operands contained in an instruction are called immediates).

Not all machines or individual instructions have explicit operands. An accumulator machine has a combined left operand and result in an implicit accumulator for most arithmetic instructions. Other architectures (such as 8086 and the x86-family) have accumulator versions of common instructions, with the accumulator regarded as one of the general registers by longer instructions. A stack machine has most or all of its operands on an implicit stack. Special purpose instructions also often lack explicit operands (CPUID in the x86 architecture writes values into four implicit destination registers, for instance). This distinction between explicit and implicit operands is important in code generators, especially in the register allocation and live range tracking parts. A good code optimizer can track implicit as well as explicit operands which may allow more frequent constant propagation, constant folding of registers (a register assigned the result of a constant expression freed up by replacing it by that constant) and other code enhancements.

Programs

A computer program is a list of instructions that can be executed by a central processing unit. A program's execution is done in order for the CPU that is executing it to solve a specific problem and thus accomplish a specific result. While simple processors are able to execute instructions one after another, superscalar processors are capable of executing a variety of different instructions at once.
Program flow may be influenced by special 'jump' instructions that transfer execution to an instruction other than the numerically following one. Conditional jumps are taken (execution continues at another address) or not (execution continues at the next instruction) depending on some condition.

Assembly languages

A much more readable rendition of machine language, called assembly language, uses mnemonic codes to refer to machine code instructions, rather than using the instructions' numeric values directly. For example, on the Zilog Z80 processor, the machine code 00000101, which causes the CPU to decrement the B processor register, would be represented in assembly language as DEC B.

Example

The MIPS architecture provides a specific example for a machine code whose instructions are always 32 bits long. The general type of instruction is given by the op (operation) field, the highest 6 bits. J-type (jump) and I-type (immediate) instructions are fully specified by op. R-type (register) instructions include an additional field funct to determine the exact operation. The fields used in these types are: 

   6      5     5     5     5      6 bits
[  op  |  rs |  rt |  rd |shamt| funct]  R-type
[  op  |  rs |  rt | address/immediate]  I-type
[  op  |        target address        ]  J-type

rs, rt, and rd indicate register operands; shamt gives a shift amount; and the address or immediate fields contain an operand directly.

For example, adding the registers 1 and 2 and placing the result in register 6 is encoded: 

[  op  |  rs |  rt |  rd |shamt| funct]
    0     1     2     6     0     32     decimal
 000000 00001 00010 00110 00000 100000   binary

Load a value into register 8, taken from the memory cell 68 cells after the location listed in register 3: 

[  op  |  rs |  rt | address/immediate]
   35     3     8           68           decimal
 100011 00011 01000 00000 00001 000100   binary

Jumping to the address 1024: 

[  op  |        target address        ]
    2                 1024               decimal
 000010 00000 00000 00000 10000 000000   binary

Relationship to microcode

In some computer architectures, the machine code is implemented by an even more fundamental underlying layer called microcode, providing a common machine language interface across a line or family of different models of computer with widely different underlying dataflows. This is done to facilitate porting of machine language programs between different models. An example of this use is the IBM System/360 family of computers and their successors. With dataflow path widths of 8 bits to 64 bits and beyond, they nevertheless present a common architecture at the machine language level across the entire line. 

Using microcode to implement an emulator enables the computer to present the architecture of an entirely different computer. The System/360 line used this to allow porting programs from earlier IBM machines to the new family of computers, e.g. an IBM 1401/1440/1460 emulator on the IBM S/360 model 40.

Relationship to bytecode

Machine code is generally different from bytecode (also known as p-code), which is either executed by an interpreter or itself compiled into machine code for faster (direct) execution. An exception is when a processor is designed to use a particular bytecode directly as its machine code, such as is the case with Java processors.

Machine code and assembly code are sometimes called native code when referring to platform-dependent parts of language features or libraries.

Storing in memory

The Harvard architecture is a computer architecture with physically separate storage and signal pathways for the code (instructions) and data. Today, most processors implement such separate signal pathways for performance reasons but implement a Modified Harvard architecture, so they can support tasks like loading an executable program from disk storage as data and then executing it. Harvard architecture is contrasted to the Von Neumann architecture, where data and code are stored in the same memory which is read by the processor allowing the computer to execute commands.

From the point of view of a process, the code space is the part of its address space where the code in execution is stored. In multitasking systems this comprises the program's code segment and usually shared libraries. In multi-threading environment, different threads of one process share code space along with data space, which reduces the overhead of context switching considerably as compared to process switching.

Readability by humans

Pamela Samuelson wrote that machine code is so unreadable that the United States Copyright Office cannot identify whether a particular encoded program is an original work of authorship; however, the US Copyright Office does allow for copyright registration of computer programs and a program's machine code can sometimes be decompiled in order to make its functioning more easily understandable to humans.

Cognitive science professor Douglas Hofstadter has compared machine code to genetic code, saying that "Looking at a program written in machine language is vaguely comparable to looking at a DNA molecule atom by atom."

Units of information

From Wikipedia, the free encyclopedia
 
In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure the entropy of random variables and information contained in messages.

