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63-433: 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

126-461: A binit as an arbitrary information unit equivalent to some fixed but unspecified number of bits. Units of information In digital 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 information contained in messages and

189-733: A bridge circuit . The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the voltage. A common voltage for flashlight batteries is 1.5 volts (DC). A common voltage for automobile batteries is 12 volts (DC). Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) and 220 to 240 volts (AC). The voltage in electric power transmission lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200 kV (AC). The voltage used in overhead lines to power railway locomotives

252-409: 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

315-537: A random access memory chip with a capacity of 2 bytes would be referred to as a 256-megabyte chip. The table below illustrates these differences. In the past, uppercase K has been used instead of lowercase k to indicate 1024 instead of 1000. However, this usage was not consistently applied. On the other hand, for external storage systems (such as optical discs ), the SI prefixes are commonly used with their decimal values (powers of 10). Many attempts have sought to resolve

378-501: 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

441-541: 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 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

504-404: A byte, is sometimes called a nibble , nybble or nyble. This unit is most often used in the context of hexadecimal number representations, since a nibble has the same number of possible values as one hexadecimal digit has. 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

567-588: 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 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

630-490: 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 , the orientation of reversible double stranded DNA , etc. Bits can be implemented in several forms. In most modern computing devices,

693-456: 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 log b 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 log c N = (log c b ) log b N . Therefore,

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756-472: A physical scalar quantity . A voltmeter can be used to measure the voltage between two points in a system. Often a common reference potential such as the ground of the system is used as one of the points. In this case, voltage is often mentioned at a point without completely mentioning the other measurement point. A voltage can be associated with either a source of energy or the loss, dissipation, or storage of energy. The SI unit of work per unit charge

819-423: A well-defined voltage between nodes in the circuit, since the electric force is not a conservative force in those cases. However, at lower frequencies when the electric and magnetic fields are not rapidly changing, this can be neglected (see electrostatic approximation ). The electric potential can be generalized to electrodynamics, so that differences in electric potential between points are well-defined even in

882-463: Is a well-defined voltage across the inductor's terminals. This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads. The volt (symbol: V ) is the derived unit for electric potential , voltage, and electromotive force . The volt is named in honour of the Italian physicist Alessandro Volta (1745–1827), who invented

945-548: Is affected by thermodynamics. The quantity measured by a voltmeter is the negative of the difference of the electrochemical potential of electrons ( Fermi level ) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted electrostatic potential (not measurable with a voltmeter) is sometimes called Galvani potential . The terms "voltage" and "electric potential" are ambiguous in that, in practice, they can refer to either of these in different contexts. The term electromotive force

1008-427: Is between 12 kV and 50 kV (AC) or between 0.75 kV and 3 kV (DC). Inside a conductive material, the energy of an electron is affected not only by the average electric potential but also by the specific thermal and atomic environment that it is in. When a voltmeter is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that

1071-417: Is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages. Therefore, the conventional current in a wire or resistor always flows from higher voltage to lower voltage. Historically, voltage has been referred to using terms like "tension" and "pressure". Even today, the term "tension" is still used, for example within

1134-486: 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

1197-552: 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

1260-547: Is the joule per coulomb , where 1 volt = 1 joule (of work) per 1 coulomb of charge. The old SI definition for volt used power and current ; starting in 1990, the quantum Hall and Josephson effect were used, and in 2019 physical constants were given defined values for the definition of all SI units. Voltage is denoted symbolically by Δ V {\displaystyle \Delta V} , simplified V , especially in English -speaking countries. Internationally,

1323-530: Is the intensity of the electric field. In this case, the voltage increase from point A to point B is equal to the work done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration. Mathematically, this is expressed as the line integral of the electric field along that path. In electrostatics, this line integral is independent of the path taken. Under this definition, any circuit where there are time-varying magnetic fields, such as AC circuits , will not have

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1386-450: Is the sum of the voltage between A and B and the voltage between B and C . The various voltages in a circuit can be computed using Kirchhoff's circuit laws . When talking about alternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added for direct current (DC) and AC, but average voltages can be meaningfully added only when they apply to signals that all have

