DOCSLIB.ORG

Berber Numerals

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Berber Numerals 57 BERBER NUMERALS §1. Classification In recent years the most detailed classifications of Berber languages have been presented by Ajxenval'd (1987), using a structural-typological approach, and by Militarev (see Ajxenval'd & Militarev 1991: 157-59) working with lexicostatistics. Their results are as follows: 1. East Berber branch Siwa (oasis Siwa in West Egypt), Zurg (oasis Kufra in East Libya), Fezzan (oases Tmessa and El Fodjaha in South Libya), Augila (oasis Djalo in North- East Libya), Sokna (North Libya), Ghadames (oasis Ghadames in West Libya). 2. South Berber (= Tuareg) branch North group: Tuareg of the oasis Kufra, Tuareg of the oasis Ghadames, Imanghassaten, Uraghen, Ghat, Ahnet (Plateau Muydir); "Tamahaq": Em- midir, Taitoq, Aizer (Plateau Tassili), Ahaggar; Ayr (Plateau Ayr, Kel Ui, Kel Fenian, Kel Tafidet, Ibabidayan etc.), Tuareg of Borku (Chad), Tuareg of Zinder (Niger), East Tawllemmet (= Iulimidden or Awlemidden; Niger-Mali- Burkina bordeland). South group: Kel Arokas; "Tamaseq": Heyawa, West Tawllemmet, Takarangat, Tagdhaq (= Ifoghas; Plateau Adrar), Taneslemt; "Tamazeq": Ida u Sak (= Dausak), Ighauilen, Imaioghen (= Iguhadaren). 3. West Berber group Zenaga (= Taddungiyah; Mauretania — Senegal). 4. North Berber group 4.1 Atlas group: a) TaSelhait (= Silha): Tinduft, Ait Umbribed (basin of Dra and Djebel Bani); Izemdaln, Imeizad, Ida u Zikri, Ait Isaffen, Amanus, Ait Mzal, Igliwa, Ait Wazgit etc. (Antiatlas); Tazerwalt, Ait Baamrani, Hawwara, Ida u Semlal, AStuken, Masst, Tiguga, Seksawa, Ait Wadjes, Ida u Izimmer, Demsira, Ida u Geriun, Demsira (basin of the river Sus); Tuggana, Igedmiun, Ait Immur, Iha- han, Imeghran, Ida u Tanan, Ida u Zikki, Ida u Zal, Ntifa (High Atlas); b) Tamazight (= Beraber): Ait Messad (region of Demnat); Ait Izdeg, Ait Yahya, Ait Sliman, Ait KhebbaS, etc. (upper river Dades, High Atlas); Ait Sadden, Ait Yusi, Izayan, Ait Sgugu, Ait Mgild, etc. (Middle Atlas); Ait Ndir, Ait Naaman (region of Meknes); 4.2. Zenatiya group: a) "compact": Ait SeghruSen; Ghmara, Zbala (region of Tanger-Tetuan); Rif: Ait Uriaghel, Ibokkoyen, Ait Tuzin, Temsaman, Ikrayen, Ait Said, Ait 58 Ittift etc.; Bettiwa; Senhaza; Ait Warain; Beni Iznasen; Beni Snus, Beni bu Said (region of Tlemsen); Matmata, Harawa, ASaSa, Halima, Beni Rased, Beni Ferah, Gheraba etc. (region Frenda-Warsenis); Beni Menaser; Senua; Beni Salah, Beni Messaud, Beni Misra (region of the mountain Blida); Sawiya (= TaSawit); East Zenatiyan: Sened, Tmagurt (region Gafsa in Tunis), Djerba (island Djerba); Zrawa, Tauizut, Tamezret, Snini, Dwiret (South-East Tunis), Zwara; b) "of oases": Nefusa (Djebel Nefusa, North-West Libya); Righ (Tuggurt), Wargla Mzab (all in East Algeria); Figig (South-East Morocco); Tamentit, Tittaf (Twat); Tit (Tidikelt); Ksurs (Gurara — all the oases are in Central Al­ geria); 4.3. Kabyle (= Taqbaylit) group: At-Halfun, At-Yiratena, "Zuawa", Irzen, At-Hi§ema, At-Mangellat etc. (North Algeria). §2. Data Table 1: Proto-Berber and South Berber Proto-Berber Tawllemmet Tahaggart Taitoq Kel-Ui Ghat Prasse 1974 Alojaly 1980 Prasse 1974 Masqueray 1893 RB 1883 RB 1883 m. (It.) m./f. m./f. m./f. m. m. 1 *yTwSn ayyin/ayyit iyan/iyat yen /yet Ian ran 2 *sTn / *sinSt f. s&natit f. sanit(St) sen / senatet sin *hissTn m. sshin m. assin issin 3 *karad kZnuj/St kirad/kSridat kendh karadh karadh 4 *hakkQz 3kkoz/-St dkkoz/okkdzat okkoz okkoz sekkuz ! 