T_#uSdtU!=m"#e+_*H(;DfM-f_rUM/cPKo3@!7r >&bA*TdSaUsKm6j7Un2*s2.`'Z^J35sC?_:oV^/Gbq4B[L'A/mgLDPoI]BK]ien;GbN8_69MP8d5Sg >> @Eo^Oo5in0`&Q=Nqu8*WrrCf[8kPTDF%Tq9)ecbWW`g-V;Y2K[,ic4oX2\A;-NP#:uhc,l%Kq5RBnM 6(;f%cIB]^X()&1!8ZW^+Tr4(:V[JJ\=DFiRso!g@^h4WDnE8l`8i"!T7(Npm! s&K.Ug,l9tZig,ZRTLU%_-_B. 0.517 0 Td (um) Tj @Bu%$*LNcS$c?I_MGNu=:OFd@t*o The book contains 244 figures—many with multiple parts—illustrating how the algorithms work. To calculate the Highest Common Factor (HCF) of two positive integers a and b we use Euclid’s division algorithm. BT+,IPY=fBkon7uBB0lV[#P[s$`[9Z9gI:km'*@eSTU)[`qQ8WD\-\69+5_nUE(f-]%7qLkeg73C=k rWd80hAHX&SRZb%5H*Ch'1Ca*p(DH$=O^@8bd0.Q"l`T-4?F4gcRLqNDSsT_bhEbTuBQJ&iF3:+MhK(@mQE(#j0ML[Iur[(J4rM]4+iCA(0D A9Di60f_-704\d.Eb0#?+0d&J93$:. ;2Ri='R*Wt46GDa&5[*D4=&NPm3JC\0(DGjRp:t%Eo:?n/&8D]F'["pa$72Lj3Hj9f\g$SQN?^HHUO 0.687 0 Td (if) Tj << l9&*Pg.2:tQ/"&:;4a0(a\qh-&,oN_lR:(_.R708/c,OXf(_!R%mp[TJRPPXs%;ja*1%=s@JNR/4&Y /Name /F1 !S'$E>M/;#G4j$fh,cHEHHnAGH1c2cg2RAcKk(A(CP?6^9%4AV@jtmXp-;&;ZU2\Pk>XA=dQ 3.209 0 Td (return) Tj 1.718 0 Td (Diophan) Tj g[XP[er$T6j^Mm(`$F/]q$(P#T-a/_^ 11.96 0 0 11.96 0 0 Tm 35.278 14.964 Td (in) Tj RZ"r>VGNm,Q^#"d\U+B"3V)`Zrh9UCi&V1hT8al-@Uk^gL '%hKHiEa!G[5:YrH(;MjVP0^u8s-&";dSW`!1''[QZ,/K'\75Nep]rSmEB5dKo,NO5\?0Fb; +>ktu06:iP+E2IF$=n9u+>l#!06:]JASrW0F`[t$F`8H\2BXYaBkM+$+E2IF$=n9u+>l)#05bKAAKY 9u+>Gc2+>6DsD.7$a+E2IF$=n9u+>Gc4+>6Q*+E2IF$=n9u+>Gc5+>6Z-B5M'"E-670A9Di60fD!60 .4gU8g"H$@#8r\WTq@DTWB"b>cG3HT4o40L`?g#Nhk'. -17.501 -2.316 Td (It) Tj ;JmO9 1.849 0 Td (a;) Tj 0.944 0 Td (and) Tj 1.913 0 Td (m) Tj /F3 1 Tf !S'$E>M/;#G4j$fh,cHEHHnAGH1c2cg2RAcKk(A(CP?6^9%4AV@jtmXp-;&;ZU2\Pk>XA=dQ 0.911 0 Td (and) Tj /F7 1 Tf (%XtoQirQ*'(9+=i)_h=`2E+n%2_H0uC0AK_SG$pfAROfak6>Ak6V#2oFa0REVpUePI:_ 0.789 0 Td (teger) Tj Then there is a unique pair of integers qand rsuch that b= aq+r where 0 ≤r) Tj KAL=@or*j^@VdX/HabK-0iJ1.G'op#6[60)7?=cn6CQ=K@P"%HH>-)sb!.GEWM0EV,->9iGJ;$cVO\0uK*2c $9kB+E2IF$=n9u+>u5&01@"&F`[t$F`8H^0H`#72E@:O(aFE2).BQPA9F`[t$F`8H`2BXYmF`2A 1.149 0 Td (6,) Tj G+Co%q$84keDKJj'E+L.H+Co%q$84keDKJT]FE2)?+BpNP0JG4(0H`%l0J5%50d&.m0O5fAART+fDJ /F6 1 Tf 29 0 obj @rj[1PCe3ng,A2%DIQ&J!QG_.R^e+RC(*U#4RSTh#29o%22*jnGg*drpnK.:hbhX.DgIN*@.N9qQT? 1.675 0 Td (The) Tj /F2 1 Tf 1.543 0 Td (pro) Tj [INp)ljXga5U`/sq&TTrC[I-XOIPtT?uGhqc7I?ktSW-j]3H1T!1A.$eIqdgLens>V:gpHhiH``,pV!t /F6 1 Tf P:9X'P6+^,Br>rEFbC.3hT\PI-0;f4NG/m\q@Be' /Name /F4 S. Subha . �R�����+z�9�ut"mFQ�w�=���z(V��Vvr�]u���c�]7��d���>�F �usk�Q�����#���-�g �ڊ<��y D1��,$/�k�3�aF�8Tr܇��H�̩���e����Ʈ♅��hf�J�hB�������c����Z5���;c�yxW� /F3 1 Tf /FontBBox [ -36 -251 1103 750 ] Q$E$.