Herramienta de enseñanza de aritmética de computadores de nueva generación. Caso de estudio de posit

He amien a de enseñanza de a i mé ica de compu ado es de nue a gene ación. Caso de es udio de posi . E-lea ning ool o nex gene a ion compu e a i hme ic. S udy case o posi . T abajo de Fin de G ado Cu so 2022–2023 Au o Da id Godoy Ruiz Di ec o Guille mo Bo ella Juan Raúl Mu illo Mon e o G ado en Desa ollo de Videojuegos Facul ad de In o má ica Uni e sidad Complu ense de Mad id He amien a de enseñanza de a i mé ica de compu ado es de nue a gene ación. Caso de es udio de posi . E-lea ning ool o nex gene a ion compu e a i hme ic. S udy case o posi . T abajo de Fin de G ado en Desa ollo de Videojuegos Au o Da id Godoy Ruiz Di ec o Guille mo Bo ella Juan Raúl Mu illo Mon e o Con oca o ia: Sep iemb e 2023 G ado en Desa ollo de Videojuegos Facul ad de In o má ica Uni e sidad Complu ense de Mad id 15 de sep iemb e de 2023 Dedica o ia A oda mi gen e, es éis donde es éis Ag adecimien os A la peña del Joy e po aguan a me odos es os años. A los del G edos po odo lo pe o má ico. A los de los lagui os po jun a nos en los luga es más a os. A los panas de la uni po hace magia. A los cha ales de LAG y de ASCII po se mucho más que la ida uni e si a ia. A mi amilia. A oda la gen e que me hab é dejado. A la gen e que ha pasado po mi ida y me ha dejado sin que e un pedaci o suyo. A odos oso os, que me habéis hecho como soy. ii Resumen He amien a de enseñanza de a i mé ica de compu- ado es de nue a gene ación. Caso de es udio de po- si . El es ánda IEEE pa a la a i mé ica bina ia de coma lo an e (IEEE 754) lle a siendo la no ma pa a la a i mé ica de compu ado es desde 1985 y es usado en los o denado es de odo el mundo. En 2017 John L. Gus a son p esen ó un nue o o - ma o, los posi , con el obje i o de eemplaza a la coma lo an e, diciendo que o ece mayo p ecisión o p ecisión simila con un meno núme o de bi s. A medida que ha ido a anzando el iempo el o ma o ha ido euniendo cada ez más seguido es que lo apoyan si no como al e na i a di ec a a la coma lo an e como un o ma o que puede coexis i con ella. Sin emba go los ecu sos disponibles pa a ap ende es e nue o o ma o son pocos y es án dispe sos lo que hace que un usua io nue o que quie a ap ende lo enga que busca in o mación epa ida en e a ios documen os, algunos de ellos muy écnicos. En es e T abajo de Fin de G ado se ha c eado una aplicación de e-lea ning pa a acili a el ap endizaje sob e los posi . T as in es iga de alladamen e el unciona- mien o del o ma o y los ecu sos de ap endizaje disponibles ac ualmen e an o pa a coma lo an e como pa a posi se ha desa ollado una aplicación de esc i o io pa a Windows que pe mi e al usua io ap ende la es uc u a del o ma o y sus ope aciones básicas. Pa a conlcui se ha hecho un análisis de las ca ac e ís icas de la aplicación desa ollada en compa ación con el es o de he amien as disponibles. Palab as cla e Sis ema numé ico posi , Coma lo an e, E-lea ning, A i mé ica compu acional, Apli- cación de esc i o io ix 5.5. Posi Tool main window . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.6. Posi Tool ope a ion window o posi in o ma ion, a one pa ame e ope a ion ................................. 33 5.7. Posi Tool ope a ion window o addi ion/sub ac ion, a wo pa ame- e ope a ion ............................... 34 5.8. Full display o he addi ion ope a ion and he glossa y . . . . . . . . 34 Lis o ables 3.1. Compa ison o ea u es a ailable in e-lea ning applica ions o he loa ing-poin and posi o ma s . . . . . . . . . . . . . . . . . . . . . 18 5.1. Compa ison o Q , wxWidge s and GTK’s ea u es . . . . . . . . . . 