5 *sammQs sammosZ-it sammus / samm&sat semmus f-et sammus sommus 6 *sadTs sodis Ait sadis / sadisat sadhis /-et sadis sadis 7 *sih (sahJ-at RB) sa *hissBh 3ssa/-y&t assa/ass&hit essa/essahet essi 8 *tSm (taman/-et RB) ettam /-et ettam tarn *hittSm attain/St attim / attamat 9 *tiz(z)ih tSza/-yit tazza /tazzahat tezza / tezzahet tezza teza 10 *marSw m&raw/St maraw / marawit maraw / merawet maraw meraw 20 s6mt(6t) sanit senatet essin senat tamarwen tamarwin temerawin maraw merawin 100 *te-mihday tented temede timidhi timad hi timedi (pl.) *ff-muhSd timad timad timadh 1000 *§-giHm agim adjim ajim RB = Rend Basset 59 Table 2: East Berber West Berber Ghadames Ghadames Zenaga Zenaga Lanfry 1973 Motylinski 1904 Basset 1909 Nicolas 1953 m./f. m./f. m./f. m./f. 1 yuun lyuut iun/iut iun & ni-iun / dual m. (9y)yu'nh, n9yu'nh f. £-uw9t 2 san / sonet sen / sinnet Sinan 1Senaneth $9n9nh 1 £a-ten9nh 3 kaared / kerdet karedh / karet karad / karadeth kSrSd." 1 karifel 4 aqquz/ aqqtfzet akkiz /akkizet akoz akkuf 1 akku&l 5 sammas / ssmmasst semmis SonvnuS / iomuSeth Sammui 1 SamnwSai 6 suzl sudset foz/fotset iodei1lodelet iudpi1 Sodetet 7 saa/saat sa/sat iSSa/USadet 3$teh 1 eSSB'dat 8 taam / taamet tarn ittem itt3mh 1 ittSmaL 9 asyy 1tesyyt tegu/teput tuza tu$h 1 tudfiat 10 marawImaraawet meraw /merawt merig 1 meregeth mar3gh, pi. ftnarm* 20 teSinde tallsndsh 30 tukarda tukarda 100 timadi, pi. temadan tamSdih, pi. tmuda'nh Table 3: North Berber Taselhait of Taselhait Taselhait of TaSelhait of Tamazight of Beni Mzab Tazerwalt Aspinion 1953 Semlal Sus ('Amiln) Demnat Hanoteau Stum me 1899 after Penchoen Woelfel 1954 Klingenheben Woelfel 1954 1860 m./f. m./f. m./f. m. m./f. m./f. 1 yinlyat yanlyat yan /ySt yi/i yan lyat iggen/igget 2 sin 1 snat sin/ snat sin/snat sin sinlsenat sen Isenet 3 krid/kritt knd/kntt kiadlkiatt karit kradh iaredftaret 4. kizl-t kkuz/kkust qquflqqust kds akkozl-t okkoz l-t 5 summits l-t ssmmus /-t ssmmQs l-t sipmiis s(em)mus 1 semmustsemmes l-t 6 sddis l-t sdisl-t sdisl-t sddfi s(ad)dis / saddist sez Isesset 7 ssS/-t sa/-t salsSt sa? sal-t saa l-t 8 lam At ttam/-t t(t)am/tamt sSm ! tanutem / tamtjtmunttarn l-et 9 m*/-t ttzal-t tzal-t dwuz dzal-t tes 1 tesset 10 mitiu l-t mraw l-t mraw l-t mfriw mraw I merawt meraw l-t 20 miriwin 100 twinest Table 4: Non-decimal (quinary, ternary, trigesimal) numeral systems all Mozabi UedGhir Djerba Djebel Neftisa m. Hanoteau Letoumer R. Basset Klingenheben 1 igguen ighem ! iSen udiun 15 iaret n ifessen 3 hands 2 sen tzem ! thin ! sen 20 okkoz n ifessen 4 hands 3 Saredh iaret saredh iaret 25 zegni n uyer d '/2 30 + sen n ifessen 2 hands 4 okkoz occas Saredh tfiiien 3 + 1 okkoz 30 uyer month 60 all Mozabi UedGrrir Djerba Djebel Nefusa m. Hanoteau Letoumer R. Basset KlinKCnheben 5 fus hand fus afiis ufes 50 zegni n temiti >/2 100 6 fus-igguen fus-ignem afiis diSLen hand + 1ufes d udlun 60 sen n yaren 2 x 30 7 fus-sen fus-tzem ( sebyath < Arabic) ufes d sen 80 zegni n temi(i '/2 100 d uyer + 30 8 fus-Saredh fus-faret attom ufes d iaret 90 iarel n yaren 3 x 30 9 fus-okkoz fus-occas attam diSen 8 + 1 ufes d okkoz 100 lemifi 10 meraw merawn akardai sen n ifessen 2 hands Klingenheben 1926-27: 44 found traces of the vigesimal system in the dialect of the tribe of Amiln (region of Sus) based on the Arabic borrowing iSerin "20": ?