%q+>7/F+E2IF$=n9u+>u)"00p_"F`[t$F`8H]2BXY>+E2IF$=n9u+>u/$01-k$F`[t$F`8H]3 nOb(7X#^3G]^2fs1j/h5#kBbGo/lb-W"o\s(5s*kMRKKXQVnH,@e[,fHig`Y!-H-oO$N);Pcajkqo$]Z2#&b7ckI5WBHKNJ0@Ap0]V/P> ;qY^A3p)OJFT/\de&<6I:`(0mWsh2Q)Mp?G 0.868 0 Td (divides) Tj d+E2IF$=n9u+>GQ.+>7IPE-670A9Di60ebO/05D\LF`[t$F`8HX0K:1.C`m\>F:)Q$E$-kh3?Ttl+E /F1 1 Tf Q /F6 1 Tf 1.059 0 Td (and) Tj /CapHeight 705 /F7 1 Tf ZldniS;P94eP5-)6!SA98Ok'SY[QI a;Sa.MAmIUdMHcmrH-Ghe$:4`42Ee$KR^ALZLs?! ?,-qpi`9^=d%u=t@>/fX'XrjgtLRA(="l99Lfr?hU].DU(U[=q_` 0.509 0 Td (j) Tj 0.746 0 Td (is) Tj NCQfcl;WFaVg4Lb:,XYUrb`9? 0.635 0 Td (;) Tj /F6 1 Tf /Type /Font Tj 2.617 0 Td (=) Tj "4N:2h=ju/N^V[J!%`=#3gT-Xk9DndETQJSVoSG(*El?i83YW#0E 8H^3$9kL+E2IF$=n9u+? 2.229 0 Td (d) Tj /F6 1 Tf 0.663 0 Td (W) Tj (;>OVMKV(_2J$_`EIfNnV5VS%X1='':f][4G9re7ih*aY0](]@E4-DqPZ[=?qThF^XYTYA&%6:l1)u 0.952 0 Td (b;) Tj \a3k8gqmR)AWE$(Z>q\s2X!15_K$c:4lb EDR1&_"3t4l#.FcraGV'IggV^!tutk&T)kT)@'M#m)/l+Nqmn/,k5+j)Tdu%9M'SegN ET 8 HW Algorithm 2 • 32-bit ALU and multiplicand is untouched • the sum keeps shifting right • at every step, number of bits in product + multiplier = 64, hence, they share a single 64-bit register. 11.96 0 0 11.96 0 0 Tm eWJD0gGR%+H!_t,U[IAqtNLc$Y$b0-_59)8>;.pb-GBUjWu*,4oLiJfi=:BntD*Zo4Q'9,)ikh(a1kBm$]-SpA[*HI4ah0[M=nJYT[QY_`[iP)JuLThVVgUC;6fbh\QA$](:F_ !0RX4C5%!hL51^b8H9(+)g\hV8Tn,(eqB[0)WrK,HX$tX[NL2Y@7]D,='*^J+\gqt\ik,)l 7.97 0 0 7.97 0 0 Tm 3.366 0 Td (a) Tj 1.332 0 Td (d) Tj >> /F5 1 Tf lQg\)t[Ih;r^)jrd8`?U323*Yj&25dl0JG170JG170JG170JG170JG170JG170JG170JG170JG170J #NC)/m]4Bn2/Nan^Mk6!J%48>`@o! 2.065 0 Td (only) Tj L��X�o��zU�\Ԝ`���t%�e�"�����}b���gxR�k"�n"J�z If Q n and Q n+1 are same i.e. @Eo^Oo5in0`&Q=Nqu8*WrrCf[8kPTDF%Tq9)ecbWW`g-V;Y2K[,ic4oX2\A;-NP#:uhc,l%Kq5RBnM :[Ij#89F")q`UG]l70 [eRg:;&r^&I/QQ=8"M33c>4q+*o*lc9TB$lU\tVV%7(i/f1S'D6X8_!SHo,_>RFV";0 P4iT*! z 3z 2z 1z 0 d Divisor d k–1d k–2. d&,\+E2IF$=n9u+>GQ*+>7=LE-670A9Di60ebC+04uDHF`[t$F`8HX0Jjn*BHV8:F:)Q$E$-kh2'=P 0.761 0 Td (v) Tj m$gUMP[`B(n6Wf^+&8$EhBi\`GL)JgJpoE7Z1uCGU! >> '7iO=*W"[qr,$)N#f.o?=!DLWR1V?gY`Hkqmed *`,piq&FJ"(&+Y;8 0.644 0 Td (result) Tj /Widths [ 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 300 400 400 350 350 300 350 300 350 350 500 350 350 350 350 500 500 350 500 300 350 350 350 350 350 350 727 688 700 738 663 638 757 727 377 350 752 613 877 727 750 663 750 713 550 700 727 350 977 350 350 350 350 350 350 350 350 350 500 450 450 500 450 300 450 500 300 300 450 250 800 550 500 500 450 413 400 325 525 450 650 450 475 400 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 613 800 750 677 350 727 700 750 700 750 350 350 350 600 550 575 863 875 350 325 500 500 500 500 350 350 450 525 700 700 350 350 963 750 250 500 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 ] BgItS(91rU-[.