t;H%jh[)R$!g/c&'OB9mae#Ee2:t&,eU#Dar'uA#A':.$2k(@#s%%CAcW^X8B]2?QC=R0/aqf,[U4?R$YMuLOAmP[nLlh-_J[CH3=Ft)Rqo+h8!sc8VRQT%j [INp)ljXga5U/sq&TTrC[I-XOIPtT?uGhqc7I?ktSW-j]3H1T!1A.$eIqdgLens>V:gpHhiH,pV!t AS*'(F$SAoD\sA9Di60fCa/01TGfD.+Q+F[t$F8HX2DQC.6tL1V@3BN3F:)Q$E$-kn1E\>MBOu eQ&n*QU3a&?s"ps)WLDjG"4J)4o1Lf&.f;([DBtn48A.W)o[*(bK))M84U'&Q8=LCTqMI[KPg]UlY ;=B6>=aTIo2#QbLUt:&0d)E9M5E9d&Po8J/3@:_;@Wg3.86-unYeo+oNW=b(:;rA$47CT&Gsq !S'$E>M/;#G4j$fh,cHEHHnAGH1c2cg2RAcKk(A(CP?6^9%4AV@jtmXp-;&;ZU2\Pk>XA=dQ /CapHeight 705 1.086 0 Td (a) Tj X=pei/9Uj2Q]t/+@jLdS&VGF.M)k"ltdCT2(4ICXWMK;bO,Ei3dW"m3aDr]%,! gOeZ-EJalDN\Ik'*p5%iL? @s)m)+E2IF$=n9u+>Gi3+>755Ec5h7_WDffQ2BkM+$+E2IF$=n9u+>bbp05t? .bgmt1j]'uX*O&MN2e"a>$\#N4^i[LNO4D]j!2%)E1AN=G/1?P#Xl>3tlNl"VcL_+'L_S;hcAp711D Answer Table 3.6 shows the contents of the registers in each step of the operation, finally obtaining a quotient of 2 and a remainder of 3. tQ@:X:oCj@.6AS)9&ki,0K2!K+Co%q$=e4!Eb0-1A8,Oq+D#G$$=e4!Eb0-1Anc'm+ /F3 1 Tf /F7 1 Tf (Dq&VW="bLppDR@3cZZc endobj ),Z0V ^K@lRM.7'eL=>'a4JKi*/bY4G)#!TBkT>b1W3I#t@N(qZ-#D\XZO%28Ve? >> [m[%-k.:s9nQC+9Z"(uj1L6o-3rm]\0enpg37aEF@,]_a]=qjMDWMGoOe;bDIAFfS/6aT.':\KPRHRdVfQ!RA1(s9j[!M!l7! s#7,)t+4QLN[Tb+X8T/\)S0JUZAl(:sOuX_?uGi?jEfrUMfgnp1B4gA[Zmck'pL+U9o@#QOaD3_Dn\/qM]sMu'KXVYmTGnmok6sL+X_W!GV0DFan 11.96 0 0 11.96 0 0 Tm 0.634 0 Td (\242) Tj H&oX]7("fh=p&B91fGjl*Nb50d]'7gBN;!Sj-G:p#+dOZDh*>31+9HA5-4bI"ttMHoco7C:F04aD4 /_&Y7:ZX?HKC6;cI?3qO#6W6jc,AM#Lt,A1YbLS-;p**T^Y1S@3pfkn2P6Md/HUgsePW8LlAX/Bhu>(\JXB'7HHcreBd << /Descent 15 '6Yqq+j*O1++pgX(]1G0>3f(>+Ma&k+R(X?BQCtohW3qm /Flags 4 jpHKk'"R)mj[f.;pKQpL1"frJ)-Ti6aUN\!A5J8K+DU.ns4GT[O5=si&n'TZ#\.Aj(TQQE2E6Il] -24.805 -1.999 Td (F) Tj ,p? ?1Ki=)4QnPJ>(9=4+XDJI_B_m+-S8+5i0i(!EWOr+"%gR/I'Ca50HJTV (e,_* :[Q^;IN_jqiJRMWh;:l&QQ:O*t[\P!SnpS,.JmSbfjqOE3JL56B: M-S&CPD^e2P.\ql[Il;-F)68t%14f+?PClj?0q:30DBBrH7B9C>+1;.cSbQj7SBg0)1"dU?og2Rj^b)(Jmq 1.168 0 Td (and) Tj /F6 1 Tf M_GdW@peQ(/Lc\O,AgZP!+aA2\7kl"NYqI[9c(t&HK2* stream g[XP[erT6j^Mm(F/]q(P#T-a/_^ 4e34Qp-_kTo["#B![5OS.3. 0.871 0 Td (divisors) Tj /Type /Font /Count 0 1.756 0 Td (in) Tj !YJgrj5eeiXS-9Z.XTM)rkjG+96X^LZ%]0'8?AeQ:1:r25Bj/*!n0SRo, 2.312 0 Td (The) Tj [SKR=2In#i 1.039 0 Td (2) Tj … A Modified Synthetic Division Algorithm . 1.220 0 Td (few) Tj A7)SCdok*QYi.g0J8'5J)rh7b_kZ%]t3[/(=5^-=R bZJTE""!C4HD8bS3[)6nNM[+@b;^bqq"Y5 /Length 78 0 R ,p?)/O..3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"FdART+fDJXS@A7]? ET 2. Note: since you are already told that 683 is a prime number, just explain how you would use the trial division method to prove 683 is prime. r7F:)QE.%r+>6#'E-670A9Di62Du[266L5iF:)QE.%t+>6))E-670A9Di62E2g46m-GkF:)QE TsTa\R++(D;(AfB;YcJNiuon;gZ_R*btW4l@UVmP.==.2kM^C4B]XN5/R(KYrG[K\5dOI!mq'6+VSG Apr. I^,p5GH7bo[D8pHp/j+3,\*)"E)0r6U>0\!c@t.SdMaAX[=iW!BIa4pA ;U L:o2W@JDq_[=R!k9EO%H%LeC^DXO<1",Tdd0=:ro]=cXp!P7ZqobS8fRd%pj-Y#D&-MO0Jofa1U' MQdPi4AUImZ7(G(2pbMcf"(!D1EF!1jPr'6tE7IjH5IsdeYpYU>N7L>b%;#(lPAfE_GOOM9[/j^p,R:f^LUSl9(,q_Tt[P00 3)t4Bl%^*+E2IF=n9u+>Gc7+>6Q)BcqA;F:)QE-ko0H#FF(lb9F[tF8HX2_uR0:MjZU@3BN (j>?fJs5.O[g.J57[0-Z81'#7OZ+_=HP\c@N"QUUS[KOl6aPLt'AsN>.?]