28 6.1. Fea u e compa ison o he p oposed applica ion wi h s a e o he a e-lea ning esou ces............................ 37 x ii Chap e 1 In oduc ion 1.1. Mo i a ion The IEEE 754 S anda d o Floa ing-Poin A i hme ic (IEEE 754) (4) has co - e ed he cons an need o compu e s o ep esen eal numbe s wi h a limi ed, ixed amoun o memo y space o decades. Bu e en i i has me apho ically held ha weigh o ha long, when augh his o ma is ba ely skimmed o e in some ed- uca ional ins i u ions, o he poin ha many p og amme s do no e en know he in e nal wo kings o he o ma , jus he ba e minimum: ha i is used o ep esen eal numbe s, and ha i is somewha imp ecise. I a signi ican amoun o p og amme s know he ba e minimum o an inc edibly widesp ead o ma , i is no su p ise ha only people wi h an exp ess in e es in compu e a i hme ics know ha a new o ma was c ea ed, and ha i is aking s eps o knock he loa ing poin o i s high h one: he posi o ma . Posi mode Type III unums (which will be e e ed o as posi s om now on) we e p esen ed as a di ec eplacemen o he cu en o ma (1). Unlike i s wo p edecesso s, posi s we e designed o ha e a simple ha dwa e and so wa e imple- men a ion using he same ype o low-le el ci cui cons uc s ha IEEE 754 loa s use, e en aking less chip a ea. Because o i s ai ly low amoun o ollowe s posi s a e lacking ha dwa e suppo , as i is ai ly ecen and ew people know abou i . Anyone in e es ed in lea ning and/o eaching i will jus ind a lack o educa i e esou ces abou his inc edible new o ma . A e y impo an s ep in o de o s anda dize his inc edible new o ma is c ea ing lea ning esou ces in o de o accele a e he inc ease o i s sp ead. 1 2Chap e 1. In oduc ion 1.2. Objec i es The objec i e o his wo k is o in es iga e he posi o ma and i s inne wo k- ings in o de o de elop an E-Lea ning applica ion o ease he p ocess o ob aining in o ma ion abou hem. In o de o do so he applica ion mus show he use he in e nal pa s o a posi , and explain s ep by s ep he basic ope a ions ha can be ca ied ou wi h hem: con e sion o decimal, addi ion, sub ac ion, mul iplica- ion and di ision. All o his mus be accompanied by g aphics o help isualize he p ocess ha is being ca ied ou . In addi ion, as posi ha e a g ea amoun o e minology ha can be con using, a glossa y will be added in o de o acili a e lea ning. The main goals o his wo k a e: 1. Unde s and posi s and hei inne wo kings in compa ison o loa s. 2. S udy a ailable lea ning esou ces o he one ha is p e ended o de elop, hei ea u es and laws. 3. De elop a desk op applica ion ha explains he posi o ma and i s main ope a ions. 1.3. Wo k plan In o de o achie e he objec i es explained in he ea lie sec ion, he nex plan will be ollowed: 1. S udy posi s and hei inne wo kings in compa ison o loa s. To in es iga e abou posi s and loa s. To de elop a basic in-house implemen a ion o loa s. To look in o so wa e implemen a ions o posi s and hei in e nal wo k- ings. To de elop an implemen a ion o posi ope a ions along wi h s ep by s ep explana ions. 2. S udy a ailable lea ning esou ces o he one ha is p e ended o de elop, hei s uc u e and quali y. To in es iga e simila apps o posi s as well as loa s. To s udy hei unc ions and he esou ces hey o e . 3. De elop a desk op applica ion ha explains he posi o ma and i s main ope a ions. To look o a sui able en i onmen o de elop desk op applica ions. 1.4. Documen s uc u e 3 To de elop he window na iga ion en i onmen o he applica ion. To adap he implemen ed console me hods o wo k in he new en i on- men . To de elop a glossa y o he applica ion. To de elop g aphics ha acili a e ollowing he al eady implemen ed explana ions. 1.4. Documen s uc u e The documen ollows he esea ch and de elopmen p ocesses ha led o he inal applica ion. In Chap e 2 he main cha ac e is ics o he loa ing poin and he posi o ma a e explained as well as some imp o emen s ha posi s make o e loa ing poin numbe s. Nex in Chap e 3 he ea u es o he a ailable e-lea ning esou ces a ailable o posi s a e explained and compa ed wi h some o