§Serfn ze meriw "30" = "20 + 10", sfn ize ^aSerin "40" = "2 x 20", sfn ize ?aSerfn ze meriw "50" = "2 x 20 + 10" etc. There were at least two or three ancient epigraphic "Libyan" languages related to the Berber language family: East Numidian, West Numidian and Fezzan-Tripolitanian. The best known East Numidian (= "Massilian") lan­ guage was used in old Numidia (North-East Algeria and North Tunis). Unfor­ tunately, in the known texts from the 2nd cent. BC no numerals are identified. Besides the "continental" Berber-Libyan languages there are their insular relatives — the languages of the Guanches, aborigines of Canary Islands, de­ finitively assimilated in the 18th cent. The exhaustive information concerning numerals of Guanches was collected by Woelfel 1954: "able 5: Guanche Gian Canaria ? Tenerife? Niccoloso Cedefio Marin y Berthelot Pseudo-Sosa Pseudo-Sosa daRecco deChil Cubas after Rixo 1 nail 1 ben been been ben ben 2 smetti = *sin- 2 lini liin or lini lini lini sijn or lini 3 amelotti 3 amiet amiat amiat amiat amiet or -at 4 acodetti 4 arba arba arba arba arba 5 simusetti 5 cansa conza cansa cansa cansa 6 sesetri 6 sumus sumus sumus sumus sumus 7 satti 7 sal sat sat sit sa or sat 8 tamatti 8 set set set set set 9 alda-morana 9 acol acot acot acot acot 10 marava 10 marago marago marago marago marago 11 nait-marava 11 ben y marago benir marago beni marago benir marago benir marago 12 smatta-m. 12 lini marago sinir marago lini marago 13 amierat-m. 20 limago linago linago 14 acodat-m. 30 amiago amiago amiago 15 simusat-m. 40 artogo aibago aibiago 16 sesatti-m. 50 oamago cansago cansago 60 sumago 61 Gran Canada? Tenerife? Niccoloso Cedeflo Marin y Bertheloi Pseudo-Sosa Pseudo-Sosa da Recco deChil Cubas after Rixo 70 satago 80 selago 90 acotago 100 bemaraguin bemaraguin beemaragoin Berber-Libyan-Guanche (shortly Berber) languages represent one of the six branches of Afroasiatic macro-family together with Semitic, Egyptian, Cushitic, Omotic and Chadic. Only the Semitic and naturally the Egyptian numerals can be projected on the proto-language level, cf. table 6: Proto-Semitic (Dolsopolsky 1995, p.c.) Proto-EKVPtian (Vycichl // Loprieno) 1 *?afi(b.)id-u(m) m. *?ab(b)id-at-u(m) f. *wi?yaw // *ivurruw m. Vifi.f f. 2 Bom.*t(n-8(-ni) *tfn-at-S(-ni) *siny-u-Sy *s(ni.t-8y acc.-gen. *tfn-ay(-ni) *lfn-at-ay(-ni) *sinya,t-By 3 *s/talSt.-u(m) f. *S/»Ul-it-u(m) m. *banuaw *h,amta.t 4 *?arMT-u(m) *?arbaf-il-u(m) *ifdaw *ifda.l 5 *ljamO-u(m) *hami!-il-u(m) *dfwey // *dtyaw *diwi.t 6 *!(d[u]l-u(m) *iid[u]t-Sl-u(m) *si[r]sa\v // *si?saw *si[r]sa.t 7 *sib?-u(m) *sab?-il-u(m) *safhaw *safha.t 8 *tamBna'y-u(m) *tamS nay-it-u(m) *hami/unaw *hamS/0na.t 9 *t(ST-u(m) *tiXY-4t-u(m) *pis!dav/ *pisi(ja.t 10 *?iSar-u(m) *?agar-it-u(m) *mtidaw *mdd.a.t 20 *?iSar-t = dual of *Tagar- "10" *dawitay < *mudawataydua = l of"10"f.
