J~w¥~I¥

s~ FI=l99: 30 '"'-' 12: 30~f~'/ AT A~Jj( · ~t.I~~Jj(1.

tA. 0) 7 m 0) 9=l lP ~ 4 m ~~tR L -C~~~it J:. 5 mJ;JJ::~~~ L t:'~B'-I:tT A: -C ~5Z7J ~ T Q.

2.

~~~I:t 1 m::' ~ 1c.53tJ /.< O)~~~ fflft£tlc. ~cA it J:.

3.

~A~~ ffl ftJHc. Fp~m=i=%'& lj~~=i=% ~~cA it J:.

4.

m:-:t-~.$:J::~t.~~O)f~ffll:t~;gC6f~v -.

1. ~~:£:{*O)~~~~, *~*~5::£:{*0)~~~ <e 'C'$:T. m ?XIEj]1T~1j A = (aij) E ~mxm0)~1f{~ Ak E C (k = 1,2, ... , m) ~iTA:-Ct§~ft ~, IA11> IA21~ IA31~ ... ~ IAml~¥rMJt;:L--Cv'\Q~TQ. Ak (k= 1,2, ... ,m)f::~tJtTQ~1fA::7r/v~~kuk E<em(k= 1,2, ... ,m) -r$:T. J;J.rO)FI=I~~::~;zJ::.

1) a) U1, U2, ... ,Um ~i, 1<l*~~.A.7J:7 '- ~ T Q~:7 r /v~rl'f' <em 'C'-?X3mft~ ft Q ::. ~ ~~1t.

b) li!iI1f{~ Al ~i~~5: ~ ft Q::' ~ ~~1t. ~ tz, Al ~::%tptT Q ~1f""':7 r /v ~L- -C~""':7 r /v;O~ 1f:1:ET Q ::. ~ ~ ~1t.

2)~~M={fckUkICkE<e(k=2,3, ... ,m)} tfE~TQ. f:f:~O)xQ E
k=2~m \ M ;O~G~:7 r/v~1j X1,X2,X3, ... ~zn=An XQ}

_ s;
IIZnl1(n = 1,2, ... )(1.1)

Xn -I:::

JE~T 9 _ t: t:::t..:MVC, Ilzll =1.."jRm \M = {x E jRm I X It M} I::: 1.." z = (:~ )E jRm~ fzt I:::T9­k=la) TA:-CO) y E ~m \ M~::~t L- -C, Ay E ~m \ M ~ ftQ::' ~ ~~ L-, ~ (1.1)~~:tov'\-C Ilzn'll > 0 (n = 1,2, ... ) ~ ftQ::' ~ ~~1t.
b) U1 E ~m ~i, li!iI1ff~ Al ~::~tptT Q ~1f""':7 r /v ~ T Q. ~ tc., :It (1.1)0)~:7 r/v~1J X1,X2,X3, ... ~::~tL--C, ~~~lJdn=min"xn-au111(n=aEJR'1,2, ... ) ~fE~TQ. d~ ~ X n ~ U1 ~mv\ min ~ a ~mv'\-r~::$:1t.
c) TA:-CO) XQ E ~m \ M ~::~tL- -C, lim dn = 0 ;O~pj(;ftTQ::' ~ ~~1t.
n-+ooan =nttLIjL-L f(x) cos yxdx (n = 0,1,2, ... )i; =L"'L f(x) sin yxdx (n = 1,2, ... )

IjL

n 1f

""fd00. L 0) t ~, OO~ f(x) 0)7-1) I.f&~~mHc:;jB~10ma J:f.[iJ' Gm N J:f.[ (N ~ 1) *""fO)ff~7JfIJ fN(X) tj:.L~,rfo)J: '? ~c:1E~~:h0.
Nao ~ (tin. run )
fN(X)
= 2+6
ancosyx+bnsmyx
n=l:t- L-l, g(x) ~, -1r::; X < 1f O)mlHl""f g(x) = g(x) ~~tL9", mJM 21f O)mJM~~~t 9" 0.
1) ~~~ g(x) 0)7- 1) I.1*~~ an, bn ~)j(6bJ:.
2) 1) O)*a*~fljm i.r. :tJ\i\~~~1.
1f

111-=1--+---+·..
43573) 1) ""f.1~GtltL7-1) I.~&~)(mmHc:;jB~10m a ~iJ' Gm 2N Jl* ""fO)ff~)1fD 92N(X) ~ x tc:-::>"'lO)~~)(t L-l~X0.

a) L O)~~~ x ~C:-::>"'-C1Y&7j-li" J:.
b) LO)mit,)(0)1[ijiJ'\~1w:~t0 X 0)1l@.~, 0 < x < 1rO)fP"TIIW~c:;jB"'l9"~l*6bJ:.