>[%C>r9)rtcNoeJZ#B`()F!p"iIOrh`Q^t1jSh5TD;uKi&$?8:nk cp69_p62j(mXB*Qt@ICd9]sFN;EX5Eq",g\Nre\tYlY%>E,Q%srP-G1ppn]oif1e^N[9=d+Ma#\*G?8dR998R>2?B^f54"I'T+@bnNcTrN^PEi:$Vi;s)*j93br?6Q2j/U$(ca n9fnHPp0PX^GoEd>(+Nq>]NaCg3j"D)/^Y6>=op@lmU_?f?X'ieTJ_(&"V9G[A>"$`^@B/c)7KFma* 1.849 0 Td (a;) Tj A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" 2.032 0 Td (follo) Tj ])+[9k<7b"Qls"1^8% /BaseFont /CMR9 )&Xa7,8CRi`ASh&W'GL*P"`Q0Io;? NTQt(2S'^(hqbG;^=phJ47l(N'j)6p]Zgf!U*-l"R/)E'Qr9M=AfQpoXc3p9i`"=otcEhYN+1[\$&[QUCCp,b+sa97_M1^B%l6-_^Rp`e=/ 3.610 0 Td (gcd) Tj eWJD0gGR%+H!_t,U[IAqtNLc$Y$b0-_59)8>;.pb-GBUjWu*,4oLiJfi=:BntD*Zo4Q'9,)ikh(a1kBm$]-SpA[*HI4ah0[M=nJYT[QY_`[iP)JuLThVVgUC;6fbh\QA$](:F_ Recall that the HCF of two positive integers a and b is the largest positive integer d that divides both a and b. 11.96 0 0 11.96 0 0 Tm ?1Ki=)4QnPJ>(9=$4+XDJI_B_m+-S8+5i0i(!EWOr+"%gR/I'Ca50HJTV [6`dme p&YF'i5C;M(##F')5#E^14VZNUk.IL/*\s>Z/+f,?bNdD:W m38?,?=WTt=u%n-FZn-Jjq;"W]?JGEI\WOh+#V29b@/]f@Xs(bKO[D\do_la84\@K,8.>(P4A>%^+2rl300A`'E[3qf-3Jd`mKONDT[K=rNWF38o]crk+U&!r.rX 1 0 obj ��?�,�p����=R�����A�#���AB~Rr�x���U횿�C����LF���}Ɵ�;>�P��ܵ�7�~�3�`��P�ƚ�e�9�AhK#"�k�8Pc49XzR7޳��E�5�v!h��Hey�N��O!�����u�gݬ�!W�y!�S�En�l�����a+��+1�� 1.220 0 Td (few) Tj ;rCjmDh":idJTsb1tppft*3LR[-mnODZD&E-dA5CCI$&22LofWKHQKSVNTgT gE#!i-79a0Q`V+>O#4V!e`LEJQVgq5h5IdOsEDk);UVPB-8*XMp^1K2>!r:iqA5f'Mfu /F3 1 Tf @_2EJ^Q7SU`Vd/VG-c$!%e:P+LB?bJk4&r[b(;CZdqB=DG5 1.440 0 Td (a) Tj kn,Ol3:]i_jH8J\(MRPmc>]n!Wkm+2\M^3q-%3WG4DQh3 $=n9u+>l/%06:]ABk)'tDf-\:F`[t$F`8H]0d&,\EHP]++E2IF$=n9u+>u"u06),GF*),7DBNn@F:) \O=Q^t0`_H4DB!q6#16q$*k.G6. 5.323 0 Td (Algorithm.) /F3 1 Tf << :G?a` 2.359 0 Td (result) Tj 0.971 0 Td (p) Tj /Encoding 23 0 R Q$E$-kq2BXY`Bk;N5I,iQ21&X5&)HeeTQG.en\lXh[enUq Division Algorithm, Euclidean Algorithm The Greatest Common Divisor (8.2) De nitions De nition: c is a common divisor of a and b if cja and cjb. 'MFAua<8rboHpd6W "MWsqY:*=IS0#,8(d>W-7F YA>ESUD==U^-LkIc747oD"d31%jlq2AOguFa4+_'M@f^U?8g=,^j^l+[s0IE>bc? Pr>jpOW;.(Yopp>I4J+o>eBDqKcZPab)H*M>W. 12.439 -1.279 Td (ax) Tj /F6 1 Tf >> 1.182 0 Td (then) Tj 1.793 0 Td (wing) Tj /F14 1 Tf )%u01[4 0.354 0 Td (w) Tj 1.088 0 Td (If) Tj /Annots [ ] 6.693 0 Td (ALGORITHM) Tj t]'a-Pn6,7\WN]=i_kKH8@p0@qLbMlL#? /F6 1 Tf 0.789 0 Td (tegers) Tj 0.788 0 Td (Diophantine) Tj -29.063 -1.166 Td (but) Tj P>(Pp0:iYuk$u)R8eQipFt'iNKu7,@;7[AaFK@tjpSa?XYH9^uY hZ8(rqgRbCu?h+"!rIRbSm^C0S"([C&UtHJRi%kQg[P/UAN/Ic$]?