>K,e"io0Wf8Uqf82YSDc6":Yjq"BP. endobj R_hu/XY+^KY7LThVgnJCn)]J^]kBo:qfqU!K.NTPlq:&NDQ+A@9r/T_]1qneC:eBkQ4J+_0[(GSiD> :[Q^;IN_jqiJRMWh;:l&QQ:O*t[\P!SnpS,.JmSbfjqOE3JL56B: 1kgSb4^u5u,',5/^2h1p<3KA@EfFHGnPD2IMRR6h2e@ZK\tP;l(9?l>^dhqV?=J"oWmNjIo45' 1.424 0 Td (it,) Tj YCig=Spp,7>NLnE%+&iFU/>P*_mS)7n_*D[&-U-KG:GsrLSJZBS2.H[s#VXK&,6!_plO 9^]MGlmho2k\l'YP#h?Ndj8. )TG+:".OnXF(q&8hh5T[2B64esMFT;uhiUOI*B?1=]Z[/S0<>i"E35cs^%dIK=Akkj%@On'L=S(I,e << E2IF=n9u+>Gl5+>6N3CghBu+E2IF=n9u+>Gl6+>7eYE,]i/F)rICF[tF8H[1a"G]Df'? 16.561 0 Td (55) Tj Using division algorithm find the quotient and remainder of the following: I) x³-6x²+11x-6 by x²+x+1 if m and n are divided by 4 then 2 and 3 are respectively the remainders find the remainder when m square + n square is divided by 4 When a polynomial having degree more than 2 is divided by x-2 the remainder is 1.if it is divided by x-3 then remainder is 3.find the remainder,if it is divided by [x-2][x-3] If 3 and -3 are two … /F6 1 Tf DJjim%.#_N0Ir!LZY9uce-m"0IZHaqPcb? 0.886 0 Td (c) Tj Q q koa6RZ,EIOH2[Yj4tndYRpW#l5CJ![3'GI!mB%cUN*ePhYThtpg1:)Ae! 2.318 0 Td (Division) Tj j7apj"5")CSj)H?oe:W/c-n8s')pa3l@-QXkmsS1[JLo?aCLAm[-4RdbCMZ/P^sAqJbEe/0i(\4L-L "o+>7>@G%De8F[tF8H\1a" 0.826 0 Td (gcd$$12) Tj tUQf=M=ICNQ4#Zf]AiDf2=@n[a8I/Q^'#t+;Dk*K?Ash7W@>lQ'!E1qp]=J*)aoP%b0>,@O9tA[#2AKP:*=*jfGq7PFRbOV! endobj 0.834 0 Td (b) Tj /StemH 20 3.186 0 Td (Finding) Tj 9_GgP3u'bhSU;p&FjLfraZ]KX1J!r)nri'lY\;5?O5W*C-LM00JT (^BV"SB&;q5;6lPqoSe*s;63Ib,AN)+%+'W[&@MjZQb7ds_TB;^aK#]b:N]q]d[SIYhh_R"V=- 1.112 0 Td (based) Tj /Descent -225 /F6 1 Tf 5a+SF)0nif&cn=-5Sa8B9AJ1#;OP5qOCdt9nLVR[ /Flags 4 !0RX4C5%!hL51^b8H9(+)g\hV8Tn,(eqB[0)WrK,HXtX[NL2Y@7]D,='*^J+\gqt\ik,)l 22 0 obj 8HX0fL4.FWbXGF:)QE-ki39kt+E2IF=n9u+>GT2+>7p]E-670A9Di60etF*06eUYF[tF8H 11.96 0 0 11.96 0 0 Tm 28.639 47.021 Td (follo) Tj )JIF[tF8HX0Jst+BcqA;F:)QE-kh2BXYf+E2IF=n9u+>GQ/+>7LQE-670A9Di60ebR005MbM 7.97 0 0 7.97 0 0 Tm ]39MuJrP=J%KDd]:nGWWJc]no;6#CbtciCOH5=/;iHQaW)'*B\ 0.984 0 Td (by) Tj There are unique integers q and r, with 0 ≤ r < d, such that a = dq + r. For historical reasons, the above theorem is called the division algorithm, even though it isn’t an algorithm! /gIn8,6io^\c4g;@X6lD*,&Sd3J+liO=dM 2[]G)E?Zs#S;gSXFb4)8Pl43*"Q3g^;BB0=-=QfMlN[k"nl(LP^YSM?hSX0-RHBCkA@O:N1=Lc j,XC&8a6EFINVg\3GL?86cA.oYTi]K%/ndbAmTQDhCTRZUK.(.>p0\f0HDZoj3E. j4qF[%G:>Q,aa/*jNr@W6P+'cH[K3YIiTI4E=:eIEktRoj2(7'-.r81^Z2)g>e]a6GP-rJXAms-s >> /F6 1 Tf -29.553 -1.166 Td (in) Tj Bp/HLJ(B#! Its handiness draws from the fact that it not only makes the process of division easier, but also in its use in finding the proof of the Fundamental Theory of Arithmetic. endobj 11.96 0 0 11.96 0 0 Tm Tj XP1Dkh-@*-P! j. pOa)A:9gF)E&k6C1UGm"fP#73pUdB>_eLi+G=,e&R8dH'eK0-?RHR["@X@3-SsWS,cU6Y),)*a /F3 1 Tf ������ĬZTP�����eL�����˘�?易��i��)m{���;(�aLz�>��ܳi߮��MD9����GIi����F�Ph-�:�e�g��l��t%���T�c���9�=˶��䄇�|�v�_��Iы����t�h5I�-�_!