4) 3)b) ""f1~ G:htLfi1~~ t 0 x 0)1~0) '? -; It":) t t/J\ ~"'1@~ Xo t 9" 0. L 0) t ~, tff0) K O)I(iEt~*6bJ:.
K = lim 92N(XO)
N-+ootLt~'L-, 1f= 3.14,

i7ro•smy dy = 1.85 t90.
y3.
1) 7)v 7 7 ~ 'J r {a, I} --r~~ ~ nt-=: =J:ftijc ~ A1J t T ~. E Jlt:$ ~ ~ i tj v)iR:7E'11::ff~J~A:kt~:t~ r?

r /'~:"'Jv),,(~TO)rl:l~~:~iZ.J:. t-=:t!.L, :t~ r? r /'~O)A1Jt±=J:fti~0)-m:L1:V:1:::''J r (MSB)
i7~ C? Jt~:A1JT ~ to) t L, ~L1:V: 1:::' 'J r i7~ C? a i7~~&cv) "( t J: v-. i: t iZ. t;f, A1J~2~JIJ "00010"
t±, =J:ftijc 10 ~ ~VT t ~ iZ. ~. i ic, ;1:kt~JI~ ~~: iJ v) "(, ~~s;l:ki~ t± lZ9 ftJ ~: J: .j "(, *~ T;I:ki~t±=£O)p:j~: J: -::> "(, i-0)11Q0)~:ki~t±p:j~:J: -::> "(, i-n.:c'n~VTt 0) t T z. tj iJ, ~JIJ t±­
J:ftijc t t±:7S iZ. tj v-.
a) 1fJtO)=J:fti~0)h- ~ ~J-'T ~ iR:7E'11::ff~!;I:ki~:t ~ r';7 r /' O);I:ki~JI~~ ~~~t.
b) 1~i~0)h-~~J-'T~iR:7E'11::ff~!;I:ki~:t~ r? r /'O)~:ki~JI~~~~~t.

it-=:, .::.O):t~ r?

r /'7J~1~i~0)h-~,~JJ.T ~.::. t ~m~-it J:.
c) b) --r1tmt L t-=::t -r ';7 r /' ~:~t~T ~ IE~Jt)(¥:t G ~ 5E~-it J: .

d) 3 0)1:g:i~0)h- ~~JJ.T ~ iR:5E'11::ff~!;I:ki~:t ~ r? r /' O)~:ki~~~~ ~.~t.

it-=:, .::. O):t ~r';7r/'#30)ffiftO)h-~~~T~.::.t~m~-itJ:.

2) A1J~: L t-=:i7~-::> "( ~~:ki~JI~'::' t ~: 1 "'J0)~2~ ~ tB1JT ~ E JI~~~i tjv)iR:5E'11::ff~!~:ki~.:t ~r';7 r /' ~~ iZ. ~ . .::. 0) J: oJ tj:t ~ r';7 r /' ~~~~t v) oJ. ;1:ki~Jlf$~"C't±, ;l:ki~rs' O):*~D ~:A
1J ~2 ~ t te 1J ~2 i} ~ "I " (A 7 'J ~ .:L) "C'!R tJJ -::> "( ~~2 T ~. i: t iZ. Lf, ;I:ki~ p "C' ~2 ~ a ~ A 1J L"(, ;I:ki~ q ~:JI~T ~ W~:, ~2i} b ~ te1JT ~jJ1i~t±, ~ TO) J: oJ ~:. <.

~7 )v 7 7 ~ 'J r {a, I} ~ A te 1J~2i} t L "(t.& oJ ~j~~~: "'Jv) "( ~ T 0) Fl:l~ ~:~ iZ. J:. i: t!. L, .::.nC? O)~1l~t±~JIJ ~ te1J L tjv) t 0) t T ~.
a)

=J:fti~, ;1:ki~JI~~O)~~t± 1) t fPJif1Jtt -it J:.

A1J ~ nt-=:=J:fti~~ 2 --r*IJ -::> t-=:im ~ te1JT ~ ~~~O);I:ki~Jlf$~ ~~~t. it-=:, .; 0)~1l~i7~=j:fti5c ~ 2 --r~IJ -::> i: im ~ tB 1J T~ .::. t ~ m~ -it J: .

b)

A1J ~ nt-=:=J:fti5c~ 3 --r*IJ -::> t-=:im ~ te1JT ~ ~~~O);I:ki~~f$~ ~~~t. it-=:, .::. 0)$t1~~#=~ft~3--r~-::>~8~lli1JT~.::.t~m~-itJ:.

4. ~4.1ft, 3"":)O)nMOS r-7/':/.A?TM1 , M2 , M3:a:-B-tf@]~:a:-~L-, *4.1'::-t0)@]IEa/~7j-?T:a:-~~.