1449-485: Is the unit byte , coined by Werner Buchholz in June 1956, which historically 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

1512-451: Is widely used today. However, because of 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

1575-457: The entropy of random variables. 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). In 1928, Ralph Hartley observed

1638-430: The voltaic pile , possibly the first chemical battery . A simple analogy for an electric circuit is water flowing in a closed circuit of pipework , driven by a mechanical pump . This can be called a "water circuit". The potential difference between two points corresponds to the pressure difference between two points. If the pump creates a pressure difference between two points, then water flowing from one point to

1701-409: 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

1764-407: The 1950s and 1960s, these methods were largely supplanted by magnetic storage devices such as magnetic-core memory , magnetic tapes , drums , and disks , where 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

1827-418: 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 , 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

1890-424: 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

1953-399: The build-up of electric charge (e.g., a capacitor ), and from an electromotive force (e.g., electromagnetic induction in a generator ). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect , and the thermoelectric effect . Since it is the difference in electric potential, it is

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2016-414: The capacities of computer memories and some storage units are often multiples of some large power of two, such as 2  = 268 435 456 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 2  = 1024, mega for 2  = 1 048 576 , and giga for 2  = 1 073 741 824 , and so on. For example,

2079-564: 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 b 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 log 2 8 = 3 bits of information. Other units that have been named include: The trit, ban, and nat are rarely used to measure storage capacity; but

2142-413: The circuit are not negligible, then their effects can be modelled by adding mutual inductance elements. In the case of a physical inductor though, the ideal lumped representation is often accurate. This is because the external fields of inductors are generally negligible, especially if the inductor has a closed magnetic path . If external fields are negligible, we find that is path-independent, and there

2205-862: 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 32 bits, but other past and current architectures use words with 4, 8, 9, 12, 13, 16, 18, 20, 21, 22, 24, 25, 29, 30, 31, 32, 33, 35, 36, 38, 39, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 72 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

2268-636: The computer's main storage into even larger units, traditionally called pages . Terms for large quantities of bits can be formed using the standard range of SI prefixes for powers of 10, e.g., kilo  = 10  = 1000 (as in kilobit or kbit), mega  = 10  = 1 000 000 (as in megabit or Mbit) and giga  = 10 = 1 000 000 000 (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 = 8 000 000 bit ), and gigabyte (1 GB = 8 000 000 000 bit ). However, for technical reasons,

2331-668: The confusion by providing alternative notations for power-of-two multiples. The International Electrotechnical Commission (IEC) issued a standard for this purpose by defining a series of binary prefixes that use 1024 instead of 1000 as the main radix: The JEDEC memory standard JESD88F notes that the definitions of kilo (K), giga (G), and mega (M) based on powers of two are included only to reflect common usage, but are otherwise deprecated. Several other units of information storage have been named: Some of these names are jargon , obsolete, or used only in very restricted contexts. Voltage The voltage between points can be caused by

2394-431: The device with respect to a common reference point (or ground ). The voltage drop is the difference between the two readings. Two points in an electric circuit that are connected by an ideal conductor without resistance and not within a changing magnetic field have a voltage of zero. Any two points with the same potential may be connected by a conductor and no current will flow between them. The voltage between A and C

2457-413: 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

2520-446: The electric field in the region exterior to each component is conservative, and voltages between nodes in the circuit are well-defined, where as long as the path of integration does not pass through the inside of any component. The above is the same formula used in electrostatics. This integral, with the path of integration being along the test leads, is what a voltmeter will actually measure. If uncontained magnetic fields throughout

2583-428: The electric field, rather than to differences in electric potential. In this case, the voltage rise along some path P {\displaystyle {\mathcal {P}}} from r A {\displaystyle \mathbf {r} _{A}} to r B {\displaystyle \mathbf {r} _{B}} is given by: However, in this case the "voltage" between two points depends on

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2646-409: 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