Load more

Recommended publications
  • Unicode Request for Kaktovik Numerals Design
    Unicode request for Kaktovik numerals L2/21-058R Eduardo Marín Silva, [email protected] Kirk Miller, [email protected] Catherine Strand, [email protected] 2021 April 29 This document supersedes L2/20-070 by Eduardo Marín Silva. The Kaktovik numerals are a set of base-20 digits with a sub-base of 5—that is, a penta-vigesimal system. Graphically, the sub-base forms the upper part of the digit and the remaining units the lower part, an iconic design that lends itself to graphical manipulation for arithmetic. Kaktovik numerals are part of the curriculum in the North Slope Borough School District of Alaska. Though designed by speakers of Iñupiaq Eskimo (ISO code [esi]), they are equally suited to the penta-vigesimal systems of other Inuit and Yupik languages of Alaska, Canada and Russia, and they have the support of the Inuit Circumpolar Council. Thanks to Deborah Anderson of the Universal Scripts Project for her assistance. Design Kaktovik numerals were made intentionally distinct from decimal Hindu-Arabic digits so that there could be no confusion between them. In speech as well, Kaktovik digits have been named in Iñupiaq and Hindu-Arabic digits in English in order to keep them distinct. There are 19 counting digits, composed of straight strokes joined at sharp angles, and a graphically distinct zero . The counting digits occupy the space of an upright golden rectangle, with a unit square at bottom and a smaller golden rectangle at top. The top rectangle is occupied by up to three horizontal strokes that tally the quinary sub-base (null, 틅, 틊, 틏).
    [Show full text]
  • Chapter 6 MISCELLANEOUS NUMBER BASES. the QUINARY
    The Number Concept: Its Origin and Development By Levi Leonard Conant Ph. D. Chapter 6 MISCELLANEOUS NUMBER BASES. THE QUINARY SYSTEM. The origin of the quinary mode of counting has been discussed with some fulness in a preceding chapter, and upon that question but little more need be said. It is the first of the natural systems. When the savage has finished his count of the fingers of a single hand, he has reached this natural number base. At this point he ceases to use simple numbers, and begins the process of compounding. By some one of the numerous methods illustrated in earlier chapters, he passes from 5 to 10, using here the fingers of his second hand. He now has two fives; and, just as we say “twenty,” i.e. two tens, he says “two hands,” “the second hand finished,” “all the fingers,” “the fingers of both hands,” “all the fingers come to an end,” or, much more rarely, “one man.” That is, he is, in one of the many ways at his command, saying “two fives.” At 15 he has “three hands” or “one foot”; and at 20 he pauses with “four hands,” “hands and feet,” “both feet,” “all the fingers of hands and feet,” “hands and feet finished,” or, more probably, “one man.” All these modes of expression are strictly natural, and all have been found in the number scales which were, and in many cases still are, in daily use among the uncivilized races of mankind. In its structure the quinary is the simplest, the most primitive, of the natural systems.