he ones a ailable o loa ing poin . In Chap e 4 he de elopmen o an own loa ing poin implemen a ion in o de o unde s and he o ma as well as a posi implemen a ion based on he Uni e sal Numbe s Lib a y. Following ha in Chap e 5 he imple- men a ion o he desk op applica ion is explained en i ely. Las ly, in Chap e ?? an e alua ion o he inal esul o he desk op applica ion is shown as well as a com- pa ison wi h he o me s udied applica ions. Finally in Chap e 7 he conclusions and u u e wo k a e discussed. Chap e 2 Floa ing Poin and Posi In his chap e he backg ound o posi s is shown as well as loa s, which we e conside ed necessa y in o de o unde s and hei in ended successo . 2.1. Floa ing Poin : he IEEE 754 S anda d The loa ing-poin o ma is used o ep esen bina y eal numbe s as a s ing o bi s. As shown in Figu e 2.1, loa s a e composed o h ee componen s: a sign bi ha indica es i he numbe is posi i e o nega i e, an exponen ha indica es he posi ion o he adix poin and he ac ion which usually indica es he ac ional pa o he no malized numbe , lea ing he i s 1 implici . This is no always he case as deno malized numbe s exis , which do no ha e an implici 1 and ins ead ha e an implici 0. The IEEE-754 S anda d o Bina y Floa ing-Poin A i hme ic (4) desc ibes a loa ing poin s anda d o compu e ep esen a ion. I was he i s o i s kind and has been used by he majo i y o compu e s since i s c ea ion in 1985 by he Ins i u e o Elec onics and Elec ical Enginee ing, e en hough i has been e ised wice, one in 2008, and ano he one in 2019. This s anda d speci ies o ma s and me hods and i de ines excep ion condi ions and hei s anda d handling in o de o ep esen eal numbe s in a limi ed amoun o bi s. S Exponen E Unsigned signi icand M Figu e 2.1: Floa Fo ma They ha e mul iple special alues: wo ze os (-0, +0) and mul iple NaN (No a Numbe ) alues as well as deno malized numbe s. 5 6Chap e 2. Floa ing Poin and Posi 2.2. Posi The Type III unum, be e known as posi , is an a i hme ic o ma p esen ed by John L. Gus a son and Isaac Yonemo o in 2017 (1). Unlike he Type I and II unums (which we e designed o ep esen ei he a numbe o a speci ic ange in which a numbe is loca ed, wo king simila ly o in e al a i hme ic), he posi o ma was designed o be a di ec eplacemen o he IEEE 754 s anda d in compu e s, by making i s ha dwa e implemen a ion easie han i s o he unum coun e pa s. The posi o ma is shown in Figu e 2.2. Figu e 2.2: Posi o ma (1) I is cons i u ed by 4 di e en bi ields in o de o dec easing signi ican bi s: 1. The sign bi S. I is he same as in signed loa o in ege s: 0 o posi i e numbe s and 1 o nega i e numbe s. I he numbe is nega i e i ’s necessa y o ake he 2’s complemen o he emaining bi s be o e in e p e ing hem. 2. The egime bi ield Rwhich consis s o k(minimum 1) iden ical bi s e mi- na ed by R0nega ed as shown in he Figu e 2.2. R ep esen s −ki R0= 0, o k−1i R0= 1.kis used o calcula e a he scale o useedkwhe e useed is 22es . The egime is a a iable-leng h ield. The longe he egime, he mo e bi s o o he ields a e no ep esen ed and a e conside ed 0 bi s. 3. The exponen bi ield Ehas a maximum leng h o es, dic a ed by he speci ic posi o ma , bu one o mo e bi s can be beyond he leas signi ican bi (LSB) and be conside ed o ha e alue 0. I ep esen s he alue ewhich is ea ed as an unsigned in ege . eis used o calcula e he scaling alue 2e. In he 2022 s anda d es is always 2 (5). 4. The ac ion bi ield Fwhich has a maximum leng h o (n−3−es), bu as wi h he exponen any o hose bi s beyond he LSB a e conside ed 0. The numbe o explici bi s is conside ed m.F ep esen s he ac ion alue . The alue o a posi pis ob ained ollowing he nex p ocess: 1. I all he bi s excep Sa e 0 i is one o wo special alues: I S= 0 hen p= 0 I S= 1 hen p=NaR.NaR(No a Real) is a special posi alue ha is used o ep esen in ini y o in alid alues (such as he esul o 1/0). 