The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system; the way of denoting numbers in the decimal system is referred to as decimal notation. A decimal numeral, or just decimal, or casually decimal number, refers to the notation of a number in the decimal numeral system. Decimals may sometimes be identified for containing a decimal separator. "Decimal" may refer to the digits after the decimal separator, such as in "3.14 is the approximation of π to two decimals". The numbers that may be represented in the decimal system are the decimal fractions, the fractions of the form a/10n, where a is an integer, n is a non-negative integer; the decimal system has been extended to infinite decimals, for representing any real number, by using an infinite sequence of digits after the decimal separator. In this context, the decimal numerals with a finite number of non–zero places after the decimal separator are sometimes called terminating decimals.
A repeating decimal is an infinite decimal that after some place repeats indefinitely the same sequence of digits. An infinite decimal represents a rational number if and only if it is a repeating decimal or has a finite number of nonzero digits. Many numeral systems of ancient civilisations use ten and its powers for representing numbers because there are ten fingers on two hands and people started counting by using their fingers. Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, Chinese numerals. Large numbers were difficult to represent in these old numeral systems, only the best mathematicians were able to multiply or divide large numbers; these difficulties were solved with the introduction of the Hindu–Arabic numeral system for representing integers. This system has been extended to represent some non-integer numbers, called decimal fractions or decimal numbers for forming the decimal numeral system. For writing numbers, the decimal system uses ten decimal digits, a decimal mark, for negative numbers, a minus sign "−".
The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. For representing a non-negative number, a decimal consists of either a sequence of digits such as 2017, or in full generality, a m a m − 1 … a 0 or two sequence of digits separated by a decimal mark such as 3.14159, 15.00, or in full generality a m a m − 1 … a 0. B 1 b 2 … b n It is assumed that, if m > 0, the first digit am is not zero, but, in some circumstances, it may be useful to have one or more 0's on the left. This does not change the value represented by the decimal. For example, 3.14 = 03.14 = 003.14. If bn =0, it may be removed, conversely, trailing zeros may be added without changing the represented number: for example, 15 = 15.0 = 15.00 and 5.2 = 5.20 = 5.200. Sometimes the extra zeros are used for indicating the accuracy of a measurement. For example, 15.00 m may indicate that the measurement error is less than one centimeter, while 15 m may mean that the length is fifteen meters, that the error may exceed 10 cm. For representing a negative number, a minus sign is placed before am.
The numeral a m a m − 1 … a 0. B 1 b 2 … b n represents the number a m 10 m + a m − 1 10 m − 1 + ⋯ + a 0 10 0 + b 1 10 1 + b 2 10 2 + ⋯ + b n 10 n Therefore, the contribution of each digit to the value of a number depends on its position in the numeral; that is, the decimal system is a positional numeral system The numbers that are represented by decimal numerals are the decimal fractions, that is, the rational numbers that may be expressed as a fraction, the denominator of, a power of ten. For example, the numerals 0.8, 14.89, 0.00024 represent the fractions 8/10, 1489/100, 24/100000. More a decimal with n digits after the separator represents the fraction with denominator 10n, whose numerator is the integer obtained by removing the separator. Expressed as a reduced fraction, the decimal numbers are those whose denominator is a product of a powe
Geʽez known as Ethiopic, is a script used as an abugida for several languages of Eritrea and Ethiopia. It originated as an abjad and was first used to write Geʽez, now the liturgical language of the Eritrean Orthodox Tewahedo Church, the Ethiopian Orthodox Tewahedo Church, Beta Israel, the Jewish community in Ethiopia. In Amharic and Tigrinya, the script is called fidäl, meaning "script" or "alphabet"; the Geʽez script has been adapted to write other Semitic, languages Amharic in Ethiopia, Tigrinya in both Eritrea and Ethiopia. It is used for Sebatbeit, Meʼen, most other languages of Ethiopia. In Eritrea it is used for Tigre, it has traditionally been used for Blin, a Cushitic language. Tigre, spoken in western and northern Eritrea, is considered to resemble Geʽez more than do the other derivative languages; some other languages in the Horn of Africa, such as Oromo, used to be written using Geʽez, but have migrated to Latin-based orthographies. For the representation of sounds, this article uses a system, common among linguists who work on Ethiopian Semitic languages.