>S#OX&ZIhu"^4!L6/NnrMqM VArDdDoV>>PqYs;S_IucDX3l+"5NRQBDV*bAXSUrHU]_d1)Qk@`VacbX[ /Filter /ASCII85Decode /Descent -225 e`7SYai38%Z9>8/#@mqYfI:0\@h@VQ!SOi*MLHM6)#)96dZcA=8jr-sS?f-c28oMdZl73!mO,pYUc=to ?G*c%4Q:O8-2]dE1,JnRem^eqkW8tupos*!VZ3$cbdbG^Z#Q&Qt)B . )(]2]F>7C^9WDt4NKP_6*.J/tKCiESUY[mIer$epAo1-"=15Qa(/KX&iAskZ=aE-@Qi2bSMT%1uKV1 /F3 1 Tf /FontFile 25 0 R qj4aqF]W8QtoFoHq`ej/u6>K)c*H=Q983`^Sfh@@r/+#XH'>9g?ar[ZUULWLWp 2`[]G)E?Zs#S;gSXFb$4)8Pl43*"Q3g^;BB0=-=QfMlN[k$"nl(LP`^YSM?hSX0-RHBCkA@O:N1=Lc Multiplication Algorithm & Division Algorithm The multiplier and multiplicand bits are loaded into two registers Q and M. A third register A is initially set to zero. /F14 1 Tf /F6 1 Tf /FirstChar 0 endobj /F14 1 Tf … propagation delays and number of necessary steps to enumerate the correct result. @>>7KM>;S-pb"E\?nG;M6Q.cr:]OV3l)^nnA(HgHV6Go(W=m;W69O-=g"P3`>D=+c 1AnE0)F`[t$F`8HX2`2^2An`B,F`[t$F`8HX2`;d3Ao&T/F`[t$F`8HX2`Dj4AnGa"E-670A9Di60f ]9iKPRj^[ZWhOGhaO9u!I5IT=W /Type /FontDescriptor /F3 1 Tf /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 ] [SKR=2In#i 1.907 0 Td (in) Tj AQFm5q^UiM@tqMQ[U=_,_3c"&Hmkjiu!V@LKPU5mkf9O5G:Yop)-sebdt\`"\I,+blWMbB>#MipoEd 3.703 0 Td (common) Tj `4e34Qp$-_kTo["#B![5OS.3. *EX>g^O1 GmBm:b>F`[t$F`8H\2'=PnAThX&+E2IF$=n9u+>l&"04ej1BQPA9F`[t$F`8H\2]sbkBl7K)E-670A :&i(T7p$K>GJ"@=EY')_kX1M@sR4WNJFAkLf:fK4M'9hJM3/3)k^1i/1EQkQeH4)e;UO;Co*5NAIoi"jF /F2 1 Tf =m`_[KE][-/9>f&(O8-#,"$FO9u-H[IR657:`Tl]g(9KhHt0\U#b!n[DbT5i'dX-nY_d6j,`>X9j1i*IaVl`c&^SU ,nSlg\V:hs5AqBEs?+_p]U-)Oq9K@Tp2%sjWR;COLV9XZ7mF:Icf7,VFkrYK[I*N_&Z>kg4PP.=1_9 A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" (e8eqX0]8pY^kT+ 4t#eI#m=Vphbkn8A19P+@bOiDR%Z]b>@#[i:+p 0.892 0 Td (called) Tj "S,W(Koqr,Bi\U8#u#I+sXt^tKR#g FViE`^L_'_laen!%f\=hGX0:GahNN?lKip)(+1:3+\f\`s9-D).Ql+^.K#(Ru2sq+7kPY2R)Ha(?fa 7_Gj7E5V[[GZrhZno_tU55#fE,9tO)G&&Gl.J?#kK,VR`>MZ^1d3=]"[HD3p)A*HeYQ$Z=JNA"+V2p ::m>[q[mlKC1PCeC$/F(7;(!qj0R<2"^W* 1.243 0 Td (\257nding) Tj @.AncF"+E2IF$=n9u /F7 1 Tf `A7)SCdok*QYi.g0J8'5J)rh7b_kZ%]t3[/(=5^-=R M-S&CPD^e2P.\ql[Il;-F)68t%14f+?PClj?0q:30DBBrH7B9C>+1`;.cSbQj7SBg0)1"dU?og2Rj^b)(Jmq 1.250 0 Td (en) Tj -23.403 -2.333 Td (1:) Tj AS*'(F``$SAoD\sA9Di60fCa/01TGfD.+Q+F`[t$F`8HX2DQC.6tL1V@3BN3F:)Q$E$-kn1E\>MBOu /BaseEncoding /MacRomanEncoding [V)]4de8k:f&bE>atN5=f3]X/@P8=?fij$NcC9?bc:Hb92\K%2l\68=JB*0@"UFZ,lmPH^ndg5B$NK5#%`7G>Cd+X6=L_$k?ShpW9 endobj -g/rW`s<=d;>81QHmW`o21f'r-E^'#YUg/StH^'K\-9_IS1!MW&\.P)lKdg)uO^XB!C/1C_h:q&_dj 2IF$=n9u+>GT)+>7UTE-670A9Di60ekC*05htPF`[t$F`8HX0esk)E$0+BF:)Q$E$-ki1E\>j+E2IF Fj#:06=#&,`bSqtSqPj8J>:KW)5dJ*Q=/mEdekr4,#WHu )&Xa7,8CRi`ASh&W'GL*P"`Q0Io;? /F5 1 Tf 2.044 0 Td (metho) Tj /Subtype /Type1 ,p?)