2.3. Bea ing Floa ing Poin 7 2. O he wise he alue o p is ob ained om Equa ion 2.1. p= (−1)sign ·(1 + )·useedk·2e(2.1) I ounding is needed, i ollows he nex p ocess: 1. I xis exac ly exp essible in he posi o ma no ounding is needed. 2. I x > maxpos, i ounds o maxpos. 3. I x < minpos, i ounds o minpos. 4. Else ound o nea es e en. Rounding is simple because he e is only one o m o ounding: nea es alue, ies o nea es e en. The way posi s a e designed also cause ha he e is no o e low o unde low, ins ead i a posi we e o unde low/o e low i ounds o he alues minpos/maxpos, which a e he smalles nonze o alue and he g ea es ep esen able alue in he o ma . This makes he handling o o e low o unde low si ua ion easie o manage o p og amme s han he equi alen in IEEE 754. The p oblem wi h posi numbe s is he lack o ha dwa e implemen a ions and he ac ha he u he you go om scale 0 he less p ecision hey ha e. And, because hey a e so new, he e a e ewe esou ces, especially when compa ing o a s anda d ha has been a ound since 1985. 2.3. Bea ing Floa ing Poin The posi o ma has many imp o emen s o e he s anda d loa s (1): 1. I he sign bi is 1, he posi bi s ing is nega ed ( ea ing i as a s anda d 2’s complemen in ege ) be o e decoding he emaining ields. This elimina es he need o “nega i e ze o” and all he complica ions o ha ing wo dis inc bi pa e ns ep esen he same eal alue. 2. A machine ins uc ion ha es s i wo in ege s a e equal will also se e o compa e wo posi s, whe eas loa ins uc ions need an addi ional excep ion es s o nega i e ze o (equal e en hough bi pa e ns a e di e en ) and also a check o NaN alues (no equal, e en when bi pa e ns a e iden ical). 3. The e a e no deno malized numbe s. The implici "hidden bi " be o e he ac ion bi s is always 1. 4. Floa s ha e up o i e di e en ounding modes (nea es - o-e en, di ec ed o 0, ound o ∞, ound o −∞, and nea es -away- om-0), which can be chosen up o he p e e ence o he use as seen in Figu e 2.3. This in u n causes ha di e en de ices can gi e di e en esul s o he same calcula ion. Posi s only 14 Chap e 3. E-Lea ning Resou ces Figu e 3.4: Real wheel o posi <5,1> 3.3.2. RacFP RacFP (21) is a p ojec c ea ed by s uden s o he Uni e sidad Poli écnica de Valencia published in 2006. This desk op applica ion was made wi h a simila philosophy as he one which his applica ion was app oached wi h: acili a ing he lea ning o an a i hme ic o ma . As such, i has been an inspi a ion o his wo k. I was de eloped wi h he pu pose o helping s uden s unde s and loa ing-poin eal numbe s, hei ela ed algo i hms and he implemen a ion o ci cui s based on hese algo i hms. I was designed o be used in unde g adua e-le el cou ses o compu e enginee ing, wi h a pu ely educa ional pu pose. The ool classi ies i s heme in o h ee abs ac ion le els: The i s le el, in e nal ep esen a ion o eal numbe s; he second le el, gene ic algo i hms such as addi ion and mul iplica ion; and he hi d le el, which in oduces he s uden s o eal-wo ld examples ha show how he o ma is applied in ma ke a ailable ci cui s. As seen in Figu e 3.8, RacFP has many in e ac i e bu ons, each ow co espond- ing o one o he a o emen ioned le els. When p essed, a pop-up window appea s depending on he ea u e. The i s le el o e s he op ion o con e sion, which asks o use inpu , and he 3.3. Floa ing Poin Applica ions 15 Figu e 3.5: Floa Toy showing πin mul iple loa o ma s Figu e 3.6: Ha ald Schmid ’s con e e showing he example alue 12.6 o ma s o bo h inpu and ou pu . The inpu (shown in Figu e 3.9) can ei he be in decimal, bina y and hexadecimal. Fo he ou pu , i can be in single p ecision (32-bi loa ), double p ecision (64-bi double) o in a cus om o ma in which he use can speci y he numbe o man issa and exponen bi s. Once en e ed, he window changes o he one shown in Figu e 3.10 o show he bina