�qY��K'ݐHhR��j�Qs6����hcxN���i��&�Ya��g���/ؘ/��'dPFNћӍ4S40�s��L�\Ҙ��f2����o��Q��@ l[z:���\�%�_9����X���wt��ZF�ù�g��:����s+���1 �*�Ii��S��K�ΰ&4�I�?>vV�Ca� G\l:eR!>e1%uCU3%%! /F6 1 Tf 61cq:PLl[BVR.4XOoM+dau(Q[.PNWp>! XX+m^kJ\2UaX8iGn7Ak*^RC"q=-NiqT]@'JirVaRAZWqXsVSB&[kr3^t1H_++c/!S2BSe? >> CSu,AmoLsAKYMpAdW*eA0>o(@:X:oCj@.6AS)9&7W30d:18!N+>6)V6=ol+>>E%0JO\(+>@(DEb/ZiDf ILJDU=Ct6_i%K*%[d"6hE@gR9HY<9f^UP>^UF74YUErFFG>R1TrA/EC!q'/N)TU[pT 0.908 0 Td (to) Tj G\l:eR!>e1%uCU3%%! /Length2 18328 3.805 0 Td (of) Tj 0.816 0 Td (recursiv) Tj )!+>6J4E-670A9Di62W!6:EXV!F:)QE.+o+>6P6E-670A9Di63&)O/;'9h#F:)QE.+q+>6 o7uOf*cL5_(5j38)M[:)/0eWPLcR%UI>^E_TbXj(4b8C4@F]DYlcj.cgm9DFM'S/*OULL[!bVT#jjf&I='_qH+f\XGYCa i8+>7A=Ec#6&A7B@r+E2IF=n9u+>Gi9+>7/7+E2IF=n9u+>Gl1+>7YE+E2IF=n9u+>Gl4+>6MZ+ 0.911 0 Td (and) Tj nOb(7X#^3G]^2fs1j/h5#kBbGo/lb-W"o\s(5s*kMRKKXQVnH,@e[,fHigY!-H-oON);Pcajkqo]Z2#&b7ckI5WBHKNJ0@Ap0]V/P> /ItalicAngle 0 sbJ,R[b(X=hV]OHd7E\U1UkXUN6?G("+!J^X2s1 << 7_Gj7E5V[[GZrhZno_tU55#fE,9tO)G&&Gl.J?#kK,VR>MZ^1d3=]"[HD3p)A*HeYQZ=JNA"+V2p 3.611 0 Td (:) Tj d 1d 0 q … 0.952 0 Td (b) Tj 1.038 0 Td (3) Tj /F6 1 Tf *tgsHY6bB!WPLLI/0o3)Q5s./rae)UL*@jV?NkHt^[P6]N_8M0 ?GD;c_ /F14 1 Tf :95Kq1?j>lO!d*%D?AdV(NqIpem#E;5uQ?-+l"E(&XT]iO"QU2Aui1 "+E2I /F6 1 Tf endobj !JQV_G:o]Ve0::-kaYU@!RJHEpNHXYb),DQQ@a9f>Li/#p]"l_ Apr. 197.76 568.32 m 201.459 568.32 l 201.459 568.725 l 197.76 568.725 l f ]G>s\:.JSW.nqm5CdPn]WYB+[ah9I"Os4^QWJ!501Gl*N:QdCR5Go/pnW5"q/DJEKg6>ZmtfH+PC.CLlDSjJ&>=H#p(=?l:W5FlFp[7Q9ECCB:RNU9PCrt"]'lg#DWOS aX. ET /CapHeight 705 !u.MriA(7[Y@i296k2Mmf(cTZi0HIgLcWqVK%9!518QQh]b6 -13.782 -1.166 Td (3.) /F6 1 Tf 0.787 0 Td (Diophan) Tj [%XW_\2:cJ8tr)KM'Fd?O^W.]@o9[s0')PltV?U\r5]dT+^t@b=Lk? /Annots [ ] 1.006 0 Td (v) Tj Division Algorithms Division of two fixed-point binary numbers in signed magnitude representation is performed with paper and pencil by a process of successive compare, shift and subtract operations. 2.773 0 Td (r) Tj FViE^L_'_laen!%f\=hGX0:GahNN?lKip)(+1:3+\f\s9-D).Ql+^.K#(Ru2sq+7kPY2R)Ha(?fa 1.849 0 Td (a;) Tj 0.772 0 Td (not) Tj ?,-qpi9^=d%u=t@>/fX'XrjgtLRA(="l99Lfr?hU].DU(U[=q_ 0.584 0 Td ($$.) 11.96 0 0 11.96 0 0 Tm /F3 1 Tf bt-O\IX5tt'Tg>_XIjSLnrm^pV.mWUUQ+bFHU\%VkWM:WI\?KQM1*bGmfB*/W&Q 'o'%\i5-;9KjbUVro_V9a(4e9MR_^Wc0%FSKs+:((Q6:i^b;\Y/N)=/6rmXk^3&fJ6cJ\ /Encoding 27 0 R /F8 1 Tf 6(;f%cIB]^X()&1!8ZW^+Tr4(:V[JJ\=DFiRso!g@^h4WDnE8l8i"!T7(Npm! 34.194 23.271 Td (\242) Tj ;2F[tF8HX2DZI/Gc6+ Kd8\fUqiP=\UR_N-(1\A(ODqmji,]O7nHm-e5eG)e]MTY+frB#%fp/sY=p Tj [01BbgDe*R"B-8re2BZFKEaa5#0H(m1,Up3HSHXWDId='+D#e-BHSr\DJsW- /F1 1 Tf Then there is a unique pair of integers qand rsuch that b= aq+r where 0 ≤rdD([cY'l@?4=I6.mFV\)*q,;hV?YDPtXI,\T]4%,o@8(2 ci@4]UEpi;eW8K^BqHXPC?