The most commonly used units of data storage capacity are the bit, the capacity of a system that has only two states, and the byte (or octet), which is equivalent to eight bits. Multiples of these units can be formed from these with the SI prefixes (power-of-ten prefixes) or the newer IEC binary prefixes (power-of-two prefixes).

Primary units

Comparison of units of information: bit, trit, nat, ban. Quantity of information is the height of bars. Dark green level is the "Nat" unit.
 
In 1928, Ralph Hartley observed a fundamental storage principle, which was further formalized by Claude Shannon in 1945: the information that can be stored in a system is proportional to the logarithm of N possible states of that system, denoted logb N. Changing the base of the logarithm from b to a different number c has the effect of multiplying the value of the logarithm by a fixed constant, namely logc N = (logc b) logb N. Therefore, the choice of the base b determines the unit used to measure information. In particular, if b is a positive integer, then the unit is the amount of information that can be stored in a system with N possible states.

When b is 2, the unit is the shannon, equal to the information content of one "bit" (a portmanteau of binary digit). A system with 8 possible states, for example, can store up to log28 = 3 bits of information. Other units that have been named include:
  • Base b = 3: the unit is called "trit", and is equal to log2 3 (≈ 1.585) bits.
The trit, ban, and nat are rarely used to measure storage capacity; but the nat, in particular, is often used in information theory, because natural logarithms are mathematically more convenient than logarithms in other bases.

Units derived from bit

Several conventional names are used for collections or groups of bits.

Byte

Historically, a byte was the number of bits used to encode a character of text in the computer, which depended on computer hardware architecture; but today it almost always means eight bits – that is, an octet. A byte can represent 256 (28) distinct values, such as non-negative integers from 0 to 255, or signed integers from −128 to 127. The IEEE 1541-2002 standard specifies "B" (upper case) as the symbol for byte (IEC 80000-13 uses "o" for octet in French, but also allows "B" in English, which is what is actually being used). Bytes, or multiples thereof, are almost always used to specify the sizes of computer files and the capacity of storage units. Most modern computers and peripheral devices are designed to manipulate data in whole bytes or groups of bytes, rather than individual bits.

Nibble

A group of four bits, or half a byte, is sometimes called a nibble or nybble. This unit is most often used in the context of hexadecimal number representations, since a nibble has the same amount of information as one hexadecimal digit.

Crumb

A pair of two bits or a quarter byte was called a crumb, often used in early 8-bit computing. It is now largely defunct.

Word, block, and page

Computers usually manipulate bits in groups of a fixed size, conventionally called words. The number of bits in a word is usually defined by the size of the registers in the computer's CPU, or by the number of data bits that are fetched from its main memory in a single operation. In the IA-32 architecture more commonly known as x86-32, a word is 16 bits, but other past and current architectures use words with 4, 8, 9, 12, 13, 16, 18, 20, 21, 22, 24, 25, 26, 29, 30, 31, 32, 33, 35, 36, 38, 39, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 72, 80 bits or others. 

Some machine instructions and computer number formats use two words (a "double word" or "dword"), or four words (a "quad word" or "quad"). 

Computer memory caches usually operate on blocks of memory that consist of several consecutive words. These units are customarily called cache blocks, or, in CPU caches, cache lines

Virtual memory systems partition the computer's main storage into even larger units, traditionally called pages.

Systematic multiples

Terms for large quantities of bits can be formed using the standard range of SI prefixes for powers of 10, e.g., kilo = 103 = 1000 (as in kilobit or kbit), mega- = 106 = 1000000 (as in megabit or Mbit) and giga = 109 = 1000000000 (as in gigabit or Gbit). These prefixes are more often used for multiples of bytes, as in kilobyte (1 kB = 8000 bit), megabyte (1 MB = 8000000bit), and gigabyte (1 GB = 8000000000bit). 

However, for technical reasons, the capacities of computer memories and some storage units are often multiples of some large power of two, such as 228 = 268435456 bytes. To avoid such unwieldy numbers, people have often repurposed the SI prefixes to mean the nearest power of two, e.g., using the prefix kilo for 210 = 1024, mega for 220 = 1048576, and giga for 230 = 1073741824, and so on. For example, a random access memory chip with a capacity of 228 bytes would be referred to as a 256-megabyte chip. The table below illustrates these differences.

Multiples of bits
Decimal
Value SI
1000 103 kbit kilobit
10002 106 Mbit megabit
10003 109 Gbit gigabit
10004 1012 Tbit terabit
10005 1015 Pbit petabit
10006 1018 Ebit exabit
10007 1021 Zbit zettabit
10008 1024 Ybit yottabit
Binary
Value IEC JEDEC
1024 210 Kibit kibibit Kbit kilobit
10242 220 Mibit mebibit Mbit megabit
10243 230 Gibit gibibit Gbit gigabit
10244 240 Tibit tebibit
-
10245 250 Pibit pebibit
-
10246 260 Eibit exbibit
-
10247 270 Zibit zebibit
-
10248 280 Yibit yobibit
-

Symbol Prefix SI Meaning Binary meaning Size difference
k kilo 103   = 10001 210 = 10241 2.40%
M mega 106   = 10002 220 = 10242 4.86%
G giga 109   = 10003 230 = 10243 7.37%
T tera 1012 = 10004 240 = 10244 9.95%
P peta 1015 = 10005 250 = 10245 12.59%
E exa 1018 = 10006 260 = 10246 15.29%
Z zetta 1021 = 10007 270 = 10247 18.06%
Y yotta 1024 = 10008 280 = 10248 20.89%

In the past, uppercase K has been used instead of lowercase k to indicate 1024 instead of 1000. However, this usage was never consistently applied.

