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Possible 4. chet t er titer __in__the _Neceiveel dota. oe —— We 7 The volue__ o} additional bits ckepemda on thease. = ee Dates as el as thee —dype of — oer —— dledecding cece which _ Usted. -clasing fhe + ___ 4aansmission- macitnacenle _— Pe : r] —anith a the bp ren _cebecking —tede_,it is possible _# re _cleteed the evyou th the veceivel eboda. ‘ Methods 0} enor defatione - - Cee eso CRC J Pay Simplest one _& +0 adol _ the paarly bil ——ebeng. with the data: i ° 1 x Data Bit Detify Bit (&} CamScanner fol) lool \ my Even be ; Rans.nittey ee _ _ Resoiver _ _ ____CEvrey) _ i => Ak _ Yecciver Paxi y _cuveyit ~~ will ehk the paxity o} the earived — tole. SF there "i no _exyoy the f= pasity shod be caval to och. = = —_ =) But eye's an eyvov = bez No dh 4's Be even, fr rs . Per “Ll fel [it fe] a 7 iv 4v0lo ; : {000 aa x odd x ee __CEvyy) eS His Wa we. can chetet thet there tw an _ _eaYonv____ fb t we can nok Find the _evack Location _ _ 2 She @>vov. : a — hea Moreover _ Mneve neve than 2 eey iy Neuiwed coche. ten _rvmber__°}_exgers inthe tale _ then with the help} the ___paaify bik __ we _____ Cannot dedech the eyver a etn No _ A cums Even moe pieeninsipeerenineen ein _odd ei odd Sf edd Ne Dens ven edt Ervey . ia odd ———_— Even . Dekeates | — ee > _ Exior Coneehing — codes. — So —corecdting - codes ave usech in __apphradionms ye wheve the __yetvansmission is very. costly oy it ik not S34. ——Thiy te __vsech__in one away communicabion stn menses a ak te in _satebite (&} CamScanner ——Hamming Distance. . —— amming Distance ig te _nvmloew 9} bits _pasitivn Oo ea Sf You Yook these we coclea anol 1_oo 4 _ they —“u_dliffev__bay_ two bit position Thats means the arming Distance — bf Ahese___twe coder “tava fo 2. 0 © 06 1 - S£__ yoo Leck Mitse _ coeleg_, they That means the homing clistance blw these hwo cooles 48 en val + 3. | im mm —Hamni9g Distance i a i smallest Harmming Distance between tot pee in _the given _¢ enesding scheme. __ Decimal 842) Bcd D Oo 9a oo > 4——- _ ~ ' oo oS, So the minimum __ Hammirg ~~ x o o |} o DD istane c 2 3 Co a 4 1 2 0% (Means if rarer a =@ we get next valid code) CamScanner PPESS: | | | | | | | | ] | j i a ill saeerenensinenanlil » Unies al the 3 bits get — a we wil nok vec ste the ned abil codes he 9 Showt , Mininwm Hamm Distene Hos us | ry —_— CL numberof — ee ne hs tothe anak Velid ode lala P | : yi pip i Sn General _vsing “pate ney scheme 5 a Nl pe Ea nom the —_minimum__Hammin in that _pavticufay __ ceiling scheme __shovd he egpual to 8A a bits co} _ewnr olefeetion ; — Minimem__Hamming Distance Amin —= A+4d JSF _ Ac covert ol number e+. CONS. —— then Mae nin mm —_veazuived Havin! “A clistance in Tt shold be eval + i ALLL ie len a, bid: a ewer _coweckion - ee Mirman Hamming —Distnce Al gig = 2h AL 6 = (&} CamScanner Hamming Code. In vepetiten code 1 = A444 } Same _ bike ig tans mi thed — Z 0= C00 m4tulkple time ae ficiel—tde : : _ 4411, 000 =2__For_4 bit of emor cover trin tue extra bits axe Sok _ ad's ems the Yfy othe Ad bi ave tedundent bik. _ => Fox the game number of exyor correct aan lpolaopeppepP eee ‘ail, a | | the