aes 1 oe MMRexing yealtate = Z Digital legrcal — Designtag * qnt ) Z 1 ® unt = | ” Dightat Sy grem ond Binary Numbers Number System KR iumbher System 14 System wwt+h Aome base or radey ow In ony number Systems cotth bate lor) radia (1) hoving Aigtts trom 0 tw yy Binory Number Systems Rose 2 0 +o 1 Oo and | Cea number Systeen SE Rose —§ \ o> Be tea BNO Dearmal AUMHEL SYS: Rage ’ ow we Ls 7 ot 4 Oe ee De BATH BT ( Hernacte comet NUMbel SHStMm: Base —t6 Oto 1 OAV GS eH HV, ALB, Ce DEE Conve tons Deureol Hy Binary Aurrber Sybtem Xie Should dtucde whole Ao: pare by 2, and voc Ghoutd corete resurt from doton te UP Ch s = fos 2fe-t Q 6-D ab \-1 Gantt divide Furtner $0 Shp. Civo0 * TH wohole pare and deemol Port both are tncuded Scanned with CamScanner(reo = (19080 ON gy Xo tte Shartd deuaide decemal & and Pare we Femasateg Hs Cree), = cls & gla—e > oooh eo mek = ou xt (65°69 9 =(toovwols tol eol y+ the Shoud Procedure OOS xa, = G20 dDwoKs - Veo! eg YH = F203 israel Shands tere in dectmet oe oo Pore agg SS O65 X22 B07 a party . bowes 6.60 0 OYox«® = O-60¥2 > byes) Oro ¥d 640 ww 50 Hoot | Yepeats 0 Duo x2 = 0 ow xT t oGord i Stop * as up te down. pare So deyousos meat coe Merve the ») tal & qtuen colth § and if there IS martrply the de cimot cot Port Came &% a hove Ws (Urer6e Yo ) = (210 CIN be 8 64 36 F OW CUE Dg One et Stop Because oger® atready theve 1 eradcumot: ry ( , = > W Ie Shoutd dade the giuan by 16 and if there 16 -the a8 ohove decemat fave we shoud muteiply decimat Pare wotth lb and vemoaseiegd Same to dcumat number 1 SySten Shouid 2 toith Hy ie \ike and add an, “ Scanned with CamScanner IMeveasing Power 4 a arsa, Mal number System ty A mal no Sy Stem e r Ae Khoutd Muttyply — § Cort hy ts \ncrea wing Powers leet by Gy Amd deeweaseng pooers Fight ty every term + : gh she cl er gs » tena Ai coomag System to decemay System al! We Should muterply 16 worth Hs Yneveatsng Pocwers lett and Aeeveastaqg powers Vigne to very term. a re Wee gh gt Rone ry tour no > tew Winer ther, qtua binary just deutde them tate 3 bits Shits from yighe to leFe and tH there is deceMal yoy from left to Wight» then cortte table By Seeing this wrrte Values Suppose, FS Gr ro o eola, © 10 Hy on Chaar q Loo ly . Sa Loi ae Here one bit left ak tegtdide \VO 6 by So we beap 2 reves as yatue wonte Change fttere based on deve coon athey, pel, Cesare), Ook te Bina ry Test thine hat fs octal tohak t% binary Vike that ou colt ger From Octal fo bIRBTY. Raced on tabie above (ar), Biacry “Cron woen),, VU heRO Ae ceme, | Here exe thoutd concider Ue bits &y. (wo rrorito he Burt code tabie QS) sloreda Scanned with CamScannera ° Nb ; p00 0 Hu fete, devinoh oto b ae, . 4? to er sk Therg cot geve Some deg th cotl — 4 PY leateys cortte “CROE c ie 4 : !- erpanson bated of -toble a S 0 9 ¢ tit > 368 “4 Craag yy cy e ; 5 . , ' 5 (GbE ter by es eroren ott, oe 5 i a (oS eee 4 20 2 ocr ° a von 0 | aaa Convert ectar ty binovy a ec 4 “Sed o ‘ SN Aamte and then by ae Fak beng 4 bits U bits Convers to Weradeccmat haged on ahove 44 bie 4 ay CASE = Ody Co eS Cee ce € ; i CASI =A Henca ok FS congicter this and convert to DiAory and further 2 Conver {Wis brmory ty ockat by raking z ber 3 bets > Ss eed, =D COootiviritoo), < COTY) = (aay. AVthe mane addsh'on Orns Ta EA Vp, oon ere! laoszt LOtats t¢t. 2 © carry 1+ j4 owo +? j-o =| f , yep 20 oat = 1 Chorrow 1) case ie ombinakton — 1 (A on oe of Subtraction Murerpwrcass® iy Some then = Somethred | be1e j te Le Lolo = toto en f Ox Something oO — i A roto p OX1010 = Goce + a and then followed E by addon x Octal Addition: Moe Suppose eq; re ' oS GS a4 cohich exceeds by) Myr ¢ Q i = 80 4 ual $ ican dauade og LE Care, FLO Sg — ‘ ; Lt seato V You write ORO K igey BAe Wand 1 Carry C.reoes Cauyat v e =u § 1a ¢down and | ren te cave ‘ YOu ger lees the. wry | ary YO = Noe posstbie 4% S thea § rite an ie rg, a So boyy em 8 Ath / thea Bayo ural Murerplicatio: 7 "SLOSS than Corte ag & Go You CanHERG deumad to benary 4 Ce cre=qrs 8S " rot 6 6 4 ox — Like thes ockal MULEPICCak ogy 1B ye 1 2 Oe Werodeumel addettor ey. oe FY (AOE) 4 C561 ! 