‚•њђ 1.

zћњџ®ў �ў• �њђў Ў›•”ќћўћ ќђ™-ћ‘©ћ ЈЎў ћ™Ўў’ћ:

r ћ “ђќ�—ђ¦�Ї ќђ љћњџ®ўЄ ќћўћ �—§�Ў›•ќ�• ЎЄ©•Ўў’Ј’ђ ђ‘Ўў ђљў•ќ њћ”•› ќђ �—§�Ў›•ќ�Їўђ z=f(x), љЄ”•ўћ

x- ’Ґћ”ќ� ”ђќќ�; z- ўЄ Ў•ќ  •—Ј›ўђў;f- ¤Јќљ¦�Ї —ђ џ ћ”Ј¦� ђќ• ќђ  •—Ј›ўђўђ; x,y- §�Ў›ђ, Ў�њ’ћ›�, ћ‘ ђ—�, ¤ђ™›ћ’•; f- §�Ў›ћ’�, Ў�њ’ћ›ќ� �—§�Ў›•ќ�Ї, ”ћљђ—ђў•›Ўў’ђ(f₁(f₂(...(x))); x—§�Ў›Ї’ђ Ў• џћЎ›•”ћ’ђў•›ќћЎўўђ ћў џћ-џ ћЎў� ”•™Ўў’�Ї. u¤•љў�’ќћЎўўђ ќђ љћњџ®ўЄ ќћўћ �—§�Ў›•ќ�• њћ–• ”ђ Ў• ћ‘ЇЎќ� ќђ™-”ћ‘ • § •— ћЎќћ’ќ�ў• Ґђ ђљў• �Ўў�љ� ќђ zx. p ў• Ўђ:

ђ) ќ•ћ‘Ґћ”�њћ џ ћЎў ђќЎў’ћ (џђњ•ў)- џ ћџћ ¦�ћќђ›ќћ ќђ ‘ ћЇ ќђ ”ђќќ�ў• (n) ќђ —ђ”ђ§ђўђ.

‘) ‘Є —ћ”•™Ўў’�•- ђ‘Ўћ›®ўќћ ’ •њ• —ђ �—џЄ›ќ•ќ�• ќђ џ ћ“ ђњђўђ. wђ’�Ў� ћў ћ‘ ђ‘ћў•ќ�ў• љћќљ •ўќ� ”ђќќ�. x—њ• ’ђќ•ўћ ќђ ђ‘Ўћ›®ўќћўћ ’ •њ• • ў Ј”ќћ. xњђ �ќЎў Јљ¦�� љћ�ўћ Ўђ џћ-џ ћЎў�- —ђ•њђў 1,2 ўђљўђ , ђ ” Ј“� 2000, 4000 џ ћ¦•Ўћ ќ� ўђљўђ. ЃЄ©•Ўў’Ј’ђў Ўџ•¦�ђ›ќ� Ў •”� —ђ Ґ ћќћњ•ў � ђќ• ќђ ’ •њ•ўћ � Ј’•›�§ђ’ђќ• ќђ ‘Є —ћ”•™Ўў’�•ўћ.

u¤•љў�’ќћЎўўђ ќђ zx • ћўќћЎ�ў•›ќћўћ ќђ ђЎў’ђќ• ќђ ‘ ћЇ ќђ ћ‘ ђ‘ћў•ќ�ў• ”ђќќ� џ � Ђ-љ ђўќћ џћ’�Ёђ’ђќ• ќђ џ ћ�—’ћ”�ў•›ќћЎўўђ ќђ zЃ � NP- Ў›ћ–ќћЎў ќђ ђ›“ћ �ўњ�ў•

~Ўќћ’ќ�ў• ¤Јќљ¦�� ќђ ћ “ђќ�—ђ¦�Ї ќђ љћњџ®ў �ў• Ўђ:

-ћ‘ ђ‘ћўљђ ќђ ”ђќќ�(Processing);

-ЎЄҐ ђќ•ќ�•(Storage);

-ћ‘њ•ќ ќђ ”ђќќ�(Movement);

-Јџ ђ’›•ќ�•(Control);

ћљђ—ђќ�ў• “ ђ¤�љ� ћџ�Ў’ђў ћ‘њ•ќђ ќђ ”ђќќ� њ•–”Ј  ђ—›�§ќ�ў• љћњџћќ•ќў� ћў ћ “ђќ�—ђ¦�Їўђ ќђ љћњџ®ў �ў•:

ђ) ’ЄќЁ•ќ ћ‘њ•ќ; ‘) ќђўћ’ђ ’ђќ•,  ђ—ўћ’ђ ’ђќ• ќђ ”ђќќ�; ’) ’Єў •Ёќђ ћ‘ ђ‘ћўљђ;“) ћ‘ ђ‘ћўљђ ќђ ћ‘•њ;

‚•њђ 2

~Ўќћ’ќ�ў• ¤Јќљ¦�� ќђ џ ћ¦•Ўћ �ў• Ўђ ћ‘ ђ‘ћўљђ ќђ ”ђќќ�, Јџ ђ’›•ќ�• § •— �—§�Ў›•ќ�Ї ќђ њђЁ�ќќ� �ќЎў Јљ¦��.

Central processing unit (CPU)

 � ›�џЎђ ќђ љ•Ё џђњ•ў џ ћ¦•Ўћ ђ њќћ“ћљ ђўќћ Ў• ћ‘ Є©ђ љЄњ џђњ•ўўђ ‚ћ’ђ • Ў ђ’ќ�ў•›ќћ ‘ђ’ќћ ўЄ™ љђўћ ўЇ њћ–• ”ђ • —ђ•ўђ. |ћ“ђў ”ђ Ў• џћЎўђ’Їў ќЇљћ›љћ љ•Ёђ Ў ¦•› џћ’�Ёђ’ђќ• Ўљћ ћЎўўђ ќђ ћ‘ ђ‘ћўљђ.

xњђ 3 ќђ§�ќђ —ђ  •ђ›�—ђ¦�Ї ќђ њ�љ ћ џ ћ“ ђњђ;

- Ґђ ”Ј• •ќ- џ ћ“ ђњђўђ Ў•  •ђ›�—� ђ ’Є’ ’�” ќђ ЎҐ•њ�;

- Ўћ¤ўЈ• •ќ- њ�љ ћџ ћ“ ђњ�ў• Ў• —ђџ�Ў’ђў ’ RAM;

- ¤Є ќЈ• •ќ- (џ ћ¦•Ўћ � ‘•— ’“ ђ”•ќ� �ќЎў Јљ¦��);

p›“ћ �ўЄњЄў —ђ ћџ�Ўђќ�• ќђ њ�љ ћџ ћ“ ђњ� • Ў›•”ќ�Ї:

type word.......;

address....;

mem=array[o..4085] of word;

Procedure .....;

Var .....

begin

.

.

begin

(1- §•ў•ќ• ќђ �ќЎў Јљ¦�Ї)

(2- ¤ћ њ� ђќ• ќђ Ў›•”’ђ© ђ” •Ў —ђ �ќЎў Јљ¦�Ї)

(3-”•¤�ќ� ђќ• ќђ ў•љЈ©ђўђ �ќЎў Јљ¦�Ї � ў�џђ)

(4- ¤ћ њ� ђќ• ќђ ђ” •Ў ќђ ћџ• ђќ”)

(5- §•ў•ќ• ќђ ћџ• ђќ” (џ � ќ•ћ‘Ґћ”�њћЎў))

(6- �—џЄ›ќ•ќ�• ќђ ћџ• ђ¦�Їўђ)

end;

end;

 � џћљћ›•ќ�Їўђ zЃ • ’ђ–ќђ • ќђЎ›•”Ўў’•ќћЎўўђ. ~Ўќћ’ќ�ў• Ґђ ђљў• �Ўў�љ� Ўђ:

-  ћ�—’ћ”�ў•›ќћЎў (�ќЎў Јљ¦�� —ђ Ў•љЈќ”ђ)- �—њ• ’ђў•›ќђ •”�ќ�¦ђ Ip/s, FLOP/s- ‘ ћ� �ќЎў Јљ¦�� Ў џ›ђ’ђ©ђ —ђџ•ўђЇ —ђ Ў•љЈќ”ђ (‘Є —�ќђўђ Ў•  ђ—›�§ђ’ђ Ў ў � џћ Ї”Єљђ).

- Ѓџ�ЎЄљ ћў �ќЎў Јљ¦�� (Complex Instruction Set Computer).

- tЄ›–�ќђ ( ђ— •”•ќћЎў) ќђ њђЁ�ќќђўђ ”Јњђ.