    [Show full text]
  • About Numbers How These Basic Tools Appeared and Evolved in Diverse Cultures by Allen Klinger, Ph.D., New York Iota ’57
    About Numbers How these Basic Tools Appeared and Evolved in Diverse Cultures By Allen Klinger, Ph.D., New York Iota ’57 ANY BIRDS AND Representation of quantity by the AUTHOR’S NOTE insects possess a The original version of this article principle of one-to-one correspondence 1 “number sense.” “If is on the web at http://web.cs.ucla. was undoubtedly accompanied, and per- … a bird’s nest con- edu/~klinger/number.pdf haps preceded, by creation of number- mtains four eggs, one may be safely taken; words. These can be divided into two It was written when I was a fresh- but if two are removed, the bird becomes man. The humanities course had an main categories: those that arose before aware of the fact and generally deserts.”2 assignment to write a paper on an- the concept of number unrelated to The fact that many forms of life “sense” thropology. The instructor approved concrete objects, and those that arose number or symmetry may connect to the topic “number in early man.” after it. historic evolution of quantity in differ- At a reunion in 1997, I met a An extreme instance of the devel- classmate from 1954, who remem- ent human societies. We begin with the bered my paper from the same year. opment of number-words before the distinction between cardinal (counting) As a pack rat, somehow I found the abstract concept of number is that of the numbers and ordinal ones (that show original. Tsimshian language of a tribe in British position as in 1st or 2nd).
    [Show full text]
  • Curiosities Regarding the Babylonian Number System
    Curiosities Regarding the Babylonian Number System Sherwin Doroudi April 12, 2007 By 2000 bce the Babylonians were already making significant progress in the areas of mathematics and astronomy and had produced many elaborate mathematical tables on clay tablets. Their sexagecimal (base-60) number system was originally inherited from the Sumerian number system dating back to 3500 bce. 1 However, what made the Babylonian number system superior to its predecessors, such as the Egyptian number system, was the fact that it was a positional system not unlike the decimal system we use today. This innovation allowed for the representation of numbers of virtually any size by reusing the same set of symbols, while also making it easier to carry out arithmetic operations on larger numbers. Its superiority was even clear to later Greek astronomers, who would use the sexagecimal number system as opposed to their own native Attic system (the direct predecessor to Roman numerals) when making calculations with large numbers. 2 Most other number systems throughout history have made use of a much smaller base, such as five (quinary systems), ten (decimal systems), or in the case of the Mayans, twenty (vigesimal systems), and such choices for these bases are all clearly related to the fingers on the hands. The choice (though strictly speaking, it's highly unlikely that any number system was directly \chosen") of sixty is not immediately apparent, and at first, it may even seem that sixty is a somewhat large and unwieldy number. Another curious fact regarding the ancient number system of the Babylonians is that early records do not show examples of a \zero" or null place holder, which is an integral part of our own positional number system.
    [Show full text]
  • Mathematics As a Liberal Art Class 13: Wednesday February 25
    Mathematics As ALiberal Art Math 105 Spring 2015 Fowler 202 T 3:00- 3:55pm c 2015 Ron Buckmire http://faculty.oxy.edu/ron/math/105/15/ Class 13: Wednesday February 25 Hexadecimal: Millions Of Colors! Hexadecimal Number System Another number system which is often seen in computer systems is the hexadecimal number system, which uses 16 as a base or radix. In this case the digits are 0 through 9 supple- mented with A, B, C, D, E, and F. One issue with hexadecimal numbers is that since they use the same digits as the decimal system plus more, they can be confused for each other unless one uses a subscript to distin- guish them, like 42hex. Some places use a header to indicate a a non-decimal number, like \0x" for hex, e.g. 0x4E (which is the same thing as 7810). One can also use the header \0b", e.g. 0b1001110 (which is also the same thing as 7810). Hexadecimal numbers are usually seen in the description of colors, in describing pixel RGB values on screens in terms of how much red, green or blue are in a particular color. These pixel values range from 0 to 255 for each of these three, colors which puts the number of possible colors as 256x256x256 = 16 million colors! For example, the color pure red is represented by 0xFF0000, pure green is represented by 0x00FF00 and pure blue is represented by 0x0000FF. EXAMPLE What number in base 10 is equal to 05A3hex? How do we convert 637 into its hexadecimal equivalent? An Algorithm For Converting From A Decimal Number To Hexadecimal Use Repeated Division 1.