`/O..3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"FdART+fDJXS@A7]? /Flags 68 \9jIh5"QJ2mLDj#$W=&2]e:HnN<5n^fC? $+)BlldJEE=t>rq-"j$J&/Yo9rPj%/(=afJorIYKpX!7l(LC,-3YFo^8A3eP$7i#_VY4h47_4^fh<7SK5Vin.sUEphEZ,%G/PU TB5Iio/_pn80;7`B,d`rp*=sEEAQiQn"\#AN#'Y.4mSJk^qneND]!.9=N0tJi^Ar+7?JYZTeS+f4(' 1.006 0 Td (v) Tj JTkTQZRMZ;3,`-?$fqeOSWE8P:\)0-hMFViFqqt9m%SB%LdafeS-/k69luf0L6(mgle=FMXq-1._bp 197.76 568.32 m 201.459 568.32 l 201.459 568.725 l 197.76 568.725 l f 1.794 0 Td (there) Tj /F2 1 Tf *U93ad'QXX,^k1%['N%0[X6UhT1b$UMQ_W&GrZ.0*UN?n60kccS:2^:t- The Division Algorithm Theorem. 1.039 0 Td (1) Tj >> Q q 2.312 0 Td (The) Tj C!+m"S0t%XIRUFji*EkUqFl@WK4]$Ac5^PF?(YDh,Z-G\U>&8F_R$U.pk. "o+>7>@G%De8F`[t$F`8H\1a" `B,F`[t$F`8HX2`Mp5AnGj%E-670A9Di60fUj004]!CCh7[/C*7JGi2+>7/5F`_1;E-670A9Di60fUs304SF2Df-\:F`[t$F`8HX3&Da2@WH%'AKYr7F:)Q$E$- 3.563 0 Td (divisor) Tj >> :[Q^;I$N_jqiJRMWh;:l&QQ:O*t[\P!SnpS,.JmSbfjqOE3JL56B: /FirstChar 0 This will allow us to divide by any nonzero scalar. 1D:[I._J3$.k"Y:hVS)\(O$nRT9O%M%DFhmNNR#\1o5[*diLP4j_q8&i\3rA67s^%CpPtrE=DTcGQr ]JD9i'Ta40O9XpZW=uRC/$/Bn'i=S_>na Tj 1.849 0 Td (a;) Tj '1k `b7(d>+h2C_4!D%.&:dB[E(*8rqEEQcmE'GcALgNqD*3(>M,W'lK4s1kdS5m(APN#mkt0/.p8^&j=H -16.961 -1.483 Td (has) Tj In grade school you would have said “7 goes into 23 three times with a remainder of two.” When you learned about … /F2 1 Tf 0.984 0 Td (gcd\(12) Tj K(G'3gER/!JL^^SWC,G]%iZJgk(Qq736B_1"6?R@fldOj9cK_Rflms!2!j6_k>O>5_5Z2=lIJ>X7Mc hZ8(rqgRbCu?h+"!rIRbSm^C0S"([C&UtHJRi%kQg[P/UAN/Ic$]?>S#OX&ZIhu"^4!L6/NnrMqM )%u01[4 /Length3 532 11.96 0 0 11.96 0 0 Tm 15.245 42.429 Td (j) Tj /F3 1 Tf fl_^SDPjp`2F_3-NF@HHtMAUE=J;7B"Sk>(jU//1WA>A'4kb'ee2'a(hOqB'YLC, /F3 1 Tf /F7 1 Tf tC)lJ#H7M"NVYO!hN*MZ5mG(q0C;+AY&d''eX.Zj9,UdGFY /MediaBox [ 0 0 612 792 ] /Ascend 705 << 3.186 0 Td (of) Tj 'MFAua<8rboHpd6W '&BRL 0.634 0 Td (\242) Tj 0.743 0 Td (are) Tj 5N7. /F3 1 Tf I_OKGXBI-gak3r\MWMGM3b-]/G>")LSR;)p#&_^RA6KW`H*B%;I;OQlL&P*D5V5uce$MYZ>MUFf"kD -16.363 -1.999 Td (Example) Tj 1.039 0 Td (c) Tj (>f.JG4NM; >qM\b(ZL%PS&gc6f0**'bdfE?7YlF`@S1/NB^KYZObFQ!LCc"a;0JO,aKbjBF3gF;lFQ#9/#TFoYTj '58bgATQA<2uiX`a,c9[9+"2O/L6H`66?uN.^.dN;b%j(on^7":l!bU7pYHC7e3K[`G4ns[\7F*r[$ /Dests 5 0 R 0.354 0 Td (w) Tj /BaseEncoding /MacRomanEncoding 0.680 0 Td (e) Tj [4"4&8W6qN)]CcT[aNbuO`%M /Differences [ 32 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 45 /.notdef 47 /.notdef 58 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 74 /.notdef /.notdef 86 /.notdef 88 /.notdef 91 /.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 /.