On the other hand, for external storage systems (such as optical discs), the SI prefixes were commonly used with their decimal values (powers of 10). There have been many attempts to resolve the confusion by providing alternative notations for power-of-two multiples. In 1998 the International Electrotechnical Commission (IEC) issued a standard for this purpose, namely a series of binary prefixes that use 1024 instead of 1000 as the main radix:

Multiples of bytes
Decimal
Value Metric
1000 kB kilobyte
10002 MB megabyte
10003 GB gigabyte
10004 TB terabyte
10005 PB petabyte
10006 EB exabyte
10007 ZB zettabyte
10008 YB yottabyte
Binary
Value IEC JEDEC
1024 KiB kibibyte KB kilobyte
10242 MiB mebibyte MB megabyte
10243 GiB gibibyte GB gigabyte
10244 TiB tebibyte
10245 PiB pebibyte
10246 EiB exbibyte
10247 ZiB zebibyte
10248 YiB yobibyte
Symbol Prefix
Ki kibi, binary kilo 1 kibibyte (KiB) 210 bytes 1024 B
Mi mebi, binary mega 1 mebibyte (MiB) 220 bytes 1024 KiB
Gi gibi, binary giga 1 gibibyte (GiB) 230 bytes 1024 MiB
Ti tebi, binary tera 1 tebibyte (TiB) 240 bytes 1024 GiB
Pi pebi, binary peta 1 pebibyte (PiB) 250 bytes 1024 TiB
Ei exbi, binary exa 1 exbibyte (EiB) 260 bytes 1024 PiB

The JEDEC memory standards however define uppercase K, M, and G for the binary powers 210, 220 and 230 to reflect common usage.

Size examples

  • 1 bit – answer to a yes/no question.
  • 1 byte – a number from 0 to 255.
  • 90 bytes: enough to store a typical line of text from a book.
  • 512 bytes = ½ KiB: the typical sector of a hard disk.
  • 1024 bytes = 1 KiB: the classical block size in UNIX filesystems.
  • 2048 bytes = 2 KiB: a CD-ROM sector.
  • 4096 bytes = 4 KiB: a memory page in x86 (since Intel 80386).
  • 4 kB: about one page of text from a novel.
  • 120 kB: the text of a typical pocket book.
  • 1 MiB – a 1024×1024 pixel bitmap image with 256 colors (8 bpp color depth).
  • 3 MB – a three-minute song (133 kbit/s).
  • 650–900 MB – a CD-ROM.
  • 1 GB – 114 minutes of uncompressed CD-quality audio at 1.4 Mbit/s.
  • 8/16 GB – two common sizes of USB flash drives.
  • 4 TB – the size of a $100 hard disk (as of early 2018).
  • 12 TB Largest hard disk drive (as of early 2018)
  • 16 TB Largest commercially available solid state drive (as of early 2018)
  • 100 TB Largest solid state drive constructed (as of early 2018)
  • 1.3 ZB – prediction of the volume of the whole internet in 2016.

Obsolete and unusual units

Several other units of information storage have been named:
  • 1 bit: unibit, sniff.
  • 2 bits: dibit, crumb, quad, quarter, taste, tayste, tidbit, tydbit, lick, lyck, semi-nibble.
  • 3 bits: tribit, triad, triade, tribble.
  • 5 bits: pentad, pentade, nickel, nyckle.
  • 6 bits: byte (in early IBM machines using BCD alphamerics), hexad, hexade, sextet.
  • 7 bits: heptad, heptade.
  • 8 bits: octet, now usually called byte
  • 10 bits: declet, decle, deckle, dyme.
  • 12 bits: slab.
  • 15 bits: parcel (on CDC 6600 and CDC 7600).
  • 16 bits: doublet, wyde, parcel (on Cray-1), plate, playte, chomp, chawmp (on a 32-bit machine).
  • 18 bits: chomp, chawmp (on a 36-bit machine).
  • 32 bits: quadlet, tetra, dinner, dynner, gawble (on a 32-bit machine).
  • 48 bits: gobble, gawble (under circumstances that remain obscure).
  • 64 bits: octlet, octa.
  • 96 bits: bentobox (in ITRON OS)
  • 128 bits: hexlet.
  • 16 bytes: paragraph (on Intel x86 processors).
  • 6 trits: tryte.
  • combit, comword.
Some of these names are jargon, obsolete, or used only in very restricted contexts.

Lie point symmetry

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Lie_point_symmetry     ...