efficiency. of —the _cxde Can__be improved tM wit _* the hed) o} Hamming code. r Fa Sh case ¢). Haring code instead 0) ending _sarae__[pids Multiple om T T gd 5 ___ time re the exlia bits ave the Paap Parity Bits. e Hamming Cocke a) Xa fe) Xa X xX C om vuaat the pauily a Page caplandion J the on bits in the ovew al@ ade _ —d SS Now, Leme Foy one (4) bit of _etyoy. Covrection 5 Hor unt — pasty | 5 ave__veqwiue dl in Wis Hanning coche # 1 o 1 X3 0 xX, x, | ms Data bits ks Dawity bits. ns. Length o} the code ie (&} CamScanner =k —pasity bits the dy recaps hese Ui f feeent CHADS. =) Moweven Tey shoul be able. _to__relenbify the state ep: no exvwy That means aif hla el teh Ts — ideally tofnd att __ cli ffexent ewes using kk Paasby biks we Can vepusual 2k stetes: 1 2 = makr4 = Necessart condition fox __ Ham ming code. Ay me ane k=2 => (3,) Repedits bn code ZN Leng He o} Dabka bits code $ Popuday Hamming code in — (F,4) Harms. ode ne Lenath ie} C T em Dt bits Ke Daaty Ais z 4 B W iv (&} CamScanner a Pa ep tens the Pasty 4} ato the bik XN __positnn —_svhase sean LSB= 4 _ anne a weaver dy the bt psition 3,6 anc + Py Bb and euen _ Py = 2, OD, © Oy Likowise, Pg neprcscnd the pawits o} ald the bit postin whose Ms = 4 Se is eva fo the bit _pesiben S, 6 and + > : Ps, S 6 and F even te P3208 0, @ Dy ~ ~~ Fxomple:- _ Daty bits — |e | o te IEOEneeoe oan vw oo ed euch e = oO JN { »o (&} CamScanner Bos 6 and + cata Pp, => 1 3: Sb and q euen Pz = { o ft sy 0 So 7 TTP Et be} bef by fe} So fax we assume even _ PP axify Bat we can ase have Pai é odd _Pavity leks sce how st cont 41 bit pwey. Faumitted bit — lolootlo PP? AAHilalapvpraawnepepprprer At _yewiver dve to noise __ohe__bik get Lippe __ _ Reeves) bibs - \ijoelo ms te \ (e} [e) l Oo ] | {it | e — | eon a OF CO. 3S _F and Py \ \ ° 2) of 4 9 eve gs, fal (&} CamScanner [e] [od [e.) [oJ [e] [ol fe] Tel F Si this Hanmi cade —wsith —extva pra bit known aa the > Exton cledl Haan 2 cco eehanmeaneanianinnes This evtindecl Hammi he CXYoY. and d etect _uptn swe eonots Led Haramingy coche {_olootlo i; g __Fitenclec! Hamming cexte | | o loo 10 =) Even wllalalalalaiain anaes pepper Received) Bi Li\\oolo => odd Case 4 — One e-hyoy St means theve's an __evyoy 4 Mowover Cz Cg. Cy (che kbits) ave non zero & confirms thet there in Ae oy : Case 2 = No eticy The oweald pasty rt sf _enfite code th eyes aan p) Moresy ex Ca C. axe Zeyo and Carcfiven s that there us Ne éxyov: Case 3 = Tweet ov The overall pas bit 6) ene pode Uw exen tr T but when ue see the cheglebits C3 C, Cy these wy 20 pe pon __Z evo which indicates that thete __ aye two ers: (&} CamScanner Cose US Fyyey in the pasty bit 'p ' g The Over al paxity e} cactive code wil be odo bx when we cheek dhe Ca Cy Ca it w00 be CArval te Tet eo - Soe ih Ayes re) we Lan L ore one €yvov and aletet upd hep exer - Overadl Check bits _ Case T j Lorex} odd hon-zZero Case Lr Ans eter f evey ZENO, Case TT 422 caver} wen hon — zeyo Case TV § Ener in p} odd Zero T T We als have othe Hamming cxcbes (3,4) Hameins cole (2-1 2" ie ks) Ik = Pavitt bits Os, 1) Himaung ede 2°-\ =n (Te4nd bs) Y-\-k=m _( Bata bits) (31,26) Hamming cade ———$_ (&} CamScanner 