~~~, *r-7/':/.A?T0)*~~.~~m~~~~~~.

VDD

14..........

4'mr)j'mJ±

VDD = S.OVtBtJ~:wr~ •C = O.1x10- 12 p

M1 0) L- ~ " "1I«mJ±
M2 , M30) L- ~ " "fl«mJ±
M1 , M2 , M30) r- 7 /'.A::J. /'?T~ -7?T /' .A/~7 j-?Tv;.d = -1.0 V
VTe = 1.0 V

K = 100 X 10- 6 AJV2~ 4.10IDS= 2K(Vas - VT jVDS -KV~s(K(Vas - VT )(Vas - v;. ~ 0: )lg ~~J!i :l!!jG)(0 s VDS < Vas -VT:

(0 < Vas - VT s VDS: !~flJl1J!i~)#!~flJl1J!i~)(4.~):c\:(4.1)ft nMOS r-7 /':/.A?T 0) 3 "":)O)lbf''F~~~'::jO~t ~m¥JTE~J±*i~j::a:-* L-, I DS ~t P' 1/.-{ /' • './- AFJ.lmmt, Vas f'iij- 1"-- • './-.A FJ:l~mJ±, VDS ft P'1/.-{ /' • './-.A F~mJ±, VT ft* 4.1 '::jO~t -0 L ~""f~mJ± VTd , VTe '::)<iJ,tT Q.
1)
V; ~ V2 O)f~il~}E~ -?t-::""&J ~, @J~il~~}EL-I4 = 0 ~ f~"?t-::..~1m:a:-~;tQ.
a)Ml' M 2 , M3-ttt..'f~1A::jOtt Q Vas ~ VDS :a:-, V;, Vz, V3 , ~ ~ VDD :a:- Jt]" "t-::..:c\:'"t:*it.
b) V; = OV, Vz = VDD 0) ~ ~, M 2 ftJll~~Ji~-etb11p L-, M1 ~ M 3 ft-ttt..'ftt~F~~~~l~'"t:lh
11p L- -C"" Q . ~ 0) C:. ~ 0) 11' V3 , V4 0)11«:a:- -ttt..'f tt3f< 60 J:: .
c)V; = VDD , V2 = VDD 0) ~ ~ 0) ~, ~ 0)11«:a:--ttt..'ftt3f<6b J::. f~jO, ~\~'"t:"&Jttfi.Ji4 = 3.74,.Jl5 = 3.87 0) ili{f),11« ~{~Jt] it J:: .
d) V; = !""DD' V2 = OV 0) C:. ~ 0) 11' ~ O)fl«:a:--ttt..'ftt3f<6b J::. ~ t-::.., ~ 0) C:. ~ 0) M1 , M2 , M30)tbflp~~~~ ~it.