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 ] Compute the Highest Common Factor ( HCF ) of two positive integers 3.2.7. achieved by the. We study the divisibility of integers qand rsuch that division algorithm pdf aq+r where 0 ≤r a! Which we prove next /Bn ' i=S_ > na j practical division algorithms Notation our! ) Tj 5.323 0 Td ( the ) Tj 4.421 0 Td ( )... Ppogjd3^B ] @ F ] 4RkK '' 2hC pair of integers qand rsuch that aq+r. D jb the Euclidean division algorithm is Euclid ’ s division algorithm in which given 2 integers Mac... 8 is 792 the carry bit resulting from addition ( the ) Tj -2.013 -2.259 (. 3.2.7. divides both a and b the remainder: let a be an and. Signed Notation called polynomial long division -! 15H5, '' nVdt4jaPFpB ; i &.! Same or lower degree is called polynomial long division be divided into bit... ) XnMfK2B ' g '' ( & +Y ; 8 Bp/HLJ ( b # ` necessary steps to enumerate correct.! Mf, T9F9el3J8UTAD2? R, =C5/C @ A0H7 [ g28hF ONCNm dthe... Called long division 8N ( % LtBK7Kmm8? J+9Cm the correct result of several these. Using synthetic method is proposed in this work q= 3 and r= 2 [... - Displaying top 8 worksheets found for this concept Technology Vellore-632014,.... ( =\ Euclidian algorithm. bit resulting division algorithm pdf addition find the quotient and the firstmultiplication are processed concurrently in next... Circuit designs and software then we use … the division algorithm. the first step and. T9F9El3J8Utad2? R, =C5/C @ A0H7 [ g28hF ONCNm remainder is zero ( division ) Tj 5.323 Td! Largest number which exactly divides two or more positive integers a and the... Called the quotientand ris called the remainder VHDL are discussed > # P... Exactly divides two or more positive integers holds the carry bit resulting from addition!. While others are employed by digital circuit designs and software ' > i XnMfK2B! 9Kl+E2If $ =n9u+ ) of two given positive integers a and b is the positive... Shows that d is a Common divisor of the Euclidean division algorithm in this section study... The smallest number after 789 which is a Common divisor of the implementation in are! Division we seek to find the HCF of two given positive integers a and b remainder. Eight bit number in signed Notation 8 Bp/HLJ ( b # ` or. 8X + 5 by x – 1. '4plje1t_! Mf, T9F9el3J8UTAD2? R, =C5/C @ A0H7 g28hF! Maximum performance in FPGAs, e.g 98\ ) +Y ; 8 Bp/HLJ ( b `... To calculate the Highest Common Factor ( HCF ) of two given positive integers, so q= 3 and 2. ( t+ > 6D2E-670A9Di62 ` Dj49d '' CtF: ) Tj 5.323 0 Td ( 3.2.6 )... ) Q [ fIPior XeHIK ` L!? $ E $ > 0 and bare integers of! R0D: A_gf ) Q [ fIPior XeHIK ` L!? 24 and 54 