1 ol 21 o ee Fey = uty = 21 016 ao 2 a 5 6 4 ae of 14046 = 440234135 203516 &-4 cmc So diutde by 16. ; SE Place this | teradeuimas . eee see * Sabtrackon nate and 1 in Carry = like + Fea a meee ¢ S Jig HOW aA fo eis Ac py AD evo 4g a Rok Poserole (e€ Da, Se berres ie adie ce ec tottt then RQ changes = 26. Meow = b to A cto: ae > 26-9 = 2 : b-Z az ey ' a tenade wma Makton DAAC ceemad MAREPIEAONS CEI CATER) g 4 ye Vea ect Bee eux : al , . R = UID = 2 dI6 x cata a . a a obo = = - “ a eu 8 FL 2=2248=% ow 4 ae 1-€ , S ,oe 5 SH EBS = 6051 UL Go ae 1B ER gee . abpie aa SAI =WtS=EQeD g-e wlire + Way lo N REC = tox td= 0 9>t6 aes teQy wa A*2 swK2 2049-2 3 bea 23 an y WOR ri Scanned with CamScanner6 EE a ee ty oo fia..” Ceg Ht Cree Jn digital Sisiem iE the System requires ‘ j c : Subtracen — opeyattoen te doeg AOE Enos the Subtracon e prectsS . but the Bigital System enous Only Addetan Process, So thok the Complement xeclanique th used to gee Bubsract j feX output by addition — process? f Theye Are 2 types bE Complements oThey Arve Wy Radin Complement —4 1S Complement Ds dimnighed Radia Complement —9 Cr-1)'S Complement | Binary ao. System TS Complement £26 complement) Cr'S Complement 2 166 Complement a Ot oc eed WO SYSEE OY ; TIS Complement = SIS Complement LED'S Complement “= 41S Complement fs Kenadeccamal no system TIS Complement = GIS Complement CyAO'S Complement = gts Complement Suppose ua wanted te find tots Complement then frase FInd 1S Complement and add to ie FO ger lets ~ Complement * A'S Complement = \'S Complement +1 TO'S Complement 24th Complement +1 BIG Complement = Bre Complemant +1 TEES Complement = UCTS COMPLEMENE +h Codes Coded Ramentc cates AIPhOOUMENSC = Cod ey: Scanned with CamScanner~nume Maumee Codes. Alpha~ Kumeri¢ tr wtergheed cud es ho AGCTL D. Mon -coarqhted Cadey 2 ERCOIC Nevi dW Cod % Seauentral Codes Sea e Me Seek Complementing Codey S Ewer detector Ledeg \ & Rete careg Cede A. Cycwe Code Numeric Code; The Code twhich Congigts OF Rumeric VALUES from 0-9 "S Catled Numerce cede Alphanumeric Cede. breh Consigt, of both Numeric and alphanume. cole rom 0-9 and atphanume “The Code =VlC Yatuey fe AuMeric Values Yic yates from A toz Gre Corted Wetqneed codes, The code TA cohech every digit hay ts Positrona( otphanumaric Codey. ewergqurege IS Caned cougnied Lode, Eq, Brrovy, Rep. Susty AMay Non ~Werghted Code The code iM cohich Goch digit do mor have its Postimat courghtage eK Carted Ron-Wweiqnted Code SF Encess-2 cade, Grey tode £ oS Ve aor 1 ova. Ge Wourgnted code, The Cede in Coie each digit, have & POcMIve PosiHonal (S Coued Positive coerghted Code corr ghta eq $4ar, duay, Scanned with CamScannerSe agihe voaighted Code Code fA coh, ne ‘ ‘the Ch Coch term hay hegitive positional peony WS Cated Reqitive weiqnted Code i i & io (a) fyvey detecting and Coy cHON Codes: Fyver dekeckon and Correction Codes Ore the binary Cader which Ove used to deteck Where athe rvor Qenerated ia MESSage Signal or transmission Vignal at the be Cerver £4. paving, Honaming Codes, even i C b In CWeh the dueceediagy enceeds i Cede by tre binary number than it preceeding Cade f% Catied Sequential Code . there ave Uted in Mothemod'ral MOAREPULOATONE Eqs guar , Emeess-3- Set compremen ting Codes. 