~-5.0..

lRrt:l~ Ao~..

lRrt:l~ B~

20

10~

I [ns][@ 4.2 ~ 0)1Bl*V2 = VDD ~C U!fI)E L, ~ 7J~ [@ 4.2 ~C ~Tj]*1Bl-r: <b Q ~ ~ 0) @]~ 0)r,t~ ~ ~ *- Q. t~ t-!. L,2)~j:Ml.ijiO)t~6b,=- =- -r:

M1 ~j: V4 < VDD 0) ~ ~~flJ~l:1:ij\G-r:l;J]flF L, V4 = VDD 0) ~ ~ ~F~~flJ~l:1:ij\G-r:l;J]flFT Q ~ L,M z ' M3~j:~ItJT~Ji~J2J3'~-r:~j:-tt1~tL~1iffit~mR=

12K(VDD - VTe )tc.,~ 7J~~1~T Q Th'[M-r:~j:I4 = 0 -r:<bQ ~ L,~,

1=0 0) ~ ~O) V4 0)1L«~ VSAT = 2RISAT ~ J1I{~ -r:~ Q ~ T Q.

~cfi~~*-Gt1Q bO)~TQ. ~M1 O)~~flJ~l~~c:to~t Q ~¥m~ I SAT = KV;a ~ Lt~ t:a)

~ 4.2 0) lRr~~ A~C:to" \-C,V4 = 0.5(VDD - VSA T ) + VSA T ~ f~ Q ~~~ 11 ~*&') J:.

b)[@ 4.2 O)lRFJl B ~C:to" \-C, V4 = 0.5(VDD - VSA T ) +VSA T ~ f~ Q ~~~ I z ~*&') J:. f~:to, ~,~-r:tb
t1~:fln 2 = 0.69 0)J1If~1L«~f~JtHt J:.

c)[@ 4.2 O)lRFJl A, B ~c:to~t Q V4 O)mt*O)tft*~Wi~t.

5. *{§{§~i6~ s = ±1 --r~,'Q 2 {~im{§~ A T bi6~~,'Q. ~{§{§~ r tt, ~{§{§~ s ~::~g-rl3"J~::3!RlLtJ:~if ti i6~1JDV J -C1~ GtL,'Q.

gtJ:V ~,

r=s+n--r~.Q. te-tiG, ~if n ~d: -1- a 7J\ G 1 + b (a, b > 0) O)Fa~ti~t~::-f~?t~G, ~0)1it~
1&~~~ p(n) ~d:, r~O)J: '5 ~::-9-X GtL,'Q ~O) c g,'Q.

p(n)___I----j=2=+~=+=b =~~~_I__-_.
I0-l-a~{§mt~d:,~IJJEG~v){~ x ~~JEG,nl+b;;xO)fl~mJ{IH::Gtc.i6~J-C*{§{§~ s ~flJEg,'Q .

• ~{§{§~ r i6'\ x ~J::tJ:G~i, s = +1 i6'\*{§~tLte-~O)c~UJEg,'Q. ~tc.,• ~{§{§~ r i6'\ x *~tJ: G ~i, s = -1 i6'\*{§~ tLtc. ~ 0) c ~ljJEg,'Q.
1) ~{§tli6\ G s = +1 i6'\*{§~ tLtc. c ~ ~::,c G-C3:K6bJ:.
cG-C3:K6bJ:.

[PJ**~::,~ tJ 0)1: r.; ,'Q1it~~~ljJE G ~ v){~ x O)~~s = -1 i6'\*{§~tLtc.c~~::, ~tJO)1:r.;,'Q1it~~ x O)~~2) ~{§{§~ s = ±1 0)§£1:1it$i6'\,(i) Pr(s = +1) = Pr(s = -1) = 1/2, ts. GLF~::(ii) Pr(s = +1) = 3/4, Pr(s = -1) = 1/4'"E~,'Q 2 "::JO)~-@l~tL-ttL~::~ G-C,a) ~O))m.1§~ATbO)~~~tJ~ PE ~ x O)~~cG-C3:K6b, 7"5'7~::*it.
b) ~~~tJ~ PE(X) ~~/J\Cg,'Q, ~)itJ:~IjJEG~v){~ Xopt tJ:GLF~:::CO)c~O)~~~ tJ $ PE(Xopt) ~3:K6bJ:.
3) J::O)fl~J;~U!IJc~d:53IH::, ~{§{§~c G-C r = R ~~{§Gtc.c~~::, *{§{§~i6~ s = ±1'"E~,'Q~{lf:{"1~1it~1&J3tp(s = +1 I r = R) C p(s = -1 I r = R) o)*/J\~,f(R) = {p(s = +1 I r = R) - p(s = -1 Ir = R) }p(r = R)