    [Show full text]
  • The Sumerian Ternary System and the Concept of Number António José Gonçalves De Freitas Centro De Estudos Humanísticos Universidade Do Minho Portugal
    Paper delivered at 1st CLE Colloquium for Philosophy and Formal Sciences Campinas, 21-23 March 2013 Accepted for publication in the Proceedings of the Conference DRAFT &1 The Sumerian ternary system and the concept of number António José Gonçalves de Freitas Centro de Estudos Humanísticos Universidade do Minho Portugal Abstract It is well known that Sumerians and Babylonians used a numeration system of base 12 and 60. We still have influence of that system in our nowadays counting of the hours of a day, twelve plus twelve, each hour has 60 minute and each minute 60 seconds. Also the circle has 360 degrees. What is not so well known is that the Sumerians in an earlier period used a ternary system of numeration; the first notice about that system is in Thureau- Dangin (1928). Later Diakonoff (1983) described it in good details and recently, Balke (2010) studied the system and described it with more precision. Still the use of this system and the concept of number involved are open questions. I will answer to those problems making a formalization of the system and showing how it could be related to a cosmogonic design. DRAFT &2 1. Numeral systems. DRAFT &3 ��� 1 11 21 31 41 51 � �� ��� �� �� � ��� 2 12 22 32 41 52 � �� ��� �� �� � � �� ��� � 3 13 23 33 42 53 � �� � � � � � �� ��� � 4 14 24 34 43 54 � �� � � � � � �� ��� � 5 15 25 35 44 55 � �� � � � � � �� ��� � 6 16 26 36 45 56 � �� �DRAFT� � � � �� ��� � 7 17 27 37 46 57 � �� � � � � &4 � �� � 8 18 28 38 47 58 � �� �� � � � � �� � � 9 19 29 39 48 59 � �� � � � � 10 20 30 ��� 40 50 � �� � � The main Babylonian and Sumerian counting system was a sexagesimal system.
    [Show full text]
  • Vigesimal System of Numeration As Prevailed in the Bārelā Tribe Dipak
    Vigesimal System of Numeration as Prevailed in the Bārelā Tribe Dipak Jadhav Lecturer in Mathematics Govt. Boys Higher Secondary School, Anjad Distt. Barwani 451556 (M. P.) India [email protected] Abstract Bārelā is a tribe. It resides in the western part of India. In Bārelā system of numeration other numbers stand in relation to twenty. This paper finds that no other vigesimal system whether it was in India or from abroad has been influential in shaping Bārelā system of numeration if their corresponding terms are taken into consideration. Gunnīsa, uganīsa, and oganīsa are the alternative terms used by Bārelās for 19. This paper also offers an insight into the formation of each of them. Key Words: Bārelā, Vigesimal system of numeration, Vīsa, Vīsu. Introduction Bārelā is an Indian tribe. Most of its population lives in Barwani District of State of Madhya Pradesh in India. The surrounding region, where as well Bārelās dwell, to this District encompasses the neighboring Khargone District of Madhya Pradesh and the three neighboring Districts, namely, Jalgoan, Dhule, and Nandurbar, of State of Maharashtra. The term used to identify Bārelā in Maharashtra is Pāvarā.1 The entire region of their dwelling, which is in the western part of India, falls in the forest of Satpura range. The dialect which Bārelās speak is called Bārelī. Their system of numeration is based on twenty. It is observed to be mostly practised in Pati and Barwani Blocks of Barwani District. Bārelās dealing with retailers in its terms can be seen in weekly haat bazars2 conducted in this region (Parihar et el 2000; Thakur 2005, p.