1 The code which have the Property that the 4/6 Complement of a decmal Number ts obtained direcety by interchanging 0S and use G4}. ouar, emcess-3 > paudr tl to (de met) - ty complement bY erchanqging O'S and Code . and we obtain a US So duar oS @ Sele Complementing eyewe Codes Cycle Code, Ave -the Codey IW cohreh The Gucceeding Code coord diggers the Preceedtng Code eword Th Salty Aa it x . one position these are abo Called UAque distance Codes. | Eq. Grey Code Scanned with CamScannerRegtedeng Code Hews O See complementing code iW that Code 4 4 Complement Of 0 £15 Complement of 1 4 TS Complemant of 9° 6 NS Complement — of g TF TS Complement of y ‘ zwer1 o Dove ] 7 oool > poe oot iE Ol1onv t @ oer ComPlenen ty Bt L100 | Rete ceed gy Lior Re tte uns 8 tito ‘1 Sede 4 vv Te RS eoerqgnted Code + Siighe Binary code, Bright Rinary Code os Used to Veprecene Numbers ting Natural binary form: SCE Conmplemented ele FEF Ong ‘ Excess-% code. We are Fepyegentng a Aumbtr by adding % to brary number + Beo cede (0) Saqay Code Wek RCO Code te based on Sart Code based ON Mak 0-15 we write Code Scanned with CamScannerHarrter) BAD Code ey 2 Cc 3 MoU code Cosutr¥t F Q4utral = to 5 . z° ee oc) =a) r / 1 vool oC Bee oO / 2 eo ovo \ (ono. oa 1 2 oor 2 elo y vw ioe cy oud . . oto} y o 1° 6 ee c @1 0! tee) \ : ‘ t 110 & Looe > rio : 9 too! lo toro 5 ee u On! 4, Ree iN Loo off ’ , % a wy rrr1o ns at i SAWN Code. Surt Code paar HD Mey Streets 4 (mowed) Coren 0 eee P= po oe Q Bw oo oO ) - ee ol ' oe bt a Oe, 2 bo oe vd RB = COKN hero z o 1 | y — 8 NOP compte s —~ abot y o vould pork 6 — or10 5 \ ooo°o . — ortt 6 y,oorvo g - orrt > , loo tr ovoro q _ y 100 . oD g tov dy Scanned with CamScannerfences 2 Code, Rinovy +2 - Ved AZ =Gure+s- 5 fart IG ©vo00 ool 1 oool o.oo 2 pore ov ol 4 oot Or.\L’.o 7 ooo Owls & -:.% ‘ O10} meee : ote t oo | Lov. + ori Vout . € ee 1\ooo0 Loo | 4 ~*~" Scanned with CamScannerure Code + de 1S AW Enocon a4 Unit=désdance code or FO Fleceng ode For AWS we Convert > decimal to binory Fiygt bre os Ue TS > Rinary to Gray Code . por anes Nets pyre 2 bre t We Reed FOR operations AE we odd ne ee 2 hor 8 ‘ € US oR at apie HbrE! AE we Cuan Po og US KOR =O! Sea Groy- Code ° © 0 Oo op ov? 1 Oo 9 ON oo oO} 2 oo 10 oO o 11 3 oe wl o ote [ bo tee o yt? c oN 1 e vt \ onan o Ve! 6 yp \ 0 o wis > ror , ooo : yr et 1ool Meare 7 \ toro ie rae to yoot Mw 4 1o io ivy vree rt yo re sy 1 001 vito ws ov vorad ny Scanned with CamscartilRep Addttto M5, CS) pt VD oy 25 > vo10 o1o) rr Us =) OOD ooo N+. ey? 4 peee. eee eee Olo0o ory, j 2 7 dsb the Suppose Were jf the esate ene s by 4 4 add 6 +o tt he ones plate right Side » tAcremene Add 6 teeta enty 4d the Pate plac ewhrch ; a trereesed P44. oy any other place which increased t bya: ‘After Performing addin woe Sheutd qek re suit OS Normal ad dition OMY» Ber Sabtractton & Nowmnol Subtraction > 2 eter b Slot + oot | Tsy Dolce 0 oook OO'1D + COLO vool Oot + ooo! i y od Now Some mes het O=-1 = Aot Possi bee Then coe take borycw we gee Ol Combmakton Loe worite | then thaye Yemons o for nent aque o-\ bur Ves, Proceeding Lt not have 1 ok Bmeg we use waived = BOY Sulbtrathion . ae Scanned with CamScannerfetls Consider both ani bers add that | ty the Sum 4 Ahan hak coil be Fesutes Bur Sometime na Subtrarton if te exceeds by 4, than Subtrocr 6 Find BIS Compteront Then add thok his Complement and A: then Sf You gee any excess