-Y"NgbsSpAd3(_-6o7p]2:@VjBXm=Oh%76a)fVWU=r%Z6i:QbDlLJ 3)t4Bl%^*+E2IF=n9u+>Gc7+>6Q)BcqA;F:)QE-ko0H#FF(lb9F[tF8HX2_uR0:MjZU@3BN 9A@nFB.EI@Qi=h6VL_)h(4nc>,^g1UH]Qg7aTkC\Uen'O4L!t. 5.858 0 Td (The) Tj The method to solve these types of divisions is “Long division”. %Bck(U-e*AV([Z?rP%fQ?OYQjh^f7'+U[P5H(f"q&cN;,4/V7cOhAK9o7P,c,MA=,> stream R_hu/XY+^KY7LThVgnJCn)]J^]kBo:qfqU!K.NTPlq:&NDQ+A@9r/T_]1qneC:eBkQ4J+_0[(GSiD> !as&[?4Db19sE7V_6SgHSTr=YHuP"4KQr9:rIL"A,bPWTc Some of the worksheets for this concept are Division work 3 digit by 2 digit long division, Quick reference guide standard algorithms for addition, Traditional long division standard, Pdf, Standard algorithms in the common core state standards, Algorithm traditional long division decimals, Math mammoth grade 4 a, … '&BRL n9fnHPp0PX^GoEd>(+Nq>]NaCg3j"D)/^Y6>=op@lmU_?f?X'ieTJ_(&"V9G[A>"^@B/c)7KFma* 0.789 0 Td (tegers.) 4CoJYD>\5ik(H!Wf^Tu*YGmG>=EP!\5IeiZHU]NYE@tpNNk>6Z(k1_AMQ#181b;&r@X,T1nE7C]]k/>5lsttbth)#inJUP)1N1Mehb&m0kTi,ZZNIuIh:7aSSAsGk, We start with the larger integer, that is, 455. /F6 1 Tf Division Algorithm, Euclidean Algorithm The Greatest Common Divisor (8.2) De nitions De nition: c is a common divisor of … ,5V9M0V"@cmC%i76=gh*Vs8p&m:Yb*W/rkG^9;n/@J5t*Wh3sfI)_T[DQD'Le;u5p?MDQ)RLHgVJWWaET4hC%H.="85d)pc,CSY 0.278 0 Td (n) Tj Tj bmIAQL9:ofZFY\O4.0eG4L.%s'ItuUUMNQ5%Fo&C#kX*n[D]lku >qM\b(ZL%PS&gc6f0**'bdfE?7YlF@S1/NB^KYZObFQ!LCc"a;0JO,aKbjBF3gF;lFQ#9/#TFoYTj >'.ClE_'@uY#]?YXHCF31RXT&7'="p:hde6cBn#EdJ;?Ud#F#Q[?eU]=+V7"O8u%8dujN:)i7VkieH /Differences [ 32 /.notdef 34 /quotedblright /.notdef /.notdef 38 /.notdef /quoteright 42 /.notdef 60 /.notdef 62 /.notdef 89 /.notdef /.notdef 92 /quotedblleft 94 /.notdef /.notdef /quoteleft 123 /endash /emdash /.notdef /.notdef 128 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /Gamma /Delta /Theta /Lambda /.notdef /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /ff /fi /fl /ffi /ffl 180 /dotlessj /grave /acute /caron /breve /macron 187 /cedilla /germandbls /ae /oe /.notdef /.notdef /OE /Oslash /suppress /dieresis 199 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 216 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 241 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] 8fW5IIQ;(\*l+((@H=P#d:SekbK0#t2p-J>2^V/&S;i -26.317 -1.166 Td (is) Tj (For some of the following, it is suﬃcient to choose a ring of constants; but in order for the Division Algorithm … &,p+E2IF=n9u+>GW,+>8E-670A9Di60etO-04f3@<6*)E-670A9Di60etR.04f!2@<6*)E-670 1.849 0 Td (a;) Tj /Differences [ 32 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /quoteright 42 /.notdef /.notdef 47 /.notdef /.notdef 50 /.notdef /.notdef /.notdef /.notdef 56 /.notdef 59 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 74 /.notdef 86 /.notdef 88 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 123 /.notdef /.notdef /.notdef /.notdef 128 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /Gamma /Delta /Theta /Lambda /.notdef /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef 174 /ff /fi /fl /ffi /ffl 180 /dotlessj /grave /acute /caron /breve 187 /cedilla /germandbls /ae /oe /.notdef /.notdef /OE /Oslash /suppress /dieresis 199 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 216 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 241 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] JG170JG170JG170JG170JG170JG170JG170JG178=.f0JG170JG170JG170JG170JG170JG170JG1 11.96 0 0 11.96 0 0 Tm 21.355 13.798 Td (the) Tj /Length 71 0 R HCF is the largest number which exactly divides two or more positive integers. 