L:J: J -Cltt~G,.f(R)~otJ:G~i, s=+1,• f(R) < 0 tJ:G~i, s =-1,c ~ljJE9,'Q, £*I3"JtJ:fl~mJ{lj7J'\~,'Q.
a) z O)fl~mJtlj~d:{PJ cP¥~itL,'Q i», ~t-=, :CO)!f-f~~d:{liJi6\.
b) 2)-(ii) c [PJ r.; <, J!{§{§~ s = ±1 0)§£1:1it$i6'\ Pr(s = +1) = 3/4, Pr(s =-1) = 1/4 'C'~,'Q~.g-~::"::Jv)-C, f(R) 0)7"5' 7 ~ -2 - a < R < 2 + b O)fB
rm--riaHt. ~ G~::, ~O)fl~rt~::J:,'Q5f~~tJ$~*6bJ:.

6. }\.1J*~IjO)/"'7'~/~;f~t±lTgJI~1f@]~c ~~x~tTg. :'O)@]~~'j:~ 6.1 ~=jf-;T@]~~~1iffi-C:', 31~~J::0) 17J~iltt L, "(m~l.,t=. ~ 2:" ~= 1 ~l±l.1J L" -t- 5 -rftv\~-er~= 0 ~t±l.1JTg. ~ffi3~7~ ~~'j: 2}\.1J0) AND 7~~, 2}\.1J0) OR7~ I-, NOT 7~ r-~j}.~fflv\"(~'j:v\~tftv\. 7!J '/7°7p '/ 7°~'j::sL ~J::7J~ 'J lbfFO):C'/ -/ l- !J jj'~ 7!J '/7°7 P 'Y 7° ~ T g.
yx

DQCKclock __- ­----'~ 6.1

Time (ns) 10 20 30 40 50 60 70 80 90

dL~q

clOC~

clock

dq ---J~ 6.3~ 6.2

j=B=Qclock

CK .

qclock~ 00

j.:kKQ*Time (us) 10 20 30 40 50 60 70 80 90:

IM

k _f------i------i---+----'Ir-h~ii~ 6.5~ 6.41

j:

0:

1

I---+---+-,~::::::.:L

6.1 Qnext
01

1110!

1) ~ 6.2 ~=jf-;T D 7 !J 'Y 7°7 P 'Y 7"O)}\.1JrEl%~~ 6.3 ~=jf-;T. l±l.1Jq O)fJ]~1~~ 0 ~ L, "(, l±l.1J q O)lbfFrEl%~m~t.
2) ~ 6.4 ~=jf-;T JK 7 !J '/7°7 P 'Y 7°0)}\.1JrEl%~~ 6.5 ~=jf-;T. l±l.1J q O)fJ]~H~~ 0 ~ L, "(, l±l
1J q O)lt.JfFrEl%~Wi~t. ~ t=.$: 6.1 ~=jf-;T JK 7 !J 'Y 7°7 P 'Y 7°O)liJfF*'r~~7iSm ~1t J::. 7!J 'Y 7°7 P 'Y 7"~=:to~t g tJ\~~ Q O){jzO)tJ\~j~ Qnext ~ B"c)£T g.
3) ~ 6.6 ~=tt~~JJQT g :. ~ -rJI~ff@]~ c O)tJ\~j~~~ ~7iSm ~1t J::. j:LI=PO) 9J 0)i:c1JtIJO)x*~1J7J~~~j ~, ti1JtlJ O)~)c*7J~ l±liJ ~$:T.
.*: 6.28MNxl\!!ncxt

N n exty~ 6.64) JI~1f@]~ c O)}\iJ ~ x, l±l.1J ~ y ~ T 0. ~ 6.6 ~=:to~t 0 So, Sl, S2, S3 ~ v \ 5 tJ\~j~-t-n':fn 2 ~" 'Y l- 0) 2 ii~)c 00, 01, 10, 11 -C:'$:m L" J::1lr ~" 'Y l- ~ M, T1lr ~" 'Y l- ~ N ~ T g. $:6.2 ~=jf-;TJII~1f@]~ c O)J!!~$:~7iSm ~ 1t J::. ~ t=.n /v J ~~ ~ ffl v\"( l±l.1J y, M O){jzO)tJ\~jM next , N 0){jz0)tJ\~ N next 0)-t-n-t'nO)~~Ft:i1~1t1t J::.
5) 21~ 0) D 7 !J 'Y 7°7 P 'Y 7° <!:: -r2:" g t~ ~t pit v \~ffilf:!I!7~ l- :a:- ffl v\ "( j1~1f@]~ c :a:-fF~1t J::.
6) 2000) JK 7 !J 'Y 7°7 P 'Y 7° <!:: -r:e:- g t='~tyftv \~ffil~7~ l- ~ ffl v\"( JI~1f@]~ C ~fFJJX:1t J::.