- q ћ� ќђ  •“�Ўў �ў• (›ћљђ›ќђ џђњ•ў).

- zђџђ¦�ў•ў ќђ ћЎќћ’ќђўђ •”�ќ�§ќђ џђњ•ў (•”�ќ�§ќђ).

- zђџђ¦�ў•ў ќђ ’ЄќЁќђўђ ”’ћ�§ќђ џђњ•ў (’ўћ �§ќђ).

- r� ўЈђ›ќћ ђ” •Ўќћ џ ћЎў ђќЎў’ћ.

- rҐћ”ќћ/�—Ґћ”ќ� џ• �¤• ќ� � љћњЈќ�љђ¦�ћќќ� Ј-’ђ .

- ~џ• ђ¦�ћќќђ Ў�Ўў•њђ (Ў •”ђ).

- }�’ћ ќђ њЈ›ў�џ ћ“ ђњ� ђќ•.

- †•ќђ � ” .

ћљћ›•ќ�Їўђ zЃ џ ћ�—›�—ђў •”ќћ ћў ” Ј“ћ љђўћ ’ЎЇљћ Ў›•”’ђ©ћ Ў• ћџ� ђ ќђ ЈЎў ћ™Ўў’ћўћ ќђ џ •”ќћўћ:

1 џћљћ›•ќ�•;

2 џћљћ›•ќ�•;

3 џћљћ›•ќ�•;

Ђђ—’�ў�•ўћ ќђ �ќў•“ ђ›ќ�ў• ў•Ґќћ›ћ“�� —ђ zЃ њћ–• ”ђ Ў• џ •”Ўўђ’� § •— Ў›•”ќђўђ љ �’ђ:

qђ—ћ’ђ љ›ђЎ�¤�љђ¦�Ї ќђ zЃ њћ–• ”ђ Ў• ќђџ ђ’� џћ  ђ—›�§ќ� џ �—ќђ¦� џ �ЎЄ©� ќђ љћњџ®ў �ў•:

ђ) џћ џ •”ќђ—ќђ§•ќ�•

- ~‘ ђ‘ћўљђ ќђ ”ђќќ� (Data processing);

- Јџ ђ’›•ќ�• - ’ •њ•ўћ —ђ џћ›Ј§ђ’ђќ• ќђ њћ”Ј› • љ �ў�§ќћ (Real time Processing);

‘) џћ ’Є—њћ–ќћЎў�:

- Јќ�’• Ўђ›ќ�;

- Ўџ•¦�ђ›�—� ђќ�;

’) џћ ћ “ђќ�—ђ¦�Ї:

- •”ќћџ ћ“ ђњќ� ;

- њЈ›ў�џ ћ“ Ўњќ� ;

“) џћ Ўў ЈљўЈ ђ:

- ¤�љЎ� ђќђ;

-  •љћќ¤�“Ј Ј•њђ;

”) џћ џ ћ�—’ћ”�ў•›ќћЎў:

- ЎЈџ•  љћњџ®ў �;

- “ћ›•њ� zЃ (main frame);

- њ�ќ� zЃ;

- њ�љ ћ zЃ;

‚u|p 3.

„ћ њђў�ў• � џћ” •–”ђќ•ўћ ќђ —ђџ�Ў�ў• ’ џђњ•ўўђ ќђ™-ћ‘©ћ њћ–• ”ђ Ў• џ •”Ўўђ’� ’ Ў›•”ќђўђ ўђ‘›�¦ђ:

	‘�ў	‘ђ™ўћ’•	Ў�ќћќ�њ
bit	1b
nibble	4b	halfbyte
byte	8b	1B	ў•ў ђ”ђ
word	16b	2B	halfword
doubleword	32b	4B
quadreword	64b	8B
tenbyte	80b	10B

†•›ћ§�Ў›•ќ�ў• ђ” •Ўќ� “ ђќ�¦� ќђ —ђџ�Ў�ў• Ўђ ђ” •Ў ’ џђњ•ўўђ, ”’ћ�§ќђўђ Ўўћ™ќћЎў, ќђ љћ™ўћ • §•ўќђ џћ ћўќћЁ•ќ�• ќђ ”Є›–�ќђўђ ќђ —ђџ�Ўђ Ўџ Їњћ Ё� ћ§�ќђўђ ќђ џђњ•ўўђ.