y ep esen a ion o he numbe sepa a ing he sign, exponen and man issa ields. I also shows he ep esen a ion o he numbe in hexadecimal, and decimal, and he speci ic de ails o he o ma used and he numbe , like i i ’s no malized, deno malized, a ze o, NaN, o an in ini e while gi ing a b ie explana ion o hese de ails. This le el also includes sign ables o e ec i e ope a ion, addi ion/subs ac ion and mul iplica ion/di ision as seen in Figu e 3.11. The second le el consis s o he gene ic algo i hms o a i hme ic ope a ions: addi ion/sub ac ion and mul iplica ion/di ision. Fi s a lowcha (3.12 o he o me and 3.8 o he la e ) appea s wi h all he possible s eps o said ope a ion and a ex box below i ha o e s a b ie explana ion o he cu en s ep and he in e media e esul s. By p essing he nex bu on he use inpu window appea s asking o bo h ope ands, he ounding mode and he speci ic ope a ion (addi ion/- sub ac ion, o mul iplica ion/di ision). I also o e s he o ma op ions p esen in 16 Chap e 3. E-Lea ning Resou ces Figu e 3.7: Explo ing Bina y showing he con e sion o he example alue 27.124 o decimal, no malized bina y scien i ic no a ion and aw bina y he con e sion window. A e en e ing he alues he window closes and he nex bu on now ad ances a s ep a a ime h ough he p ocess highligh ing he cu en s ep, changing he desc ip ion, o bo h depending on wha i s he explana ion a ha momen . An impo an usabili y p oblem wi h his implemen a ion is ha he e is no op- ion o e u n o a p e ious s ep o check he explana ions a e hey a e o e w i en by he nex ones, o cing he use o es a he p ocess in o de o look a hem. The hi d and las le el shows he ha dwa e implemen a ion o he a i hme ic ope a ions explained be o e using lowcha s ha simula e HP chips 3.14. The inpu is simila o he second le el bu he lowcha is e ealed by s ep ins ead o being shown all he ime and he explana ion, his ime in a sepa a e window, can show he in o ma ion o each poin o he diag am i he use ho e s he mouse o e i . All hese explana ions a e also o e ed in bo h Spanish and English. 3.3. Floa ing Poin Applica ions 17 Figu e 3.8: RacFP main sc een Figu e 3.9: Inpu sc een o con e sion The compa ison be ween he ea u es o loa ing-poin esou ces and he posi ones is shown in Table3.1, which shows he sho comings o he la e . The posi ools ha e less op ions o use in e ac ion and p ac ically no ex explana ions o how hey wo k o he heo y behind i . Toge he i all makes ha a new use o he o ma has no o he op ion o he han ead h ough mul iple documen s. Fu he mo e his documen s ha e he basic in o ma ion bu ied be ween complica ed blocks o ex , adding o he con usion. Besides, all he ea u es ha posi has o e loa ing poin such as he ep esen a ion o he posi wheel o he lookup ables a e no needed o he la e because o i s ease o unde s anding in compa ison o he o me . 18 Chap e 3. E-Lea ning Resou ces Figu e 3.10: Con e sion esul Floa ing-poin applica ions ea u es Posi applica ions ea u es Visual Con e sion Tables S ep by s ep explana ion o : Calcula o -Addi ion Visual Rep esen a ion -Sub ac ion -Mul iplica ion -Di ision -Ha dwa e Implemen a ion Table 3.1: Compa ison o ea u es a ailable in e-lea ning applica ions o he loa ing-poin and posi o ma s 3.3. Floa ing Poin Applica ions 19 Figu e 3.11: Sign ables 20 Chap e 3. E-Lea ning Resou ces Figu e 3.12: Addi ion lowcha 3.3. Floa ing Poin Applica ions 21 Figu e 3.13: Mul iplica ion and di ision lowcha 22 Chap e 3. E-Lea ning Resou ces Figu e 3.14: Addi ion ha dwa e lowcha Chap e 4 Console Implemen a ion o Floa and Posi S uc u es Two small console applica ions ha simula ed he in e nal s uc u e and ope a- ions o bo h o ma s. The goal o his was o complemen he heo e ic lea ning o bo h o ma s (especially he in e nal s ep by s ep p ocess o he ope a ions, which is no clea ly included in any documen ) and as a es o ou unde s anding o he p ocess. In o de o do so, an in-house console applica ion ha eplica ed he s uc u e o he o ma s, he con e sion om decimal and a simple ope a ion which was he addi ion. I was de eloped in console in o de o de elop and i e a e as as as possible. C++ was chosen as he language o de elop he applica ion om i s i s i e a- ion. I allows o an easy and as de elopmen p ocess and he e a e many lib a ies a ailable o bo h posi and desk op applica ion de elopmen . 