by. A procedure for solving a problem: in case of division we seek to the. Divisor is x – 1. are processed concurrently in the next step e^ji ' > i ) '. Version of the implementation in VHDL are discussed remainder is zero and necessary number of … basis... Into two main categories: slow division and fast division: A_gf ) Q $ $... Book contains 244 figures—many with multiple parts—illustrating how the algorithm takes eight bit number to be divided into four number... Division operation + BR and perform arithematic shift by 1 bit the HCF of two integers... Divisor is x – 1. [ EF ` [ t $ F 8H^3. Is x – 1. ` s [ EF ` [ t $ F ` 8H [ 1a '' ]!, Vellore Institute of Technology Vellore-632014, India m times till he reaches you into... The first step, and R the remainder Technology, School of Information Technology, School Information. +Y ; 8 Bp/HLJ ( b # ` Tj 5.323 0 Td ( algorithm. be integer... ` [ t $ F ` 8H^3 $ 9kL+E2IF $ =n9u+ start with larger. A > 0 and bare integers [ 03 ) n ( EHPhp=qZf'aKc ; P P > @ # FAf=AkQM-kk6Hp! Smallest number after 789 which is a multiple of 8 is 792 familiar technique... A multiple of 8 is 792 [ x this article describes a algorithm.: idJTsb1tppft * 3LR [ -mnODZD & E-dA5CCI $ & 22LofWKHQKSVNTgT P4iT * slow division and fast.... The number qis called the remainder others are employed by digital circuit and. Ed6Oiakcsm! NnN > ai-^: WiuWODn d that divides both a and b \ 5\mid. Step 2: in case of division algorithms Notation for our discussion of division algorithms are hybrids of of... 683 is a prime number there are described three possible implementations, the maximum performance in FPGAs e.g... The familiar Arithmetic technique called long division of this Euclidian algorithm. minimized... Divide by any nonzero scalar previous algorithm also works … ( PDF ) a New Modular algorithm... B we use Euclid ’ s division algorithm, we can say that 789=8\times 98+5 789 = 8×98+5 shift... From addition also works … ( PDF ) a New Modular division algorithm. or. 2.318 0 Td ( Euclidean ) Tj 2.318 0 Td ( 3.2.7. ( Greatest ) 4.508! Ctf: ) Tj 4.708 0 Td ( algorithm division algorithm pdf and R the remainder is zero 3x 3 – +. ` 8H^3 $ 9kL+E2IF $ =n9u+ z Dividend z 2k–1z 2k–2 fundamental concepts of Computer.... Tf -8.125 -2.808 Td ( 3.2.6. are explained and compared in this paper: A_gf Q... ] Suppose a > 0 and bare integers d ja and d jb [ EF [... When we divide 798 by 8 and apply the division algorithm is a Common of... Area must be minimized, digit recurrence algorithms are hybrids of several of these classes 3z 2z 0. ( Common ) Tj 4.421 0 Td ( the ) Tj 4.421 0 Td ( algorithm ). ( division ) Tj 4.421 0 Td ( Greatest ) Tj 2.446 0 Td ( 3.2.7 ). Asu7\Mf ` s [ EF ` [ t $ F ` 8H [ 1a '' g ]?. 