2709-649: The nat, in particular, is often used in information theory, because natural logarithms are mathematically more convenient than logarithms in other bases. Several conventional names are used for collections or groups of bits. 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 . An 8-bit byte can represent 256 (2 ) 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

2772-407: The other will be able to do work, such as driving a turbine . Similarly, work can be done by an electric current driven by the potential difference provided by a battery . For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile's starter motor . If the pump is not working, it produces no pressure difference, and

2835-473: 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 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

2898-424: The path taken. In circuit analysis and electrical engineering , lumped element models are used to represent and analyze circuits. These elements are idealized and self-contained circuit elements used to model physical components. When using a lumped element model, it is assumed that the effects of changing magnetic fields produced by the circuit are suitably contained to each element. Under these assumptions,

2961-697: The phrase " high tension " (HT) which is commonly used in thermionic valve ( vacuum tube ) based and automotive electronics. In electrostatics , the voltage increase from point r A {\displaystyle \mathbf {r} _{A}} to some point r B {\displaystyle \mathbf {r} _{B}} is given by the change in electrostatic potential V {\textstyle V} from r A {\displaystyle \mathbf {r} _{A}} to r B {\displaystyle \mathbf {r} _{B}} . By definition, this is: where E {\displaystyle \mathbf {E} }

3024-443: 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

3087-430: The points across which the voltage is measured. When using a voltmeter to measure voltage, one electrical lead of the voltmeter must be connected to the first point, one to the second point. A common use of the term "voltage" is in describing the voltage dropped across an electrical device (such as a resistor). The voltage drop across the device can be understood as the difference between measurements at each terminal of

3150-414: The presence of time-varying fields. However, unlike in electrostatics, the electric field can no longer be expressed only in terms of the electric potential. Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of gauge . In this general case, some authors use the word "voltage" to refer to the line integral of

3213-415: The same frequency and phase. Instruments for measuring voltages include the voltmeter , the potentiometer , and the oscilloscope . Analog voltmeters , such as moving-coil instruments, work by measuring the current through a fixed resistor, which, according to Ohm's law , is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in

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3276-420: 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

3339-415: The states of electrical relays which could be either "open" or "closed". When relays were replaced by vacuum tubes , starting in 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

3402-465: The symbol U is standardized. It is used, for instance, in the context of Ohm's or Kirchhoff's circuit laws . The electrochemical potential is the voltage that can be directly measured with a voltmeter. The Galvani potential that exists in structures with junctions of dissimilar materials is also work per charge but cannot be measured with a voltmeter in the external circuit (see § Galvani potential vs. electrochemical potential ). Voltage

3465-553: 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 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

3528-502: The symbol for byte ( IEC 80000-13 uses "o" for octet in French, but also allows "B" in English). 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. A group of four bits, or half

3591-401: The turbine will not rotate. Likewise, if the automobile's battery is very weak or "dead" (or "flat"), then it will not turn the starter motor. The hydraulic analogy is a useful way of understanding many electrical concepts. In such a system, the work done to move water is equal to the " pressure drop" (compare p.d.) multiplied by the volume of water moved. Similarly, in an electrical circuit,

3654-556: 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

3717-507: 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 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

3780-465: The work done to move electrons or other charge carriers is equal to "electrical pressure difference" multiplied by the quantity of electrical charges moved. In relation to "flow", the larger the "pressure difference" between two points (potential difference or water pressure difference), the greater the flow between them (electric current or water flow). (See " electric power ".) Specifying a voltage measurement requires explicit or implicit specification of

3843-570: 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 a Bell Labs memo on 9 January 1947 in which he contracted "binary information digit" to simply "bit". A bit can be stored by

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3906-612: Was first used by Volta in a letter to Giovanni Aldini in 1798, and first appeared in a published paper in 1801 in Annales de chimie et de physique . Volta meant by this a force that was not an electrostatic force, specifically, an electrochemical force. The term was taken up by Michael Faraday in connection with electromagnetic induction in the 1820s. However, a clear definition of voltage and method of measuring it had not been developed at this time. Volta distinguished electromotive force (emf) from tension (potential difference):

3969-541: 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

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