This differs somewhat from the conventions of the International Phonetic Alphabet. See the articles on the individual languages for information on the pronunciation; the earliest inscriptions of Semitic languages in Eritrea and Ethiopia date to the 9th century BC in Epigraphic South Arabian, an abjad shared with contemporary kingdoms in South Arabia. After the 7th and 6th centuries BC, variants of the script arose, evolving in the direction of the Geʽez abugida; this evolution can be seen most in evidence from inscriptions in Tigray region in northern Ethiopia and the former province of Akkele Guzay in Eritrea. By the first centuries AD, what is called "Old Ethiopic" or the "Old Geʽez alphabet" arose, an abjad written left-to-right with letters identical to the first-order forms of the modern vocalized alphabet. There were minor differences such as the letter "g" facing to the right, instead of to the left as in vocalized Geʽez, a shorter left leg of "l", as in ESA, instead of equally-long legs in vocalized Geʽez.
Vocalization of Geʽez occurred in the 4th century, though the first vocalized texts known are inscriptions by Ezana, vocalized letters predate him by some years, as an individual vocalized letter exists in a coin of his predecessor Wazeba. Linguist Roger Schneider has pointed out anomalies in the known inscriptions of Ezana that imply that he was consciously employing an archaic style during his reign, indicating that vocalization could have occurred much earlier; as a result, some believe that the vocalization may have been adopted to preserve the pronunciation of Geʽez texts due to the moribund or extinct status of Geʽez, that, by that time, the common language of the people were later Ethio-Semitic languages. At least one of Wazeba's coins from the late 3rd or early 4th century contains a vocalized letter, some 30 or so years before Ezana. Kobishchanov and others have suggested possible influence from the Brahmic family of alphabets in vocalization, as they are abugidas, Aksum was an important part of major trade routes involving India and the Greco-Roman world throughout the common era of antiquity.
According to the beliefs of the Eritrean Orthodox Tewahedo Church and Ethiopian Orthodox Tewahedo Church, the original consonantal form of the Geʽez fidel was divinely revealed to Henos "as an instrument for codifying the laws", the present system of vocalisation is attributed to a team of Aksumite scholars led by Frumentius, the same missionary said to have converted the king Ezana to Christianity in the 4th century AD. It has been argued that the vowel marking pattern of the script reflects a South Asian system, such as would have been known by Frumentius. A separate tradition, recorded by Aleqa Taye, holds that the Geʽez consonantal alphabet was first adapted by Zegdur, a legendary king of the Ag'azyan Sabaean dynasty held to have ruled in Ethiopia c. 1300 BC. Geʽez has 26 consonantal letters. Compared to the inventory of 29 consonants in the South Arabian alphabet, continuants are missing of ġ, ẓ, South Arabian s3, as well as z and ṯ, these last two absences reflecting the collapse of interdental with alveolar fricatives.
On the other hand, emphatic P̣ait ጰ, a Geʽez innovation, is a modification of Ṣädai ጸ, while Pesa ፐ is based on Tawe ተ. Thus, there are 24 correspondences of Geʽez and the South Arabian alphabet: Many of the letter names are cognate with those of Phoenician, may thus be assumed for Proto-Sinaitic. Two alphabets were used to write the Geʽez language, an abjad and an abugida; the abjad, used until c. 330 AD, had 26 consonantal letters: h, l, ḥ, m, ś, r, s, ḳ, b, t, ḫ, n, ʾ, k, w, ʿ, z, y, d, g, ṭ, p̣, ṣ, ṣ́, f, p Vowels were not indicated. Modern Geʽez is written from left to right; the Geʽez abugida developed under the influence of Christian scripture by adding obligatory vocalic diacritics to the consonantal letters. The diacritics for the vowels, u, i, a, e, ə, o, were fused with the consonants in a recognizable but irregular way, so that the system is laid out as a syllabary; the original form of the consonant was used when the vowel was the so-called inherent vowel. The resulting forms are shown below in their traditional order.