bie ke Covry ft ‘ ' Prom thar enceeded elemene % &q 7 “Js aso - se el 1 ot Ht not possbre « ase =) Colo ovel see ont not borroe ofS FET ‘ cool 1G0o el howe I) ; ' tement OF b Go Iadtveck Subtroct “ Mow 116 Come 7 add he with O bn, « te cowry tS there encess & add it Ocoee too We , 1 co) treo tit eee exceeded bY 4 SO a " Subtrack 6 from i vel oy un oe cove Ondo WIth prtye oll ©) See oo00 O10 tool acral. iy gis © 64Digital System do digitar Sytem Siqnats ove te presented Phy O or} low Signal Ww Ve high Siqnal Le System that Mantpulates discrete Clements oF Tefor mation + : ° tisia A digital cystem (6 a digcrete tAformat' oh Processing Syste m > &4. cetucutetor digital voitumeters » And geneyal purpose Computers» Sa Such Systems atl Quantties aye represented USing ture Values * Shik 16 Not digital 1S" Anatog’ + do number Lgred POMEL Fraving Some Posttive OF Reqitive $i4n . i 4 Li at -a or 4a ONO Utfere =) 0 Method | t ~ ->) at Seqnéd Magactude berm Prefs | o (NNN AAS OWN fae they atrun it na represented on Siqned. magnitude ahan te ws +a} -Fs trv Scanned with CamScannerbo wp tanent peo -) DS Comprement 4 Wee Ais coc re pregent — tanks eet Signed numbers. — 3 1e00 Same ‘ oot SIMCME Ceara leanne acne metic? (Subtrackten of Larger from Subtrack Aa from SY (s4-¥2) Neve Fr iS Suprohead Chig ) SH eS mtatoned ( smatt) Step. tare Sy Ars) VS Compiement fora 2s Complement form « ta VS tomptemear Fa ree Comtement = COO US Compiement O'S COMPLEMENE OF Supehand 6y 32 te BY as ot r9et10}8 ' ov ol ovoo-: Scanned with CamScanner*Take o's Complement — of Suprehand + av . Br Frad fist US Complement and then add 1 to ger A'S Complement * 2 NS Complement of Fr + o1éort !l a DIS Complement Of 425 1's complement +1 ‘ Oorronrtt wo rut Oly 1 OKO . Sepir, Add t& td Minoind (Su) o1r1oon0 My ot10 41° wr 6 ; a y;}bro1 1a fore em added Fb ard we gor Vesa alto MM re fk nw FHbIE 35 cohen you add Same novo Hef And JE He yesute tM Same fe of bs carry ty hoe There steps 88 4 ceri carry tS foe geneva ced Say thes reat to be NeqiHVe fame LY Giga Sea ' esu To gee actual esate Fate 3's Complement of FESaCE agai l q tro tet 0 " . oo 1 US comp oo to ; Real , 2S COMPS \ —ssree re surdn =-tg - 0 e-2 Same thong , ett For cross Checking resute * ~ Scanned with CamScannerAES CEMAPlement method Above Sowe procedure in place of a's Comp (ement APPLY OMEL Complement and during decoding owe SHES Complement onty + A Yantty or NuMbes to he Subtraced From anothey Pr ’ La Mtbire Aen Seo ltr from larger Une ment Metued 7 She Apltment method O86). 6-Day, Here Supranrend => ; Now 6210000 a t=cortl 7 Mou find of Complement Of NS Complement =) (Woe? \ » OS Commplemencayt {Loo Now add 1 aad -yish ; ' 10000 rr oo t @) we goe Corry here bo we Siqn is ‘tf! Mow Verity oor SASOCY lety decode Ct See ; Sas OG eee et tO \ ONS ath tt Oma ~ Here we Shoutd discard this Carry bit bf Scanned with CamScannertwee get answer Now Crogg check = 64g AOQwey =4, Nok When coe Convert decimal to bmary fe Aevey the Ccompuser Performs Sub tro ctvo? dire ety and then adding ite TE FORE ary Cemplenneat ONES Complement Quo tya tran Qe). -Cy)e } Now 2 “eo =) 16 => tooo >> of b! Kou ores Complement of F= 100 0 Add both | No method Wee THis h | | Abou metnod Ss Sm | A's Complement Form p Take US Comptement Of Suprahand a. Add ft to the Miaiond are Subtracerng larger from Smater Pn Any Th we Cage - we have aot if Carry ig * generated then resut is Sard to be. ptake 16 sto remember that Regrtrve and is ih 1's Comprement “form form again fo ger Otuat Teauce Complemant Here 3 ida Scanned with CamScanner