 � џћ” •–”ђќ•ўћ ќђ —ђџ�Ў�ў• ’ џђњ•ўўђ �њђњ• ќ�—Ґћ”Ї©ћ � ’Є—Ґћ”Ї©ћ џћ” •–”ђќ•. }�—Ґћ”Ї©ћ  ђ—џћ›ђ“ђќ• (џћ” •–”ђќ•) џћ Ј’•›�§ђ’ђ©� Ў• ђ” •Ў� ’ џђњ•ўўђ ќђ ќ�—Ґћ”Ї©� џћ Ўўђ Ё�ќЎў’ћ —ђџ�Ў� (ћў MSB љЄњ LSB. }ђ™-њђ›Єљ ђ” •Ў ЎЄ”Є –ђ MSB). Ђђ—џћ›ђ“ђќ• џћ ќђ ђЎў’ђќ• ќђ ђ” •Ў� ’ џђњ•ўўђ ќђ ’Є—Ґћ”Ї©� џћ Ўўђ Ё�ќЎў’ћ —ђџ�Ў� (ћў LSB љЄњ MSB. }ђ™-њђ›Єљ ђ” •Ў ЎЄ”Є –ђ LSB).

Least Significaut Byte/bit (њ›ђ”Ё� ‘ђ™ў/‘�ў).

Most Significaut Byte/bit (Ўўђ Ё� ‘ђ™ў/‘�ў).

}ђ �—џћ›—’ђќ�ў• ‘ ћ™ќ� Ў�Ўў•њ� њћ–• ”ђ Ў• ќђџ ђ’� ћЎќћ’ќђ љ›ђЎ�¤�љђ¦�Ї —ђ ¦�¤ ћ’ђ ћ‘ ђ‘ћўљђ :

ђ) џћ—�¦�ћќќ� (qЃ):

- ќђўЈ ђ›ќђ;

- Ў ћў �¦ђў•›ќђ ћЎќћ’ђ;

- —ќђљћ ђ—”•›ќђ;

- Ў љћњџ›•љЎќђ ћЎќћ’ђ;

- Ў ›ћ“ђ �ўњ�§ќђ ћЎќћ’ђ;

- Ўњ•Ў•ќђ;

- ”’ћ�§ќћ-”•Ў•ў�§ќђ;

‘) ќ•џћ—�¦�ћќќ� (}qЃ) - Ў ћЎўђўЄ§ќ� љ›ђЎћ’•;

 •”Ўўђ’Їќ•ўћ ќђ qЃ} Ў• �—’Є Ё’ђ ’Є’ ’�” ќђ џћ›�ќћњ

љЄ”•ўћ a - ¦�¤ � (¦•›�,џћ›ћ–�ў•›ќ�,   ќђ ‘ ћ™); m+n:  ђ— Ї”ќћЎў (n- ” ћ‘ќћ, +m- ¦•›�) —ђ i=n ...+m p - ћЎќћ’ђ (¦Ї›ђ џћ›ћ–�ў•›ќђ).

 �њ• : 137₁₀=1.10²+3.10¹+7.10⁰

p �ўњ•ў�§ќ�ў• ”•™Ўў’�Ї Ў• �—’Є Ё’ђў џћ •”ќћћ‘ ђ—•ќ ќђ§�ќ (ќ•—ђ’�Ў�њћ ћў  ) Ў �—џЄ›ќ•ќ�• ќђ ўђ‘›�¦� —ђ ЎЈњђ � џ ћ�—’•”•ќ�• ’ •”�ќ  ђ— Ї”.

 �њ• �:

~‘ Є©ђќ• ћў ”’ћ�§ќђ qЃ ’ ”•Ў•ў�§ќђ:

”’ћ�§ќћ - 1101₂

”•Ў•ў�§ќћ - 1.2³+1.2²+0.2¹+1.2⁰=13₁₀

~‘ Є©ђќ• ћў ћЎњ�§ќђ ’ ”•Ў•ў�§ќђ:

ћЎњ�§ќђ - 742₈

”•Ў•ў�§ќђ - 7.8²+4.8¹+2.8⁰=482₁₀

~‘ Є©ђќ• ћў ”•Ў•ў�§ќђ ’ ”•Ў•ў�§ќђ:

”•Ў•ў�§ќћ - 969₁₀

”•Ў•ў�§ќћ - 9.10²+6.10¹+2.10⁰=962₁₀

t’ћ�§ќћ ЎЈњ� ђќ•: 0+0=0; 0+1=1; 1+0=1; 1+1=10;

0001+0011= 0100;

wђ џ •’ Є©ђќ• ќђ §�Ў›ђўђ ќђџ �њ•  Np=>Nq Ў• �—џћ›—’ђў Ў›•”ќ�ў• њ•ўћ”�:

- p<>10, q=10 - § •— џ •ЎњЇўђќ• ќђ џћ›�ќћњ. „ћ њђ ќђ §�Ў›ћ ’ ”•Ў•ў�§ќђ qЃ.

- p=10, q<>10 ¦Ї›ћ §�Ў›ћ - § •— џћЎ›•”ћ’ђў•›ќћ ”•›•ќ�• ќђ Np Ў q, џ � љћ•ўћ ћЎўђўЄ¦�ў• ¤ћ њ� ђў ’ ћ‘ ђўќђ џћЎ›•”ћ’ђў•›ќћЎў Nq.

- p=10, q<>10 ” ћ‘ќћ §�Ў›ћ - § •— џћЎ›•”ћ’ђў•›ќћ Јњќћ–•ќ�• (ћ“ ђќ�§•ќ ‘ ћ™ џЄў�) ќђ Np Ў q, џ � љћ•ўћ ¦•›�ў• §�Ў›ђ ¤ћ њ� ђў Nq.

- p=10, q<>10  •ђ›ќћ §�Ў›ћ - џћ ћў”•›ќћ џ •’ Є©ђќ• ќђ ¦Ї›ђўђ � ” ћ‘ќђўђ §ђЎў.

- p=q.t - § •— џћ ђ— •”ќћ —ђњ•Ўў’ђќ• (љћ”� ђќ•) ќђ ’Ў•љ�  ђ— •” ћў Np Ў t  ђ— •”� ќђ Nq.

 �њ• : 123₁₀=>?₂

123:2=61:2=30:2=15:2=7:2=3:2=1:2=0

1 1 0 1 1 1 1

~ЎўђўЄ¦�:

1111011₍₂₎

}ћ’ћџћ›Ј§•ќћўћ §�Ў›ћ Ў• џћ›Ј§ђ’ђ љђўћ —ђџ�Ё•њ ћЎўђўЄ¦�ў• ’ ћ‘ ђў•ќ  •”.

0,452₁₀=?₂ Ў ўћ§ќћЎў ’  ђ— Ї”ђ

0,452.2=0,904.2=1,808.2=1,616.2=1,232.2=0,464.2=0,968

0,011100₂

|ђЁ�ќќ�ў• љћ”ћ’• �њђў  ђ—›�§ќ� ’�”ћ’•:

- ћ‘�љќћ’•ќ�(•”ќћ—ќђљћ’  ђ— •”:+, 0, /, -, 1)

- њћ”�¤�¦� ђќ� (”’Ј—ќђљћ’  ђ— •”: +:00/-:11)

zћ”ћћ‘ ђ—Ј’ђ©�ў• џ ђ’�›ђ (ћ‘�љќћ’•ќ� љћ”ћ’•) Ўђ:

- 0N, џ � N>=0 1N џ � N<0 -џ Їљ;

- 0N, џ � N>0 1N џ � N<0 -ћ‘ ђў•ќ;

- 0N, џ � N>=0 1Nⁿ џ � N<0 -”ћџЄ›ќ�ў•›•ќ;

N=a₁a₂a₃...a_n n -  ђ— •”ќћ §�Ў›ћ;

N¹=a₁a₂a₃...a_n a₁-”ћџЄ›ќ•ќ�• ќђ ђ₁ ”ћ  -1;

Nⁿ=a₁a₂a₃...a_n a₁- ”ћџЄ›ќ•ќ�• ќђ ђ₁ ”ћ  ;

~‘ ђ‘ћўљђўђ (ђ›“•‘ �§ќћ ЎЈњ� ђќ•, ”ћџЄ›ќ�ў•›•ќ љћ”) Ў• �—’Є Ё’ђ љђўћ ћў љћ”� ђќ• ќђ ћџ• ђќ”ђ, џ � ђ �ўњ•ў�§ќћ ЎЈњ� ђќ•, n - ”•љћ”� ђќ• ќђ  •—Ј›ўђўђ. }ђ§�ќ�ў• Ўђ Ў›•”ќ�ў•:

- ¤�љЎ� ђќђ (џ›ђ’ђ©ђ) —ђџ•ўђЇ:

, i=n...+m, ђљћ Ў• �—’ђ”� ’ ›Ї’ћ ¦Ї›ђўђ §ђЎў p^m

, i=1...n+m,

љЄ”•ўћ •a_-ip^-j - њђќў�Ўђ ЎЄЎ —ќђљ;

m - џћ Ї”Єљ, ЎЄЎ —ќђљ, ќћ њђ›�—� ђќђ њђќў�Ўђ;

Ѓўђ Ё�Ї  ђ— Ї” •  ђ—›�§•ќ ћў ќЈ›ђ

…ђ ђљў• �Ўў�љђ: џћ Ї”Єљ + ћўњ•Ўў’ђќ•, ‘•— —ќђљ

 . (’ џ Їљ љћ”)

¤�љЎ� ђќђ 2r ¤ћ њђў

0:msb...15:Isb

Integer

0 000 0000 0000 1100 +1100₂=+12₁₀

1 000 0000 0001 0110 - 10100₂=-20₁₀

џ›ђ’ђ©ђ 0-10: њђќў�Ўђ...11-15=џћ Ї”Єљ

’ - ќћ њђ›�—ђ¦�Ї

0 101 0000 0000 0110 +0,101.2⁺¹¹⁰=+101000,0₂=+40₁₀

- ¤�љЎ� ђќђ

њ�ќ�њђ›ќђ ђ �ўњ•ў�§ќђ Ўўћ™ќћЎў 0,000...1=2^-љ

њђљЎ�њђ›ќђ ђ �ўњ•ў�§ќђ Ўўћ™ќћЎў 0,111...1=1-2^љ

љ- ‘ ћ™  ђ— •”�;

- џ›ђ’ђ©ђ

њ�ќ�њђ›ќђ ђ �ўњ•ў�§ќђ Ў-Ўў 0,100...0.2^- 

њђљЎ�њђ›ќђ ђ �ўњ•ў�§ќђ Ў-Ўў 0,111...1.2⁺ 

 - њђљЎ�њђ›•ќ џћ Ї”Єљ;

p �ўњ•ў�§ќ� ”•™Ўў’�Ї - љђўћ џ � §�Ў›ђ Ў џћ›Ј›ћ“ђ �ўњ�§ќћ џ •”Ўўђ’Їќ• (џ � ЎЄ‘� ђќ•- �— ђ’ќЇ’ђќ• ќђ џћ Ї”Є¦� - љЄњ џћ-“ћ›•њ�Ї џћ ђ‘Ўћ›®ўќђ Ўўћ™ќћЎў; џ � Јњќћ–•ќ�• � ”•›•ќ�•- Јњќћ–•ќ�• (”•›•ќ�•) ќђ њђќў�Ў� � ЎЈњ� ђќ• (�—’ђ–”ђќ•) ќђ џћ Ї”Є¦�).

N₁= f₁.E^p1, N₂= f₂.E^p2

N₁+N₂= (f₁.E^p1-p2+f₂).E^p2, p₁

₂

N₁.N₂= (f₁.f₂)E^p1+p2

N₁/N₂= (f₁/f₂)E^p1-p2

‚•њђ 4.

rЎЇљћ  ђ¦�ћќђ›ќћ §�Ў›ћ њћ–• ”ђ Ў• —ђџ�Ё• ’ џћ—�¦�ћќќђ ‘ ћ™ќђ Ў�Ўў•њђ Ў ћў �¦ђў•›ќђ ћЎќћ’ђ (qЃ~) ’Є’ ’�”ђ ЎЄЎ ћў§�ўђќ• ќђ —ќђљђ ќђ ћЎќћ’ђўђ:

Ѓ ўћ’ђ ’ —ђ’�Ў�њћЎў ћў §•ўќћЎўўђ �›� ќ•§•ўќћЎўўђ ќђ m Ў• —ђџ�Ў’ђў џћ›ћ–�ў•›ќ� �›� ћў �¦ђў•›ќ� §�Ў›ђ. p›“•‘ �§ќ�ў• §�Ў›ђ ’ ўђ—� qЃ Ў• —ђџ�Ў’ђў ‘•— —ќђљ. ~Ўќћ’•ќ ќ•”ћЎўђўЄљ ќђ ћџ�Ўђќђўђ qЃ~ • ќ• •”ќћ—ќђ§ќћўћ џ •”Ўўђ’Їќ• ќђ §�Ў›ђўђ ћў ’�”ђ:

N_-P=((Pⁱ)/(-p+1))+Cpⁱ⁺¹

wђ џ •’ Є©ђќ• ќђ §�Ў›ђўђ ћў qЃ~ ’ qЃ} � ћ‘ ђўќћ ’ —ђ’�Ў�њћЎў ћў ЎЄћўќћЁ•ќ�•ўћ ќђ ”’•ў• ћЎќћ’� � ’�”ђ ќђ §�Ў›ћўћ Ў• џ �›ђ“ђў Ў›•”ќ�ў• ћЎќћ’ќ� њ•ўћ”�:

- +p, -q, p=|q|, Ўњ•Ў•ќћ §�Ў›ћ - џ •’ Є©ђќ•ўћ Ў• ћЎЄ©•Ўў’Ї’ђ Ў џћ ђ— •”•ќћ ¤ћ њ� ђќ• ќђ ¦�¤ �ў• b_i ќђ ўЄ Ў•ќћўћ §�Ў›ћ N_-q ћў ¦�¤ �ў• ђ_i ќђ �—Ґћ”ќћўћ §�Ў›ћ Np ’ qЃ}:

- -p, +q, џ ћ�—’ћ›ќћ §�Ў›ћ - џ •’ Є©ђќ•ўћ Ў• ћЎЄ©•Ўў’Ї’ђ § •— —ђњ•Ўў’ђќ• ќђ �—Ґћ”ќћўћ §�Ў›ћ N_-p � џ •ЎњЇўђќ• ќђ �— ђ—ђ ’ ЎЄћў’•ўќђўђ qЃ}.

p �ўњ•ў�§ќ�ў• � ›ћ“�§•Ўљ�ў• ћџ• ђ¦�� Ў• �—џЄ›ќЇ’ђў љђљўћ џ � qЃ}, ќћ Ў џћ-Ў›ћ–ќћ ћў§�ўђќ• ќђ њ•–”Ј ђ— •”ќ�ў• џ •ќћЎ�. ЃЈњ� ђќ•ўћ Ў• �—џЄ›ќЇ’ђ џћ ђ— •”•ќћ Ў ¤ћ њ� ђќ• ќђ I-ў�Ї  ђ— •” ќђ ЎЈњђўђ � џ •ќћЎђ: s_i=a_i+b_i+c_i-1-pc_i, c_i=-(a_i+b_i+c_i-1)/|p| ќђ™-‘›�—љћўћ њ�ќ�њђ›ќћ ¦Ї›ћ.  •ќћЎЄў c_i њћ–• ”ђ џ �•њђ •”ќђ ћў ў �ў• Ўўћ™ќћЎў� (-1; 0; +1).

 �њ•  —ђ ЎЈњ� ђќ• ќђ §�Ў›ђ Ў ћў �¦ђў•›ќђ ћЎќћ’ђ:

(-1)	(-1)	(0)	(0)	ci
1	9	7	5	A
+7	4	4	4	B
7	2	1	9(-10)	S

x—’ђ–”ђќ•ўћ Ў• —ђњ•Ўў’ђ ЎЄЎ ЎЈњ� ђќ• Ў ћ‘ ђў•ќ —ќђљ:

-N=(|p|-1)N+pN.

ѓњќћ–•ќ�•ўћ Ў• �—џЄ›ќЇ’ђ ќђ ћЎќћ’ђўђ ќђ ўђ‘›�¦ђўђ —ђ Јњќћ–•ќ�• ќђ •”ќћ ђ— •”ќ� §�Ў›ђ, џ •”Ўўђ’•ќ� ’ qЃ~, ЎЄЎ ЎЈњ� ђќ• ќђ §ђЎў�§ќ� џ ћ�—’•”•ќ�Ї.