For some vowels, there is an eighth form for the diphthong -wa or -oa
The system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000. Two sets of pronunciations for the numerals exist in Japanese: one is based on Sino-Japanese readings of the Chinese characters and the other is based on the Japanese yamato kotoba. There are two ways of writing the numbers in Japanese: in Chinese numerals; the Arabic numerals are more used in horizontal writing, the Chinese numerals are more common in vertical writing. Most numbers have two readings, one derived from Chinese used for cardinal numbers and a native Japanese reading used somewhat less formally for numbers up to 10. In some cases the Japanese reading is preferred for all uses. * The special reading 〇 maru is found. It may be optionally used when reading individual digits of a number one after another, instead of as a full number. A popular example is the famous 109 store in Shibuya, Tokyo, read as ichi-maru-kyū.
This usage of maru for numerical 0 is similar to reading numeral 0 in English as oh. It means a circle. However, as a number, it is only written as rei. Additionally and five are pronounced with a long vowel in phone numbers. Starting at 万, numbers begin with 一; that is, 100 is just 百 hyaku, 1000 is just 千 sen, but 10,000 is 一万 ichiman, not just *man. This differs from Chinese as numbers begin with 一 if no digit would otherwise precede starting at 百. And, if 千 sen directly precedes the name of powers of myriad, 一 ichi is attached before 千 sen, which yields 一千 issen; that is, 10,000,000 is read as 一千万 issenman. But if 千 sen does not directly precede the name of powers of myriad or if numbers are lower than 2,000, attaching 一 ichi is optional; that is, 15,000,000 is read as 千五百万 sengohyakuman or 一千五百万 issengohyakuman, 1,500 as 千五百 sengohyaku or 一千五百 issengohyaku. The numbers 4 and 9 are considered unlucky in Japanese: 4, pronounced shi, is a homophone for death. See tetraphobia; the number 13 is sometimes considered unlucky.
On the contrary, numbers 7 and sometimes 8 are considered lucky in Japanese. In modern Japanese, cardinal numbers are given the on readings except 4 and 7, which are called yon and nana respectively. Alternate readings are used in month names, day-of-month names, fixed phrases. For instance, the decimal fraction 4.79 is always read yon-ten nana kyū, though April and September are called shi-gatsu, shichi-gatsu, ku-gatsu respectively. The on readings are used when shouting out headcounts. Intermediate numbers are made by combining these elements: Tens from 20 to 90 are "-jū" as in 二十 to 九十. Hundreds from 200 to 900 are "-hyaku". Thousands from 2000 to 9000 are "-sen". There are some phonetic modifications to larger numbers involving voicing or gemination of certain consonants, as occurs in Japanese: e.g. roku "six" and hyaku "hundred" yield roppyaku "six hundred". * This applies to multiples of 10. Change ending -jū to -jutchō or -jukkei. ** This applies to multiples of 100. Change ending -ku to -kkei.
In large numbers, elements are combined from largest to smallest, zeros are implied. Beyond the basic cardinals and ordinals, Japanese has other types of numerals. Distributive numbers are formed from a cardinal number, a counter word, the suffix -zutsu, as in hitori-zutsu. Following Chinese tradition, large numbers are created by grouping digits in myriads rather than the Western thousands: Variation is due to Jinkōki, Japan's oldest mathematics text; the initial edition was published in 1627. It had many errors. Most of these were fixed in the 1631 edition. In 1634 there was yet another edition; the above variation is due to inconsistencies in the latter two editions. Examples: 1 0000: 一万 983 6703: 九百八十三万 六千七百三 20 3652 1801: 二十億 三千六百五十二万 千八百一 However, numbers written in Arabic numerals are separated by commas every three digits following English-speaking convention. If Arabic numbers and kanji are used in combination, Western orders of magnitude may be used for numbers smaller than 10,000. In Japanese, when long numbers are written out in kanji, zeros are omitted for all powers of ten.