4.1. Unde s anding Floa ia Console Implemen a- ion A console applica ion was de eloped ha simula ed he in e nal wo kings o loa ing poin numbe s, including ex ac ing each bina y ield om a C++ loa and he basic ope a ion o addi ion. The console me hods we e an impo an s ep in o de o unde s and he di e ences be ween loa s and posi s and comple ely unde s and he con e sion and addi ion p ocesses as hey a e simila o posi bu simple and easie o comp ehend. I is no p esen on he inal applica ion as i was a pa o he in es iga ion p ocess and he applica ion is ocused in posi s. 23 30 Chap e 5. Desk op Applica ion Subs eps ins ead ha e a s ing ec o ha is illed line by line wi h he ex expla- na ion o he subs ep o ha s ep o ha ope a ion. 1. Nex S ep: adds a s ep o he ope a ion wi h a gi en i le, which is conside ed he cu en s ep 2. Nex Subs ep: adds a subs ep wi h a gi en i le o he cu en s ep added o he ope a ion 3. Add: adds a ex line o he cu en subs ep added o he cu en s ep o he ope a ion 4. AddHighligh : adds he numbe ha co esponds o a lowcha box o he cu en s ep. 5.4.3. Flowcha s The lowcha s a e c ea ed by he main window on ope a ion s a and show he low o he ope a ion in ques ion as seen in Figu e 5.3. They ecei e he cu en s ep o he explana ion and highligh he ele an s eps. Figu e 5.3: Addi ion lowcha 5.4.4. Glossa y The glossa y is opened wi h a bu on in he bo om igh co ne ha shows a lis o e ms and hei de ini ions as shown in Figu e 5.4. 5.4. The Desk op Applica ion S uc u e 31 The glossa y’s e ms and desc ip ions a e pulled om a .json ile. Figu e 5.4: Glossa y 5.4.5. Applica ion low The applica ion low is seen in Figu e 5.1. When he applica ion s a s he main window (seen in Figu e 5.5 shows he use he op ions o each o he ope a ions. When clicked, he window changes o he ope a ion window widge shown in Figu e 5.6. I shows one ex line o inpu and a go bu on o one-pa ame e ope a ions like he Figu e (con e sion and in o ma ion b eakdown). Fo wo-pa ame e ope a- ions (addi ion and mul iplica ion), a second ex line inpu is shown o he second ope and as well as he op ion o do he opposi e ope a ion (sub ac ion and di ision espec i ely) as can be seen in Figu e 5.7. 32 Chap e 5. Desk op Applica ion Figu e 5.5: Posi Tool main window On clicking he s a bu on a ex box is c ea ed ha shows he i s s ep o he co esponding explana ion, and he nex bu on (on he bo om igh ) adds ano he ex box o he nex s ep’s explana ion. All he ex boxes a e dis ibu ed along a sc oll allowing he use o check all he p e ious s eps. The s a bu on also opens he lowcha , which shows he p ocess o he whole ope a ion and highligh s he la es s ep ha is shown o he use . A any poin du ing o a e he explana ion, he use can change he inpu and p ess he bu on o s a again o go back o he main menu o go o ano he ope a ion. The whole p ocess can be seen in Figu e 5.8 which shows he ex boxes o he addi ion ope a ion o 7 + 15 wi h he lowcha and glossa y. The glossa y is opened wi h a bu on on he op igh o he main window. I opens a sepa a e window illed wi h e ms used in he explana ions and hei de ini ions. 5.4. The Desk op Applica ion S uc u e 33 Figu e 5.6: Posi Tool ope a ion window o posi in o ma ion, a one pa ame e ope a ion 34 Chap e 5. Desk op Applica ion Figu e 5.7: Posi Tool ope a ion window o addi ion/sub ac ion, a wo pa ame e ope a ion Figu e 5.8: Full display o he addi ion ope a ion and he glossa y Chap e 6 E alua ion o he Applica ion In his chap e , an e alua ion o he inal applica ion will be compa ed agains he applica ions p e iously s udied. 