    [Show full text]
  • Number Systems: Binary and Hexadecimal Tom Brennan
    Number Systems: Binary and Hexadecimal Tom Brennan Base 10 The base 10 number system is the common number system. 612 = 2 · 100 + 1 · 101 + 6 · 102 2 + 10 + 600 = 612 4365 = 5 · 100 + 6 · 101 + 3 · 102 + 4 · 103 5 + 60 + 300 + 4000 = 4365 Binary 101010101 = 1 · 20 + 0 · 21 + 1 · 22 + 0 · 23 + 1 · 24 + 0 · 25 + 1 · 26 + 0 · 27 + 1 · 28 = 341 1 + 0 + 4 + 0 + 16 + 0 + 64 + 0 + 256 = 341 The binary number system employs only two digits{0 and 1{and each digit is called a bit. A number can be represented in binary by a string of bits{each bit either a 0 or a 1 multiplied by a power of two. For example, to represent the decimal number 15 in binary you would write 1111. That string stands for 1 · 20 + 1 · 21 + 1 · 22 + 1 · 23 = 15 (1 + 2 + 4 + 8 = 15) History Gottfried Leibniz developed the modern binary system in 1679 and drew his inspiration from the ancient Chinese. Leibniz found a technique in the I Ching{an ancient chinese text{that was similar to the modern binary system. The system formed numbers by arranging a set of hexagrams in a specific order in a manner similar to modern binary. The systems base two nature was derived from the concepts of yin and yang. This system is at least as old as the Zhou Dynasty{it predates 700 BC. While Leibniz based his system of the work of the Chinese, other cultures had their own forms of base two number systems.
    [Show full text]
  • A Study of Our Present Numbering System: an Histo
    A STUDY OF OUR PRESENT NUMBERING SYSTEM: AN HISTO~t CAL A~RO&~H A THESIS SUBMITTED TO THE FACULTY OF ATLANTA UNIVERSITY IN PARTIAL FUIJFILLMBNT OF THE REQUIREMBNTS FOR THE DE(~?.EE OF MASTER OF SCIENCE BY MAE FRANCES WIlSON DEPA1~rMBNT OF MATHEMATICS ATLANTA, GEORGIA AUGUST 196t~ ii ~‘- TABLE OF CONTENTS Page LIST OF FIGURES. • . • • • • Iii Chapter I. INTRODUCTION. .• . 1 II. NU_~4ERATION . 3 III. SYSTE~ ND THEIR PROPERTIES. 10 B IBLIOGf?JkFHY. , • • . • • 22 ii EGYPTIAN NUMERALS I I A VtR.TICaL 10 (1 A HE~i.- BONE 10 A [email protected] I. 0~ A~~° A LÔTUS 1. ü~ I k POINTIkI6 IU A 6u9%8o1 FsU 1. 0 ~ A- (4111” 1W A-$TON~$JtM~VT Figure 1 iii AT ~ a.xn~ç~ ill III UU~Od,d, III UUU~Ø~ =(Ub4(QIJS-~o I) b4 (~c?I)/ ~b..cb1 l(1IVVU&~ =(V(oI)E09~h~Z III L)ULI = (i)S4-(o~)L 5L IIIL)L) (,)~-f-(oOZ = Ii V :~7:J ~ ~ (~~o” # ~ 0/)£ ~ (‘i, 01)1 ~1Q £ I S?~I~EJWnN NVIJ~J~-D~ A 6 —~(4oV4Q14.Q1 AAA >~~PI~P’>I~ L2 Q~. — Q?4O~ 1,1 A> II > 0l AAIAA~AA1L b AAAAAAA L 9 S ~AAA ~A4 Al Z A I ~~Wri/q fV~bNINQ7A~’d~ STht~3’~WnN ~io~ I~T~U1N ~TvINQ~UEya OOb, L~ Ob e b c9oo~’ LL8 ILOOL cOL X009 09 9 c?,QQS (LOS (LOOI7 71 Oh ~L- OQE D OO~ )I OZ 0~ 00/ 7 0/ ~IY~{~W11t~ )I~O S a.zn2T~ COb 00~ CCL 009 00.9 OOtT 001 002 00/ L~ L UQLL~ S~T3~QNnH Oh Q~OL 09 OS 0*701 OZ 0? SN3± b~~9S-&~ZI qLL[LLLLCt~~ S~LINfl $IV~WflN ~ 9 e.in2t~ ~,1- co’ 4- 01 itt b 37d WYX~ 9 -ç 4.7 z I 5 7j1≥13(AJPAJ 3~3/IVd4’I— 3S3IVIfI) 741>13W fiN ~‘flQ ~I~HflN ~S~vdvf-~9~NIHD L ‘~T~!i •~7’~74,4J Qb’ FQ~/ ~v ~, Ob~ ~J9h-6 ~ZL ‘q~’ wi ~44OA/ -% A’~VW..t f7~fs~3,4/g4/ ~ b VA L C’? ~ ~4 I Q’b’ 914 ~9A 000/ P~ ~ $~TVV~flN ~IEWV-flG$EIR CHI&PrER I INTRODUCTION The meaningful approach to the teaching of arithmetic is widely accepted.
