1.
Decimal
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This article aims to be an accessible introduction. For the mathematical definition, see Decimal representation, the decimal numeral system has ten as its base, which, in decimal, is written 10, as is the base in every positional numeral system. It is the base most widely used by modern civilizations. Decimal fractions have terminating decimal representations and other fractions have repeating decimal representations, Decimal notation is the writing of numbers in a base-ten numeral system. Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, Roman numerals have symbols for the decimal powers and secondary symbols for half these values. Brahmi numerals have symbols for the nine numbers 1–9, the nine decades 10–90, plus a symbol for 100, Chinese numerals have symbols for 1–9, and additional symbols for powers of ten, which in modern usage reach 1072. Positional decimal systems include a zero and use symbols for the ten values to represent any number, positional notation uses positions for each power of ten, units, tens, hundreds, thousands, etc. The position of each digit within a number denotes the multiplier multiplied with that position has a value ten times that of the position to its right. There were at least two independent sources of positional decimal systems in ancient civilization, the Chinese counting rod system. Ten is the number which is the count of fingers and thumbs on both hands, the English word digit as well as its translation in many languages is also the anatomical term for fingers and toes. In English, decimal means tenth, decimate means reduce by a tenth, however, the symbols used in different areas are not identical, for instance, Western Arabic numerals differ from the forms used by other Arab cultures. A decimal fraction is a fraction the denominator of which is a power of ten. g, Decimal fractions 8/10, 1489/100, 24/100000, and 58900/10000 are expressed in decimal notation as 0.8,14.89,0.00024,5.8900 respectively. In English-speaking, some Latin American and many Asian countries, a period or raised period is used as the separator, in many other countries, particularly in Europe. The integer part, or integral part of a number is the part to the left of the decimal separator. The part from the separator to the right is the fractional part. It is usual for a number that consists only of a fractional part to have a leading zero in its notation. Any rational number with a denominator whose only prime factors are 2 and/or 5 may be expressed as a decimal fraction and has a finite decimal expansion. 1/2 =0.5 1/20 =0.05 1/5 =0.2 1/50 =0.02 1/4 =0.25 1/40 =0.025 1/25 =0.04 1/8 =0.125 1/125 =0.008 1/10 =0
2.
Metric prefix
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A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand, the prefix milli-, likewise, may be added to metre to indicate division by one thousand, one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the system with six dating back to the systems introduction in the 1790s. Metric prefixes have even been prepended to non-metric units, the SI prefixes are standardized for use in the International System of Units by the International Bureau of Weights and Measures in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities, the BIPM specifies twenty prefixes for the International System of Units. Each prefix name has a symbol which is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are the SI symbols for kilometre, kilogram, prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm or 10 dam, the prefixes hecto, deca, deci, and centi are commonly used for everyday purposes, and the centimetre is especially common. However, some building codes require that the millimetre be used in preference to the centimetre, because use of centimetres leads to extensive usage of decimal points. Prefixes may not be used in combination and this also applies to mass, for which the SI base unit already contains a prefix. For example, milligram is used instead of microkilogram, in the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier,1 km2 means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres. 2 Mm3 means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×1018 m3, and not 2000000 cubic metres, examples 5 cm = 5×10−2 m =5 ×0.01 m =0. The prefixes, including those introduced after 1960, are used with any metric unit, metric prefixes may also be used with non-metric units. The choice of prefixes with a unit is usually dictated by convenience of use. Unit prefixes for amounts that are larger or smaller than those actually encountered are seldom used
3.
Megabyte
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The megabyte is a multiple of the unit byte for digital information. Its recommended unit symbol is MB, but sometimes MByte is used, the unit prefix mega is a multiplier of 1000000 in the International System of Units. Therefore, one megabyte is one million bytes of information and this definition has been incorporated into the International System of Quantities. However, in the computer and information fields, several other definitions are used that arose for historical reasons of convenience. A common usage has been to one megabyte as 1048576bytes. However, most standards bodies have deprecated this usage in favor of a set of binary prefixes, less common is a convention that used the megabyte to mean 1000×1024 bytes. The megabyte is commonly used to measure either 10002 bytes or 10242 bytes, the interpretation of using base 1024 originated as a compromise technical jargon for the byte multiples that needed to be expressed by the powers of 2 but lacked a convenient name. As 1024 approximates 1000, roughly corresponding to the SI prefix kilo-, in 1998 the International Electrotechnical Commission proposed standards for binary prefixes requiring the use of megabyte to strictly denote 10002 bytes and mebibyte to denote 10242 bytes. By the end of 2009, the IEC Standard had been adopted by the IEEE, EU, ISO, the Mac OS X10.6 file manager is a notable example of this usage in software. Since Snow Leopard, file sizes are reported in decimal units, base 21 MB =1048576 bytes is the definition used by Microsoft Windows in reference to computer memory, such as RAM. This definition is synonymous with the binary prefix mebibyte. Mixed 1 MB =1024000 bytes is the used to describe the formatted capacity of the 1.44 MB3. 5inch HD floppy disk. Semiconductor memory doubles in size for each address lane added to an integrated circuit package, the capacity of a disk drive is the product of the sector size, number of sectors per track, number of tracks per side, and the number of disk platters in the drive. Changes in any of these factors would not usually double the size, sector sizes were set as powers of two for convenience in processing. It was an extension to give the capacity of a disk drive in multiples of the sector size, giving a mix of decimal. Depending on compression methods and file format, a megabyte of data can roughly be, a 4 megapixel JPEG image with normal compression. Approximately 1 minute of 128 kbit/s MP3 compressed music,6 seconds of uncompressed CD audio. A typical English book volume in plain text format, the human genome consists of DNA representing 800 MB of data
4.