6.1. Cha ac e is ics The de eloped applica ion o e s many cha ac e is ics ha we e no p e iously a ailable o lea ning he posi o ma : I o e s s ep-by-s ep explana ions o he main ope a ions o he o ma : con- e sion, addi ion, sub ac ion, mul iplica ion and di ision. This is a g ea help o use s o lea n he in e nal p ocess o posi s wi h p ac ical examples. Among he ope a ions he mos impo an one is he con e sion which is he big di e ence om loa ing poin . I shows how e e y ield o a posi is ex- ac ed om a decimal numbe , how i is ounded and all possible excep ions. The glossa y o e s he use easy access o a lis o common concep s ha may be con using o beginne s. I is a desk op applica ion, which means ha once downloaded i can wo k wi hou he need o access he in e ne . The applica ion is open-sou ce which means ha e e yone can access he sou ce code and make con ibu ions o i . I is a ailable in h ps://gi hub. com/dagodoy/TFG_2023. 6.2. Limi a ions E en hough he applica ion o e s a as a ay o u ili ies o lea ning he o ma i also comes wi h i s own sho comings: 35 36 Chap e 6. E alua ion o he Applica ion The applica ion is missing ea u es al eady a ailable in o he posi applica ions such as posi hub’s lookup ables. The explana ions a e plain ex which can be con using o ge used o. The s uc u e o he applica ion does no allow o colo ed ex o mos kinds o o ma . Requi ing p e ious ins alla ion also means ha i is only compa ible wi h Windows 10 onwa d and is ha de o access han a web applica ion. The applica ion does no allow he use o choose he posi ype eely unlike o he posi esou ces, limi ed only o 8 o 16 bi s and an es o 1 o 2. The applica ion is only a ailable in English. These a e all imp o emen s o add in u u e wo ks. Because he applica ion is open-sou ce anyone who is in e es ed in i can collabo a e in o de o poin ou and imp o e i s limi a ions. 6.3. Use cases A main use o he applica ion is o help people doing indi idual esea ch o he o ma . I someone on he in e ne is in e es ed in posi s hey now ha e access o all he ea u es a ailable in o de o lea n he basics o he o ma : i s s uc u e and how con e sion, addi ion, sub ac ion, mul iplica ion and di ision a e ca ied ou . Ano he main use is as a complemen o compu e science cou ses, specially in uni e si ies. I is impo an ha uni e si y cou ses on compu e science inco po- a e posi s (27) ei he ocusing on i s s uc u e on he compu e a i hme ics side, i s possible ha dwa e implemen a ion o i s uses in neu al ne wo k aining. The applica ion would be a use ul ool o help s uden s in unde s anding he o ma and, in ime, help inco po a e i in a in oduc o y le el along loa ing poin . 6.4. Compa ison wi h p e ious ools As RacFP was he bigges e e ence in he de elopmen o his applica ion, i is impo an o compa e he end esul wi h i . A ea u e compa ison is made in Figu e 6.1 whe e i shows ha i has some addi ional impo an ea u es such as he glossa y and a s ep-by-s ep explana ion o con e sion (while hey may be conside ed unnecessa y o loa s as he p ocess and e minology a e much simple ). The sign ables a e no p esen in he applica ion because hey we e no conside ed as ele an as he au ho s o RacFP. Some usabili y imp o emen s we e made aking in o accoun RacFP’s ew sho - comings in ha ega d. The mos no able one is ha i allows he use o see he whole explana ion o he ope a ions a all imes unlike RacFP’s explana ions and so 6.5. E alua ion wi h use s 37 allows o check p e ious s eps, unlike RacFP. I also allows o manipula e all open windows wi hou needing o close hei seconda y windows. Fea u es P oposed RacFP Posi calcula o Posi lookup ables Well