    [Show full text]
  • Every Day We Face Many Consumer, Financial, Legal, Business And
    Every day we face many consumer, financial, legal, business and employment choices. Business Education helps us to make informed and responsible decisions. A Business and economic systems In this part, you will understand: • business environments • the nature of systems and subsystems • production and markets • the resolution of business and economic issues. 1 Business environments Whenever you step outside your home, you interact with some type of system or business organisation. It may be the transport system, a retail business or a government department. In fact, even within your home, you can have such interaction through the Internet or on the telephone. In this chapter, you will learn how business organisations operate within community systems and how they are regulated. You will: • compare business organisations • analyse their purposes and structures • identify how businesses fit within industry types • identify and investigate the need for systems and businesses to be regulated • understand the role of regulatory bodies in Queensland and Australia. Key terms public company: business owned and operated by an unlimited number of people called shareholders. asset: item of value that a business owns and that It has limited liability, and the shares may be can be given a monetary value bought and sold on the stock exchange. business: the organised effort of individuals to quaternary industry: an industry involved in the produce and sell, for a profit, the products that transfer and process of information and knowledge satisfy individual
    [Show full text]
  • Hexadecimal Numbers Teacher’S Notes
    Hexadecimal numbers Teacher’s Notes Lesson Plan Length 60 mins Specification Link 214/e_f_g Units Candidates should be able to: (e) convert positive denary whole numbers (0-255) into 2-digit hexadecimal numbers and Learning objective vice versa (f) convert between binary and hexadecimal equivalents of the same number (g) explain the use of hexadecimal numbers to represent binary numbers Time (min) Activity Further Notes 10 Using a projector, display the Interactive Starter Activity. Stress to the students that the digits we write down can represent different numbers depending on the system we use. 15 Watch the set of videos, pausing to discuss the content. 5 Discuss the videos to assess learning. Ask questions such as: • Why is hexadecimal used? It is much easier to express binary number representations in hex than it is in any other base number system. • How would you convert a two digit hexadecimal A two digit hex number can represent a number to denary? byte. • How would you convert an 8 bit binary number to Multiply the first digit by 16 and then add hexadecimal? on the second digit. Convert the binary number into two nibbles (4 bit numbers) and then convert each to denary. If one is higher than 9, then use the letters A, B, C, D,E and F for the numbers 10 to 15. 15 Worksheet 1 Answers provided. Pupils to complete Worksheet 1 either on paper or on Ask students with the correct responses computer. to explain to the class how they arrived at Ask individual students for their answers and discuss their answers.
    [Show full text]
  • Chapter 7 MISCELLANEOUS NUMBER BASES. the VIGESIMAL
    The Number Concept: Its Origin and Development By Levi Leonard Conant Ph. D. Chapter 7 MISCELLANEOUS NUMBER BASES. THE VIGESIMAL SYSTEM. In its ordinary development the quinary system is almost sure to merge into either the decimal or the vigesimal system, and to form, with one or the other or both of these, a mixed system of counting. In Africa, Oceanica, and parts of North America, the union is almost always with the decimal scale; while in other parts of the world the quinary and the vigesimal systems have shown a decided affinity for each other. It is not to be understood that any geographical law of distribution has ever been observed which governs this, but merely that certain families of races have shown a preference for the one or the other method of counting. These families, disseminating their characteristics through their various branches, have produced certain groups of races which exhibit a well-marked tendency, here toward the decimal, and there toward the vigesimal form of numeration. As far as can be ascertained, the choice of the one or the other scale is determined by no external circumstances, but depends solely on the mental characteristics of the tribes themselves. Environment does not exert any appreciable influence either. Both decimal and vigesimal numeration are found indifferently in warm and in cold countries; in fruitful and in barren lands; in maritime and in inland regions; and among highly civilized or deeply degraded peoples. Whether or not the principal number base of any tribe is to be 20 seems to depend entirely upon a single consideration; are the fingers alone used as an aid to counting, or are both fingers and toes used? If only the fingers are employed, the resulting scale must become decimal if sufficiently extended.
    [Show full text]