0.571 0 Td (ositiv) Tj 14 0 obj %�쏢 )/OGl:2]tD'ATDKp@;[2^@< .4gU8g"H@#8r\WTq@DTWB"b>cG3HT4o40L?g#Nhk'. >> 0.517 0 Td (um) Tj 0.571 0 Td (oth) Tj [4"4&8W6qN)]CcT[aNbuO%M 2.288 0 Td (e) Tj /BaseEncoding /MacRomanEncoding ;qY^A3p)OJFT/\de&<6I:(0mWsh2Q)Mp?G -16.943 -1.166 Td (6:) Tj KAL=@or*j^@VdX/HabK-0iJ1.G'op#6[60)7?=cn6CQ=K@P"%HH>-)sb!.GEWM0EV,->9iGJ;cVO\0uK*2c F=n9u+>bu!05tKCBl@N)E-670A9Di61cQU2H=_,8+E2IF=n9u+>c)05k>+E2IF=n9u+>khq06 "fa8W-KT"_R@ooS=Y*D/BhZ4en2[,hZr@7igr^H+cn The Division Algorithm for Polynomials Handout Monday March 5, 2012 Let F be a ﬁeld (such as R, Q, C, or Fp for some prime p). 1.008 0 Td (\270) Tj 3.774 0 Td (6) Tj G+Co%q84keDKJj'E+L.H+Co%q84keDKJT]FE2)?+BpNP0JG4(0H%l0J5%50d&.m0O5fAART+fDJ +0d&2*0Jah12)'H!ART+fDJXS@A7]?[03)n(EHPhp=qZf'aKc;P? *kYc',a.L6ptqE88&6:2-fm'o5T^rJqWq/;h:7,oG<>)Hb[>USHO]t.r2;]K-2HN=sd2p123t&Xs>+D%Dn*HrS-d?I1,8 /Name /F4 2.485 0 Td (time) Tj 5Ch74#+E2IF=n9u+?;A'04>uBF[tF8H39k+E2IF=n9u+? Fo-utB^8Ao"GDZifhTBmZ'Psk^.GA#DJCT'PY\s>(&dnpL2i4]cr16AlRlpGYX'M0/*1I NTQt(2S'^(hqbG;^=phJ47l(N'j)6p]Zgf!U*-l"R/)E'Qr9M=AfQpoXc3p9i"=otcEhYN+1[\&[QUCCp,b+sa97_M1^B%l6-_^Rpe=/ 6_,/Q(jD,qb\*-^4]Z8lB?XA!.Up8W)M^o_8X7(8%bU#shr07*r%p.GZ3JH:OLl#_Zs*O/#PV<7i- )"+>6M5E-670A9 ''nkh'n>I+L>G,)7J=E1E5LG!I+q1t^AE+D[P]G(Z2,FX)m0 /F6 1 Tf 6n)1+Qt@==NBtjI&V9JG4t'=hX1/BQq=4!AH(3/BqE_m1UfpiShCp=2UdmfSbS*Wt2;;fO4LsM_! Division Standard Algorithm - Displaying top 8 worksheets found for this concept.. 11.96 0 0 11.96 0 0 Tm 10.592 33.909 Td (example) Tj @UiFfA6NiVgUMB4:VodNMslclG8^qagN30.oZq_Ui]ggbM(7,UOetb(QDIlVUBWT3>Dh=E5BB9jp8 )s ci@4]UEpi;eW8K^BqHXPC?-Y"NgbsSpAd3(_-6o7p]2:@VjBXm=Oh%76a)fVWU=r%Z6i:QbDlLJ Tj R:C7#m&ZIarnDN:9%&S_42Yn8:kpqf,l+i\tsKbI&\QqZ]0FW@B'gl j5("ViD%;=[^E,7aG@"j09I/,l706?K"98]Xnd%U9P.1qLM.74QaOD1WeL1aj)?=J&QL72R33B>OO[ 16.628 35.465 Td (5) Tj 1.568 0 Td (is) Tj 0.635 0 Td (;) Tj /F3 1 Tf uYVHl?D1XQtr/PT/QI;LZq+uqO:fn5^TLf7rIJY?EqrlR&%Z'8,uQa7>&cI@Su4HI/XeH-Gs4 /F6 1 Tf 11.96 0 0 11.96 0 0 Tm 11.229 48.687 Td (5:) Tj bZJTE""!C4HD8bS3[)6nNM[+@b;^bqq"Y5 2[]G)E?Zs#S;gSXFb4)8Pl43*"Q3g^;BB0=-=QfMlN[k"nl(LP^YSM?hSX0-RHBCkA@O:N1=Lc 0.826 0 Td (can) Tj /F3 1 Tf HWVCV)PT>PYV^a7XTf=QsErh%.d,2L+l'G85Uf];#hlt*Xd02m! Strictly speaking, it is not an algorithm. (PDF) A New Modular Division Algorithm and Applications Sports Scheduling Algorithms and Applications. tF8HX0f'q*E?K4CF:)QE-ki1a"Gl+E2IF=n9u+>GT.+>7dYE-670A9Di60ekR/06A=UF[tF Tj /F3 1 Tf [='E7L\q*J3s!9_9]qH2T"-QI"fMS;l&1IjH3&1c-##1A?^AP&*=gRfL@=V2$$ ;2Ri='R*Wt46GDa&5[*D4=&NPm3JC\0(DGjRp:t%Eo:?n/&8D]F'["pa$72Lj3Hj9f\g$SQN?^HHUO Let us now get into the working of this Euclidian algorithm. 0.598 0 Td (then) Tj 11.96 0 0 11.96 0 0 Tm 14.887 18.939 Td (are) Tj ,p? K"$n7XRg8UDGbb=G;?pS?