Gigabyte
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The gigabyte is a multiple of the unit byte for digital information. The prefix giga means 109 in the International System of Units, the unit symbol for the gigabyte is GB. However, the term is used in some fields of computer science and information technology to denote 1073741824 bytes. The use of gigabyte may thus be ambiguous, to address this ambiguity, the International System of Quantities standardizes the binary prefixes which denote a series of integer powers of 1024. With these prefixes, a module that is labeled as having the size 1GB has one gibibyte of storage capacity. The term gigabyte is commonly used to mean either 10003 bytes or 10243 bytes, the latter binary usage originated as compromise technical jargon for byte multiples that needed to be expressed in a power of 2, but lacked a convenient name. As 1024 is approximately 1000, roughly corresponding to SI multiples, in 1998 the International Electrotechnical Commission published standards for binary prefixes, requiring that the gigabyte strictly denote 10003 bytes and gibibyte denote 10243 bytes. By the end of 2007, the IEC Standard had been adopted by the IEEE, EU, and NIST and this is the recommended definition by the International Electrotechnical Commission. The file manager of Mac OS X version 10.6 and later versions are an example of this usage in software. The binary definition uses powers of the base 2, as is the principle of binary computers. This usage is widely promulgated by some operating systems, such as Microsoft Windows in reference to computer memory and this definition is synonymous with the unambiguous unit gibibyte. Since the first disk drive, the IBM350, disk drive manufacturers expressed hard drive capacities using decimal prefixes, with the advent of gigabyte-range drive capacities, manufacturers based most consumer hard drive capacities in certain size classes expressed in decimal gigabytes, such as 500 GB. The exact capacity of a given model is usually slightly larger than the class designation. Practically all manufacturers of disk drives and flash-memory disk devices continue to define one gigabyte as 1000000000bytes. Some operating systems such as OS X express hard drive capacity or file size using decimal multipliers and this discrepancy causes confusion, as a disk with an advertised capacity of, for example,400 GB might be reported by the operating system as 372 GB, meaning 372 GiB. The JEDEC memory standards use IEEE100 nomenclature which quote the gigabyte as 1073741824bytes and this means that a 300 GB hard disk might be indicated variously as 300 GB,279 GB or 279 GiB, depending on the operating system. As storage sizes increase and larger units are used, these differences even more pronounced. Some legal challenges have been waged over this confusion such as a lawsuit against drive manufacturer Western Digital, Western Digital settled the challenge and added explicit disclaimers to products that the usable capacity may differ from the advertised capacity
5.
Binary prefix
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A binary prefix is a unit prefix for multiples of units in data processing, data transmission, and digital information, notably the bit and the byte, to indicate multiplication by a power of 2. The computer industry has used the units kilobyte, megabyte, and gigabyte, and the corresponding symbols KB, MB. In citations of main memory capacity, gigabyte customarily means 1073741824 bytes, as this is the third power of 1024, and 1024 is a power of two, this usage is referred to as a binary measurement. In most other contexts, the uses the multipliers kilo, mega, giga, etc. in a manner consistent with their meaning in the International System of Units. For example, a 500 gigabyte hard disk holds 500000000000 bytes, in contrast with the binary prefix usage, this use is described as a decimal prefix, as 1000 is a power of 10. The use of the same unit prefixes with two different meanings has caused confusion, in 2008, the IEC prefixes were incorporated into the ISO/IEC80000 standard. Early computers used one of two addressing methods to access the memory, binary or decimal. For example, the IBM701 used binary and could address 2048 words of 36 bits each, while the IBM702 used decimal, by the mid-1960s, binary addressing had become the standard architecture in most computer designs, and main memory sizes were most commonly powers of two. Early computer system documentation would specify the size with an exact number such as 4096,8192. These are all powers of two, and furthermore are small multiples of 210, or 1024, as storage capacities increased, several different methods were developed to abbreviate these quantities. The method most commonly used today uses prefixes such as kilo, mega, giga, and corresponding symbols K, M, and G, the prefixes kilo- and mega-, meaning 1000 and 1000000 respectively, were commonly used in the electronics industry before World War II. Along with giga- or G-, meaning 1000000000, they are now known as SI prefixes after the International System of Units, introduced in 1960 to formalize aspects of the metric system. The International System of Units does not define units for digital information and this usage is not consistent with the SI. Compliance with the SI requires that the prefixes take their 1000-based meaning, the use of K in the binary sense as in a 32K core meaning 32 ×1024 words, i. e.32768 words, can be found as early as 1959. Gene Amdahls seminal 1964 article on IBM System/360 used 1K to mean 1024 and this style was used by other computer vendors, the CDC7600 System Description made extensive use of K as 1024. Thus the first binary prefix was born, the exact values 32768 words,65536 words and 131072 words would then be described as 32K, 65K and 131K. This style was used from about 1965 to 1975 and these two styles were used loosely around the same time, sometimes by the same company. In discussions of binary-addressed memories, the size was evident from context