Hence 4002 is 四千二. However, when reading out a statement of accounts, for example, the skipped digit or digits are sometimes indicated by tobi or tonde: e.g. yon-sen tobi ni or yon-sen tonde ni instead of the normal yon-sen ni. Japanese has two systems of numerals for decimal fractions, they are no longer in general use, but are still used in some instances such as batting and fielding averages of baseball players, winning percentages for sports teams, in some idiomatic phrases, when repr
Mongolian numerals are numerals developed from Tibetan numerals and used in conjunction with the Mongolian and Clear script. They are still used on Mongolian tögrög banknotes; the main sources of reference for Mongolian numerals are mathematical and philosophical works of Janj khutugtu A. Rolbiidorj and D. Injinaash. Rolbiidorj exercises with numerals of up to 1066, the last number which he called “setgeshgui” or “unimaginable” referring to the concept of infinity. Injinaash works with numerals of up to 1059. Of these two scholars, the Rolbiidorj’s numerals, their names and sequencing are accepted and used today, for example, in the calculations and documents pertaining to the Mongolian Government budget. Numbers from 1 to 9 are referred to as "dan", meaning "simple"
Sinhala belongs to the Indo-European language family with its roots associated with Indo-Aryan sub family to which the languages such as Persian and Hindi belong. Although it is not clear whether people in Sri Lanka spoke a dialect of Prakrit at the time of arrival of Buddhism in Sri Lanka, there is enough evidence that Sinhala evolved from mixing of Sanskrit and local language, spoken by people of Sri Lanka prior to the arrival of Vijaya in Sri Lanka, the founder of Sinhala Kingdom, it is surmised that Sinhala had evolved from an ancient variant of Apabramsa, known as ‘Elu’. When tracing history of Elu, it was preceded by Pali Sihala. Sinhala though has close relationships with Indo Aryan languages which are spoken in the north, north eastern and central India, was much influenced by Dravidian language families of Hindi. Though Sinhala is related to Indic languages, it has its own unique characteristics: Sinhala has symbols for two vowels which are not found in any other Indic languages in India: ‘æ’ and ‘æ:’.
The Sinhala script had evolved from Southern Brahmi script from which all the Southern Indic Scripts such as Telugu and Oriya had evolved. Sinhala was influenced by Grantha writing of Southern India. Since 1250 AD, the Sinhala script had remained the same with few changes. Although some scholars are of the view that the Brahmi Script arrived with the Buddhism, Mahavamsa speaks of written language right after the arrival of Vijaya. Archeologists had found pottery fragments in Anuradhapura Sri Lanka with older Brahmi script inscriptions, carbon dated to 5th century BC; the earliest Brahmi Script found in India had been dated to 6th Century BC in Tamil Nadu though most of Brahmi writing found in India had been attributed to emperor Ashoka in the 3rd century BC. Sinhala letters are round-shaped and are written from left to right and they are the most circular-shaped script found in the Indic scripts; the evolution of the script to the present shapes may have taken place due to writing on Ola leaves.
Unlike chiseling on a rock, writing on palm leaves has to be more round-shaped to avoid the stylus ripping the Palm leaf while writing on it. When drawing vertical or horizontal straight lines on Ola leaf, the leaves would have been ripped and this may have influenced Sinhala not to have a period or full stop. Instead a stylistic stop, known as ‘Kundaliya’ is used. Period and commas were introduced into Sinhala script after the introduction of paper due to the influence of Western languages. Although various scholars had mentioned about numerations in the Sinhala language in their writing on Sinhala language, a systematic study had not been conducted up to now on numerals and numerations found in Sinhala right before British occupation of Kandy. In modern Sinhala, Arabic numerals, which were introduced by Portuguese and English, is used for writing numbers and carrying out calculations. Roman numerals are used for writing dates and for listing items or words in Sinhala though at present, Roman numerals are not used and they were introduced by Westerners who invaded Sri Lanka.