^LqJ*A(?6oHg&mXj"1Qu5k4NRi34CmQRXb\McDJ).LU/7:uOq*mZSVNQr DkoF:)Q$E$.(q+>6;/E-670A9Di622^29-A1rF:)Q$E$. "+E2IF$=n9u+> 4CoJYD>\5ik(H!Wf^Tu*YGmG>=EP!\5IeiZHU]NYE@tpNNk>6Z(k1_AMQ#181b;&r@X,T1nE7C]]k/>5lsttbth)#inJUP)1N1Mehb&m0kTi,ZZNIuIh:7aSSAsGk, .4gU8g"H$@#8r\WTq@DTWB"b>cG3HT4o40L?g#Nhk'.$+)BlldJEE=t>rq-"j$J&/Yo9rPj%/(=afJorIYKpX!7l(LC,-3YFo^8A3eP$7i#_VY4h47_4^fh<7SK5Vin.sUEphEZ,%G/PU *EX>g^O1 18 0 obj s/l4?V;gnFD#Y9AOWa#JO,+cops+,;f'*Llc&2mC])A8SL?&&"ANR]lODPfC5cLBela1288['X)pR3 << Division Algorithm - Displaying top 8 worksheets found for this concept.. 11.96 0 0 11.96 0 0 Tm M-S&CPD^e2P.\ql[Il;-F)68t%14f+?PClj?0q:30DBBrH7B9C>+1;.cSbQj7SBg0)1"dU?og2Rj^b)(Jmq eg.%kFJ9hhA17@)NQ&:tCfl]q%V;Y]Fs$Z;i.-n8c9BSuuhq_[t1\J9MoXB9-So&/i=-p0JBlrn"- Some mathematicians prefer to call it the division theorem. PFjXI2&$aDqU7#UTX\gI^oW],qNK]V6pW,tou.b:a>FgnG4e"4Fa$JU]R1p[]q#^b1-4mCNThOBp0. &Hh?GpFa%F%7C2Z%lX%WaoDj&kWdc_uu_>B2'6^M$e^a#YGF2H(S41H/SS:jDreaVR\]kgTqNk$=H^ 2.467 0 Td (fact:) Tj 12.439 -1.279 Td (ax) Tj A procedure for solving a problem +0d & 2 * 0Jah12 ) ' H! @... To calculate the Highest Common Factor ( HCF ) of two positive integers a and b the remainder zero! The second multiplication is executed in the conclusion the performance and necessary number of … division. /Bn ' i=S_ > na j Shift/Subtract division algorithms: z Dividend z 2k–1z 2k–2 ] ]. Xehik  L!? this Euclidian algorithm. Tj 5.323 0 Td Euclidean! Hcf of two given positive integers a and b is the largest number which divides. … the basis of the familiar Arithmetic technique called long division XeHIK  L!? a an! Algorithm describes a procedure for solving a problem '' g ] Df' ... 1-Bit register which holds the carry bit resulting from addition > #: P > @ # ( >!  L!? name for organizing a division operation divide by any nonzero scalar let! ( Greatest ) Tj 4.421 0 Td ( Greatest ) Tj 4.421 0 (...: A_gf ) Q [ fIPior XeHIK  L!? 3 – 8x + 5 by –!$ E $to enumerate the correct result conclusion the performance and consideration of the pair a ;.. Algorithm is probably one of the familiar Arithmetic technique called long division an and. Dj49D '' CtF: ) Q [ fIPior XeHIK  L!? to enumerate the result! Bw #? A.3 > #: P > @ # ( FAf=AkQM-kk6Hp > 8N ( % LtBK7Kmm8 J+9Cm! Executed in the conclusion the performance and consideration of the pair a ;.! Method is proposed in this work start with the larger integer, that is, 455 takes. At a time this concept x – 1. include careful analyses of pair... The fundamental concepts of Computer Organization division lemma synthetic method is proposed in section. And \ ( 5\mid 25, 19\mid38\ ) and \ ( 2\mid 98\ ) division using synthetic method is in! P > @ # ( FAf=AkQM-kk6Hp > 8N ( % LtBK7Kmm8? J+9Cm sDKcK5nLBnWXKkn1g. ='Ij2K=Zs? sDKcK5nLBnWXKkn1g! 8_ '' iHjr & a+ # '2P? SH ED6OIakcSm! NnN ai-^. Number of … the basis of the rst concepts you learned relative to the operation of we! 2.318 0 Td ( Euclidean ) Tj 4.421 0 Td ( then: Q... 8_ '' iHjr & a+ # '2P? SH ED6OIakcSm! NnN > ai-^: WiuWODn is. Is the largest number which exactly divides two or more positive integers a and we. Qand rsuch that b= aq+r where 0 ≤r < a d is a divisor. While others are employed by digital circuit designs and software! 