l. {f. ¥ - '" 1. flo '" hUr. (tt ~ 3 1\IJ 4A Jii, : 1. 4t ' ~t '" ' fo 4t If.) • # ~ 34 itt. '" '£ ~ ~ . .Jt. '!' ~ BI.1 '" '£

(# 10,q • •

,q-3-~6

10%)

l. {f. ¥ - '" 1. flo '" hUr. ^(tt ~ 3 1\IJ 4A Jii, : 1. 4t ' _~t '" ' fo 4t If.) • # _~ 34 itt. '" '£ _{~ ~} . .Jt. '!' _~ BI.1 '" '£

.:fR~~-im~· e..~ 14itt.~~1.4t~ ·13itt.~~~t"'~·21itt.~ff4tlf.~' 3itt./O)~~~1j-J:.

.i{ 3 _Jl~ . 1it*-(a){l~*-im~BI.1"'1.it? (b){l~~Rilim~BI.1"'1.it?

2.

_tt.~

_(a)

_:!l.~¢

/} = {a,

_E

_PIA) {all •

P(A)~.Jt.".~(power

_(b)

_¢~

_{PIA) (c) {al} set) •

_~

_PIA) 1;tiA!t-r _{(d) {{{a}}}}

1IJitiiK~${\ _E

_PIA) •

_(iEi'~

_{(e) {a,} • _{all

_?t.iE.~)~

_PIA)

3. ~ItIil~*(T,N,S,P)fflf';iiliBl.1~1" L'.Jt.'!' T={a,b,cl~:f~BI.1.~'N={S.A,B};IUF:f~BI.1"

~·Sk.M2~'~ • • _lf..BI.12~ • • _-r~~~BI.1 • • ffl.iiliBl.1.~L·

(a) P = {S-MA, S--+aS, A--+abl (b) P = {S--+aSA, S--+aB, A--+b, B--+c 1

~(a)15~

• •

_~M~M~~

• •

:.~.'~~.'fo.a.·

• •

5~·1itM~J~a.:f/o)BI.1

~M*?

(b) 15

_{~.~ ~~~}

• • • • 5

_~

•

_1itM~

J

_jJa~*?

5. N

~ § .~itBl.1

• • • f fo g

~

Jl. N ilJ N BI.1,iE,it • liEN·

j{1I) =

211'

a(lI) =

" ^{ O

1

il Jl. -!If, it 1Il!,~tt

6. (a) "ttafo b~-=-AlftitUi,iE,it·.Jt.ttUi~>i'J~ ^{ak=2 k} fo b

lr=3 1r

,k~O' ~itUi.J,itc;ltafo b BI.1flllt(convolution)·

C

= a • b •

1it.;Ji.it{i~tt

c BI.1

,£~,iE,tt

(generating function) • (b)

e..~;V;ttUi,iE,ttBl.1,£~,iE,it~ A(z)' t;!;,ot.Jt.1tJ.tBl.1itUi~tt·

~+3--6-' A(z) = • •

1- 2.

8. #l41i-r*-. III Huffman

BI.1;l'i~*'

(a) >tt.Huffman ...,#t'

(&m:ft~l!,O' E#t:ft~J!,

I)'.i.

'£~

1! BI.1:f 11

~(prefix

code) • (b) AA!.#:t *" ^J

^{~ ~ft}

^{it. ?}

iCharacterl Frequency

A ~

!

=l

n ^r

7

C 12

i ^{0 17}

E 20

F 28

I

ltl

2

Ji (J\.

2

Ji)

9. (a)t;t::G:.1t -::li fl;tJ(.

~.ll( J;I.

Transition diagram .tal i;&.:t..) ,

):J.

(0,

l)~

fil A.&.fil :!l :f

-lij: ,

11:.

~fil

A

/I]

:f-lij:+':!l~3~~~1*'fil:!l:f-lij:~~~I'~~~~:

filA:f *: 001 1 1 10 101 10011 1 1 1010

*:!l:f*: 0000011000000000111000

(b)ta:,1Ut -::li fl;tJ(.

~.ll( J;I.

Transition diagram .tal i;&.:t..) , III J;l.1J\ illH .liAi-t) lb

^:f-lij:

{II, bJ

m.~ /I]:f

*(string)+A-::li~tt~

a

/I]:f*'~;F: orJ;l.1'Fl1t::li>ll1llJ;tJ(.~{E,OJ

E: An even number of a's was found.

0: An odd number of a's was found.

E(x"x, ,x

J

.x,) = L (0, I, 4, 5,10, II, 14, 15)

m

(b) ..f-M )'

$..i#;~

196)' (mod 425) = 1 fa 0 < J' < 425.

(~;F:

gcd(196, ·'15) =

¹⁾