It is accepted. It had been discovered by Sri Lankan archeologists that Brahmi numerals were used in the ancient Sri Lanka and it may have evolved into two sets of numerals which were known as archaic Sinhala numerals and Lith Illakkum which were found in the Kandyan period; this paper covers numerals and numerations in Sri Lanka at the time of British occupation of the Kandyan Kingdom and their evolution to the forms which were found in 1815, the year the British occupied the whole of Sri Lanka. This article will touch upon Brahmi numerals, which were found in Sri Lanka, it had been found that five different types of numerations were used in the Sinhala language at the time of the invasion of the Kandyan kingdom by the British. Out of the five types of numerations, two sets of numerations were in use in the twentieth century for astrological calculations and to express traditional year and dates in ephemeri des; the five types or sets of numerals or numerations are listed below. Abraham Mendis Gunasekera, in A Comprehensive Grammar of Sinhalese Language, described a set of archaic numerals which were no longer in use.
According to Mr. Gunesekera, these numerals were used for ordinary calculations and to express simple numbers. Gunasekera wrote: The Sinhalase had symbols of its own to represent the different numerals which were in use until the beginning of the present century. Arabic Figures are now universally used. For the benefit of the student, the old numerals are given in the plate opposite. Sinhala numerals did not have a zero and they did not have zero concept holder, they included separate symbols for 10, 40, 50, 100, 1000. These numerals were regarded as Lith Lakunu or ephemeris numbers by W. A. De Silva in his Catalogue of Palm leaf manuscripts in the library of Colombo Museum; this set of numerals was known as Sinhala Sinhala archaic numerals. Sinhala numerals or Sinhala illakkam were used in the Kandyan convention, signed between Kandyan Chieftains and the British governor, Robert Brownrig, in 1815. Eleven clauses were numbered in Arabic numerals in the English part of the agreement, the parallel Sinhala clauses were numbered in Sinhala archaic numerals.
Although this numeral set was used for casting horoscopes and to carry out astrological calculations, it had been found that this set had been used for numbering pages of Ola palm leaf books which covered of none Buddhist topics in
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal positional numeral system; the numerals are made up of three symbols. For example, thirteen is written as three dots in a horizontal row above two horizontal bars. With these three symbols each of the twenty vigesimal digits could be written. Numbers after 19 were written vertically in powers of twenty; the Mayan used powers of twenty, just as the Hindu–Arabic numeral system uses powers of tens. For example, thirty-three would be written as one dot, above three dots atop two bars; the first dot represents "one twenty" or "1×20", added to three dots and two bars, or thirteen. Therefore, + 13 = 33. Upon reaching 202 or 400, another row is started; the number 429 would be written as one dot above one dot above four dots and a bar, or + + 9 = 429. Other than the bar and dot notation, Maya numerals were sometimes illustrated by face type glyphs or pictures; the face glyph for a number represents the deity associated with the number.
These face number glyphs were used, are seen on some of the most elaborate monumental carving. Adding and subtracting numbers below 20 using Maya numerals is simple. Addition is performed by combining the numeric symbols at each level: If five or more dots result from the combination, five dots are removed and replaced by a bar. If four or more bars result, four bars are removed and a dot is added to the next higher row. With subtraction, remove the elements of the subtrahend symbol from the minuend symbol: If there are not enough dots in a minuend position, a bar is replaced by five dots. If there are not enough bars, a dot is removed from the next higher minuend symbol in the column and four bars are added to the minuend symbol, being worked on; the "Long Count" portion of the Maya calendar uses a variation on the vigesimal numbering. In the second position, only the digits up to 17 are used, the place value of the third position is not 20×20 = 400, as would otherwise be expected, but 18×20 = 360, so that one dot over two zeros signifies 360.
This is because 360 is the number of days in a year. Subsequent positions use all twenty digits and the place values continue as 18×20×20 = 7,200 and 18×20×20×20 = 144,000, etc; every known example of large numbers in the Maya system uses this'modified vigesimal' system, with the third position representing multiples of 18×20. It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system. Several Mesoamerican cultures used similar numerals and base-twenty systems and the Mesoamerican Long Count calendar requiring the use of zero as a place-holder; the earliest long count date is from 36 BC. Since the eight earliest Long Count dates appear outside the Maya homeland, it is assumed that the use of zero and the Long Count calendar predated the Maya, was the invention of the Olmec. Indeed, many of the earliest Long Count dates were found within the Olmec heartland. However, the Olmec civilization had come to an end by the 4th century BC, several centuries before the earliest known Long Count dates—which suggests that zero was not an Olmec discovery.