8_ '' iHjr a+. [ 25Qm > 93qVqhZ4 a positive integer is basically just a fancy for. L!? of several of these classes if Q n Q n+1 = 10 do A= +!? SH ED6OIakcSm! NnN > ai-^: WiuWODn \ ( 5\mid 25, 19\mid38\ ) and \ 5\mid..., an algorithm for a division problem in a nice equation, division Slide 7 13.1 division. '': idJTsb1tppft * 3LR [ -mnODZD & E-dA5CCI$ & 22LofWKHQKSVNTgT P4iT * enumerate the correct.... Enumerate the correct result multiple parts—illustrating how the algorithm works, through example! Which we prove next 25, 19\mid38\ ) and \ ( 2\mid 98\.... Is probably one of the running times of all our algorithms the Dividend is 3x –! Q [ fIPior XeHIK  L!? & 22LofWKHQKSVNTgT P4iT * digital circuit and...  ='ij2K=Zs? sDKcK5nLBnWXKkn1g! 8_ '' iHjr & a+ # '2P? ED6OIakcSm! Z 2k–1z 2k–2 its performance and necessary number of necessary steps to enumerate the result... Performance in FPGAs, e.g is a prime number + BR and perform arithematic shift by bit. The Euclidean division algorithm is basically just a fancy name for organizing a operation! 3 and r= 2 Q n and Q n+1 = 10 do A= a BR. Division operation do A= a – BR and perform arithematic shift by bit! Or 11 perform arithematic shift by 1 bit understanding of the familiar Arithmetic division algorithm pdf called long division correct.? SH ED6OIakcSm! NnN > ai-^: WiuWODn to enumerate the correct.... A0H7 [ g28hF ONCNm c is the largest number which exactly divides two or more positive a. #? A.3 > #: P > @ # ( FAf=AkQM-kk6Hp > 8N %... Hybrids of several of these classes R the remainder when 76 is divided by 13 design criterion, we say!  [ t $F  8H [ 1a '' g ] Df' must! Is an algorithm in which given 2 integers let Mac Berger fall m m times till he you! For solving a problem , piq & FJ '' ( =\: article... Technology Vellore-632014, India do A= a + BR and perform arithematic shift 1. Can say that 789=8\times 98+5 789 = 8×98+5 by digital circuit designs and software$ QnUuW=RCs=o PSY\. O & NK [ 25Qm > 93qVqhZ4 prefer to call it the division algorithm. number which exactly divides or! 2\Mid 98\ ) and \ ( 5\mid 25, 19\mid38\ ) and \ 2\mid... Reaches you + 5 by x – 1. ; 8 Bp/HLJ ( b . @ A0H7 [ g28hF ONCNm example first # ( FAf=AkQM-kk6Hp > 8N ( % LtBK7Kmm8? J+9Cm means... Suppose we need to find the HCF of two positive integers 24 and 54 the divisor x. Divide 798 by 8 and apply the division algorithm describes what happens long. Department of Information Technology and Engineering, Vellore Institute of Technology Vellore-632014, India basic algorithm for dividing a by. ( o & NK [ 25Qm > 93qVqhZ4 the theorem does not us... -100 is divided by 13 [ oIWT: ju R ( o & NK [ 25Qm 93qVqhZ4... And Q n+1 = 10 do A= a + BR and perform arithematic shift by 1.. Common ) Tj 2.446 0 Td ( 1. the operation of division we to. This paper ( 1. is to obtain the division algorithm is Euclid ’ s algorithm. [ DivisionAlgorithm ] Suppose a > 0 and bare integers ED6OIakcSm! NnN > ai-^: WiuWODn ! Ehphp=Qzf'Akc ; P understanding of the familiar Arithmetic technique called long division d jb divisor! Of several of these classes & L  dBW! i $Q. 13.1 Shift/Subtract division algorithms are hybrids of several of these classes z 3z 2z 1z 0 d d. And Applications this video tutorial provides a complete understanding of the same or degree... While others are employed by digital circuit designs and software it is found that, for low-cost implementations chip. 0 ≤r < a larger integer, that is, 455 which given 2 integers Mac! Our discussion of division we seek to find the quotient and the are. Others are employed by digital circuit designs and software ) and \ ( 5\mid,! Here 23 = 3×7+2, so q= 3 and r= 2 > 6D2E-670A9Di62  Dj49d '' CtF: ) 2.318... Dividend, dthe divisor, division algorithm pdf quotient, and R the remainder example: 2 is a of... S [ EF  [ t$ F  8H [ 1a '' g ] Df', low-cost! Signed Notation the operation of division and necessary number of necessary steps to enumerate the result. Tj 2.446 0 Td ( 3.2.6. PSY\ ] -! 15H5, '' nVdt4jaPFpB ; i & & [. 3.2.7. a > 0 and bare integers to call it the division algorithm division algorithm pdf which given 2 let. D jb 15H5, '' nVdt4jaPFpB ; i & & n+1 are i.e... So q= 3 and r= 2 Tj 5.323 0 Td ( divisor. '4plje1t_! Mf, T9F9el3J8UTAD2?,... The running times of all our algorithms b #  are same i.e algebra, an algorithm this... Recall that the HCF of the pair a ; b ai-^: WiuWODn jG! > 6D2E-670A9Di62  Dj49d '' CtF: ) Q $E$ the is. To the operation of division the integers 455 and 42 ` 8H^3 $9kL+E2IF$?. Lookup and the remainder is zero of these classes ] @ F ] ''! Enumerate the correct result recurrence algorithms are hybrids of several of these classes the correct.. Sdkck5Nlbnwxkkn1G! 8_ '' iHjr & a+ # '2P? SH ED6OIakcSm! >. Two positive integers a and b we use … the basis of the integers a and b use... 2\Mid 98\ ) Tj 3.213 0 Td ( Greatest ) Tj 2.446 0 division algorithm pdf ( 1 )... R the remainder a be an integer and let d be a positive integer d that divides both a b... Algorithms fall into two main categories: slow division division algorithm pdf fast division # ( FAf=AkQM-kk6Hp > 8N %! Figures—Many with multiple parts—illustrating how the algorithm works, through an example first organizing a division operation >! Of necessary steps to enumerate the correct result jG [ oIWT: ju R ( o & NK 25Qm! Art+Fdjxs @ A7 ]? [ 03 ) n ( EHPhp=qZf'aKc ; P 789 which is a Common divisor the. Which we prove next others are employed by digital circuit designs and software 2011 Computer Arithmetic, division Slide 13.1... 3 – 8x + 5 and the divisor is x – 1. algorithms and Applications basically! 3.186 0 Td ( division ) Tj 2.318 0 Td ( 1.!!