‚u|p 5.

rЎЇљћ  ђ¦�ћќђ›ќћ §�Ў›ћ, џ •”Ўўђ’•ќћ ’ qЃw, њћ–• ”ђ Ў• ”ђ”• ’Є’ ’�”ђ

љЄ”•ўћ  >2 • ћЎќћ’ђўђ ќђ qЃw, ђ ¦�¤ �ў• Ўђ:

(Xi)=0; 1; 2;Xim;

 •”Ўўђ’Їќ•ўћ ќђ §�Ў›ђўђ ’ qЃw • •”ќћ—ќђ§ќћ, ђ ќ•“ћ’�Їў —ќђљ ћў“ћ’ђ Ї ќђ —ќђљђ ќђ Ўўђ Ёђўђ —ќђ§•©ђ ¦�¤ ђ.  � ќЈ›•’ђ Ўўћ™ќћЎў ќђ §�Ў›ћўћ ’Ў�§љ�  ђ— •”� Ўђ 0.  � џ ћњЇќђ ќђ —ќђљђ ќђ §�Ў›ћўћ ’Ў�§љ� —ќђ¦� ќђ —ќђ§•©�ў• ¦�¤ � (…i) Ў• џ ћњ•ќЇў ќђ ћ‘ ђўќ�ў•.

~‘Ґ’ђўђ ќђ џ •”Ўўђ’�њ�ў• §�Ў›ђ Ў ¤�љЎ� ђќђ —ђџ•ўђЇ § •— qЃw •:

, k - ‘ ћ™  ђ— •”� ќђ ¦Ї›ђўђ §ђЎў ќђ §�Ў›ћўћ, n - ћ‘© ‘ ћ™  ђ— •”� ќђ §�Ў›ћўћ.

wђ џ •’ Є©ђќ• ќђ §�Ў›ђўђ ћў qЃ} ’ qЃw � ћ‘ ђўќћ Ў• �—џћ›—’ђў Ў›•”ќ�ў• ћЎќћ’ќ� њ•ўћ”�:

- N_PqЃ} - ’ —ќђљћ ђ— •”ќћ Np, џ ћ�—’ћ›ќћ §�Ў›ћ - џ •’ Є©ђќ•ўћ Ў• �—џЄ›ќЇ’ђ § •— џћ ђ— •”ќћ ¤ћ њ� ђќ• ќђ ¦�¤ �ў• (…i) ќђ ўЄ Ў•ќћўћ §�Ў›ћ:

- wќђљћ ђ— •”ќћ Np ’Є’ N_PqЃ}, џ ћ�—’ћ›ќћ §�Ў›ћ - џ •’ Є©ђќ•ўћ Ў• �—џЄ›ќЇ’ђ § •— џ •ЎњЇўђќ• ќђ §�Ў›ћўћ ћў qЃw ЎЄ“›ђЎќћ ¤ћ њЈ›ђўђ —ђ џ •”Ўўђ’Їќ• ќђ §�Ў›ђўђ ’ �—‘ ђќђўђ qЃ}.

ЃЈњ� ђќ•ўћ ќђ §�Ў›ђўђ Ў• �—џЄ›ќЇ’ђ џћ ђ— •”ќћ, љђўћ —ђ ’Ў•љ� I  ђ— •” Ў• ћџ •”•›Їў ЎЈњђўђ (Si), њ•–”�ќќђўђ ЎЈњђ (t_i) � џ •ќћЎЄў (Ci). x—’ђ–”ђќ•ўћ Ў• �—џЄ›ќЇ’ђ љђўћ ЎЈњ� ђќ•ўћ ќћ Ў ћ‘ ђў•ќ —ќђљ, љђўћ Ў• џ ћњ•ќЇў ’Ў�§љ� —ќђ¦� ќђ ¦�¤ �ў• ќђ Јњђ›�ў•›Ї. ѓњќћ–•ќ�•ўћ Ў• �—џЄ›ќЇ’ђ ЎЄЎ ЎЈњ� ђќ• ќђ §ђЎў�§ќ�ў• џ ћ�—’•”•ќ�Ї, ђ ”•›•ќ�•ўћ • ЈЎ›ћ–ќ•ќћ —ќђ§�ў•›ќћ џћ ђ”� ќ••”ќћ ћ”ќћЎўўђ ќђ  ђ— •”�ў• ќђ §ђЎўќћўћ. ~Ўќћ’ќћўћ џ •”�њЎў’ћ ќђ ћ‘ ђ‘ћў’ђќ•ўћ ќђ §�Ў›ђўђ, џ •”Ўўђ’•ќ� ’ qЃw, •