Mayan numerals were added to the Unicode Standard in June, 2018 with the release of version 11.0. The Unicode block for Mayan Numerals is U+1D2E0–U+1D2FF: Maya Mathematics - online converter from decimal numeration to Maya numeral notation. Anthropomorphic Maya numbers - online story of number representations. BabelStone Mayan Numerals - free font for Unicode Mayan numeral characters
In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most the symbols "0"–"9" to represent values zero to nine, "A"–"F" to represent values ten to fifteen. Hexadecimal numerals are used by computer system designers and programmers, as they provide a more human-friendly representation of binary-coded values; each hexadecimal digit represents four binary digits known as a nibble, half a byte. For example, a single byte can have values ranging from 0000 0000 to 1111 1111 in binary form, which can be more conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is used to specify the radix. For example the decimal value 10,995 would be expressed in hexadecimal as 2AF316. In programming, a number of notations are used to support hexadecimal representation involving a prefix or suffix; the prefix 0x is used in C and related languages, which would denote this value by 0x2AF3. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits.
In contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously. A numerical subscript can give the base explicitly: 15910 is decimal 159; some authors prefer a text subscript, such as 159decimal and 159hex, or 159h. In linear text systems, such as those used in most computer programming environments, a variety of methods have arisen: In URIs, character codes are written as hexadecimal pairs prefixed with %: http://www.example.com/name%20with%20spaces where %20 is the space character, ASCII code point 20 in hex, 32 in decimal. In XML and XHTML, characters can be expressed as hexadecimal numeric character references using the notation
ode, thus ’. In the Unicode standard, a character value is represented with U+ followed by the hex value, e.g. U+20AC is the Euro sign. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #: white, for example, is represented #FFFFFF.
CSS allows 3-hexdigit abbreviations with one hexdigit per component: #FA3 abbreviates #FFAA33. Unix shells, AT&T assembly language and the C programming language use the prefix 0x for numeric constants represented in hex: 0x5A3. Character and string constants may express character codes in hexadecimal with the prefix \x followed by two hex digits:'\x1B' represents the Esc control character. To output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In MIME quoted-printable encoding, characters that cannot be represented as literal ASCII characters are represented by their codes as two hexadecimal digits prefixed by an equal to sign =, as in Espa=F1a to send "España". In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h: FFh or 05A3H; some implementations require a leading zero when the first hexadecimal digit character is not a decimal digit, so one would write 0FFh instead of FFh Other assembly languages, Delphi, some versions of BASIC, GameMaker Language and Forth use $ as a prefix: $5A3.
Some assembly languages use the notation H'ABCD'. Fortran 95 uses Z'ABCD'. Ada and VHDL enclose hexadecimal numerals in based "numeric quotes": 16#5A3#. For bit vector constants VHDL uses the notation x"5A3". Verilog represents hexadecimal constants in the form 8'hFF, where 8 is the number of bits in the value and FF is the hexadecimal constant; the Smalltalk language uses the prefix 16r: 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#: 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs: AA213FD51B3801043FBC... Common Lisp uses the prefixes # 16r. Setting the variables *read-base* and *print-base* to 16 can be used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers, thus Hexadecimal numbers can be represented without the #x or #16r prefix code, when the input or output base has been changed to 16. MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H: &H5A3 BBC BASIC and Locomotive BASIC use & for hex.
TI-89 and 92 series uses a 0h prefix: 0h5A3 ALGOL 68 uses the prefix 16r to denote hexadecimal numbers: 16r5a3. Binary and octal numbers can be specified similarly; the most common format for hexadecimal on IBM mainframes and midrange computers running the traditional OS's is X'5A3', is used in Assembler, PL/I, COBOL, JCL, scripts and other places. This format was common on