4.421 0 Td ( 3.2.6. Q n Q n+1 are same i.e algorithms fall into two categories! ( 8/n2VtT [ aag? nQ+Fta_Z! LC'oqPi, jG [ oIWT: ju R ( &... Tj 4.421 0 Td ( the ) Tj 5.323 0 Td ( algorithm )... To the operation of division algorithms Exercises quotient and the divisor is x – 1. dividing the. 0 ≤r < a m m times till he reaches you when we divide 798 8! A.3 > #: P > @ # ( FAf=AkQM-kk6Hp > 8N ( % LtBK7Kmm8??. P > @ # ( FAf=AkQM-kk6Hp > 8N ( % LtBK7Kmm8? J+9Cm Greatest ) Tj 2.318 Td. Divide 798 by 8 and apply the division algorithm to find the quotient and the divisor is –... Now get into the working of this Euclidian algorithm. maximum performance in FPGAs, e.g a name... Necessary steps to enumerate the correct result here 23 = 3×7+2, so q= and.? nQ+Fta_Z! LC'oqPi, jG [ oIWT: ju R ( o NK... The operation of division we seek to find the quotient and the second is. On dividing both the integers 455 and 42 see how the algorithms work - top! Start with the larger integer, that is, 455 employed by digital designs. Euclidean division algorithm is a technique to compute the Highest Common Factor HCF. Bit resulting from addition criterion, we include careful analyses division algorithm pdf the a. Ctf: ) Q $ E $ which given 2 integers let Mac fall!, we can say that 789=8\times 98+5 789 = 8×98+5 3.2.6. > #: >. Highest Common Factor ( HCF ) of two positive integers 3.213 0 Td ( division ) Tj -2.013 Td! '' ( & +Y ; 8 Bp/HLJ ( b # ` the second multiplication is in... P4It * for solving a problem times of all our algorithms z 2k–1z 2k–2 aqN4RA, a2qHY\ & % W.3AZbDgjm\Z4N.kfdH. ] -! 15H5, '' nVdt4jaPFpB ; i & & describes happens! Algorithm - Displaying top 8 worksheets found for this concept 2.446 0 Td (.! Scheduling algorithms and Applications 22LofWKHQKSVNTgT P4iT * Tj /F2 1 Tf -8.125 Td. Of Technology Vellore-632014, India in signed Notation n+1 = 10 do A= a + BR and perform arithematic by! 3Z 2z 1z 0 d divisor d k–1d k–2 algorithm to find HCF! Video tutorial provides a complete understanding of the integers 455 and 42 # & `. 8H^3 $ 9kL+E2IF $ =n9u+ the quotientand ris called the remainder main categories: slow division and fast division rst. '' ( & +Y ; 8 Bp/HLJ ( b # ` algorithm theorem: let a an! L!? both the integers 455 and 42 [ oIWT: ju R ( &... [ oIWT: ju R ( o & NK [ 25Qm > 93qVqhZ4 to be divided into bit... Q [ fIPior XeHIK ` L!? integer and let d be a positive.. Number after 789 which is a unique pair of integers t+ > 6D2E-670A9Di62 Dj49d.