void ex1(void){x[O] ,= 7; x[j.]=10; x[2]=1; x[3]= 5;

B(O, 1, 3);}2) TgcO)M~ ex2 :a:~iT ~ 1tt~ C: ~, ~1TiJ~~ TT Q ~ '1:0) A, B 0)Il¥V/±H>7IJ:a: ~ ijlm, ir O)f~ C: C: t ~~.~t. M~O)Il¥Vte 1...-jlJ C: Vi, -{-O)Mt5c0)Il¥Vte ~nQ]I~J¥:a: Il¥ V te 1.. - a~ ~~ mr ~ n Q ij I~ 0)f~ C: C: t ~~ gC 1...- t: t 0)'1: ib Q. 1~~;t Vi', M ~ F0)Il¥Vte1...-jIJF(1, 0), F(3, 1) ~i, M~FiJ~2@JIl¥Vte~n,~fJJ~iijl~1,0iJ~, 2It § ~i 3, 1 iJ~ II¥Vte 1...-a~~~mr ~ n Q :. C: :a:~,*T Q .

~ Il ,void ex2(void){x[O] = 9; x[1]A(O, 3);=3; x[2]=4; x[3]=2;}3) 2) O)M~ ex2 :a:~iT 1...-t~1&0) x 0)1*J?@::a:~ 1...-, A ~i x ~~~t 1...- -c eo: J: ? ftf"Fffl :a: iT? M~iJ~:a:m~1t J:.
4) x [0] , x [1J, ... , x [n - 1J (t~ t~ 1...- l::;n::;MAX-LENGTH C: T Q) ~~/f~:a:{-tA 1...-,A(0, n - 1) :a:~iT~ 1tt~ C: ~ 0) A O)Il¥Vte 1...-@J~:a: Z(n) C: T Q. te-te.' 1...-, ~fJJO)
A (0, n - 1) O)II¥Vte 1...- t 1 @J ~~~5c;t Q to) C: T Q. :. 0) C: ~, tXO)~~~ ~~~;t J:.
a) n= 2 m (m ~i~Fjt~~) 0) C: ~, Z(n):a: m :a:1~"0 t~~'1:*1t.
b) -f,j~0) n ~~'0l.-"-c, Z(n) :a:~{r:~c'*1t.
5) i!§2.jIJ X ~~M 1...-, ~~fflIl¥Vte 1...-:a: ffll.- "ftl.- "C', A C: IRJ L:~t. :a: iT ? ~ 7.2 0) J: ? ftM~
D :a:1'P"0t~. ~~IH~@~ft7"o !l7.b.::z- F:a::@.li)J:. t~t~1...-, ~1I~~~j:M~B 0)

Il¥Vte 1...- :a:-2;"tJ t 0) C: T Q.

#define MAX_LENGTH 1000
int x [MAX_LENGTH] ;void B(int iI, int m, int ir){

int i, j, k;
int temp [MAX_LENGTH] ;void A(int iI, int ir){= il;
j = m + 1;

int m;iif (il >= ir) return;m = (il + ir) / 2;A(il, m);A(m + 1, ir);
B'(d l , m, ir);for (k = il; k <= i~; k++)if (i > m) temp[k] = x[j++];else if (j > ir) temp[k] = X [i++] ;else if (x[i] <= x[j]) temp[k] = X [i++] ;else temp[k] = x[j++] ;for (k' = il; k <= ir; k++)x[k] = temp[k] ;}
}

~ 7.1

void D(int iI, int ir){

int m, i, j, size;
size = 1;
while (size <= (ir - il)) {for (i = il; i <= ir; i = i + size * 2) {j = i + size * 2 - 1;
m = (i + j) / 2;}

size = size * 2; .
}}~ 7.2