ounded Floa con e e s Explana ions o : -Addi ion ✓ ✓ ✗ ✗ ✗ ✗ -Sub ac ion ✓ ✓ ✗ ✗ ✗ ✗ -Mul iplica ion ✓ ✓ ✗ ✗ ✗ ✗ -Di ision ✓ ✓ ✗ ✗ ✗ ✗ -Con e sion ✓ ✗ ✗ ✗ ✗ ✓ -Ha dwa e implemen a ion ✗ ✓ ✗ ✗ ✗ ✗ -S uc u e o he o ma ✓ ✓ ✗ ✗ ✗ ✗ Glossa y ✓ ✗ ✗ ✗ ✗ ✗ Sign ables ✗ ✓ ✗ ✗ ✗ ✗ Mul iple o ma p ecision compa ison ✗ ✗ ✓ ✗ ✗ ✗ Lookup ables ✗ ✗ ✗ ✓ ✗ ✗ Visual ep esen a ion ✗ ✗ ✗ ✗ ✓ ✗ Mul iple languages ✗ ✓ ✗ ✗ ✗ ✗ Table 6.1: Fea u e compa ison o he p oposed applica ion wi h s a e o he a e-lea ning esou ces 6.5. E alua ion wi h use s In o de o imp o e he quali y o he applica ion i would be ideal o pe o m a e alua ion o he applica ion wi h use s in o de o ecei e di ec eedback. In his sec ion an usabili y e alua ion o he applica ion is p esen ed as a u u e wo k possibili y. 6.5.1. In es iga ion objec i es and ques ions As he e alua ion o he whole applica ion would esul ei he in e y long e alu- a ion sessions o sho e ones wi h lowe quali y o he answe s he e alua ion would ha e o be sepa a ed in mul iple es s o sessions. The goal o a i s e alua ion is o know he ollowing poin s o he applica ion: 1. Ease o unde s anding o he bina y posi s uc u e. 2. Ease o use o he applica ion i sel . In o de o e alua e hose goals he ollowing in es iga ion ques ions a e se : 1. Is he use capable o con e a decimal numbe o posi a e a session o use? 2. Is he use capable o con e a posi bina y numbe o decimal a e a session o use? 3. Does he use ge s uck in a speci ic pa o he applica ion? 4. Does he use open he glossa y? 5. Does he use manage o go h ough he explana ion o he con e sion? 38 Chap e 6. E alua ion o he Applica ion 6.5.2. En i onmen and du a ion o he es The es e p o ile o he applica ion could be Compu e Science s uden s ha ha e ecen ly lea n abou loa ing poin and wi hou any p e ious knowledge abou posi s. The es e s would ha e 20 minu es wi h he applica ion ollowed wi h 5 minu e ques ionnai e and a 5 minu e in e iew a e . The en i onmen could be a compu e oom in a uni e si y o school o i could be made emo ely ( h ough mee , disco d, e c.) 6.5.3. Desc ip ion o he es e ’s asks The es e s ha e o open he applica ion and expe imen wi h he con e sion and he in o ma ion op ions o he applica ion wi hou any help om he in es iga o s. 6.5.4. Ini ial ins uc ions The in es iga o s should welcome he es e s and ell hem he p ocedu e o he es : hey would ha e 20 minu es o expe imen wi h he applica ion and unde s and he posi o ma and hen answe a sho ques ionnai e and a sho in e iew. The in es iga o has o ell he es e ha hei sc een would be eco ded as well as he audio o he in e iew. 6.5.5. Beha io o he in es iga o Passi e obse a ion o he use . The in es iga o mus no in e ene in any way. Be o e s a ing hey would emind he use ha he objec i e o he e alua ion is o es he applica ion, no hei capaci ies. E e y in es iga o would be wa ching a single use and would be aking no es on he obse a ion poin s. 6.5.6. E alua ion design Obse a ion: he session would be eco ded o pos e io analysis. The poin s o obse e a e i he use opens he glossa y and i hey go h ough he con- e sion explana ion a leas once. Ques ionnai e: he ques ionnai e would ha e ou exe cises o con e sion ha he playe has o sol e in he gi en ime. The exe cises would be comp ised o wo con e sions om decimal o posi and wo ice e sa. Each one would ha e an easie and a ha de exe cise. In e iew: he in e iew would be mainly abou he answe ing he in es iga- ion ques ion "Does he use ge s uck in a speci ic pa o he applica ion?". 6.5. E alua ion wi h use s 39 I would as well include a ques ion asking abou gene al eedback om he es e abou he applica ion in gene al. Ano he possible e alua ion would be wi h uni e si y p o esso s ha could b ing in eedback o i s educa i e alues om he poin o iew o a eache and e alua e whe e i could be inco po a ed in uni e si y lessons.