Êóðñ ëåêöèé ïî âû÷èñëèòåëüíîé òåõíèêå

       

Ïðåäñòàâëåíèå èíôîðìàöèè â êîìïüþòåðàõ


Èíôîðìàöèÿ â ÖÂÌ ïðåäñòàâëÿåòñÿ â êîäèðîâàííîì âèäå,  à èìåííî  â âèäå ïîñëåäîâàòåëüíîñòè öèôð,  ò.å. ÷èñåë. Ïðè ýòîì ýòî ìîæåò áûòü ëèáî ñîáñòâåííî ÷èñëà ñî çíàêîì ëèáî ñèìâîëû - ÷èñëà áåç çíàêà.        

×èñëà â ÖÂÌ ïðåäñòàâëÿåòñÿ íå â äåñÿòè÷íîé ñèñòåìå ñ÷èñëåíèÿ, à  â äâîè÷íîé, ò.å. â êàæäîé ðàçðÿäíîé ïîçèöèè ìîæåò áûòü íå  10  ðàçëè÷íûõ ñèìâîëîâ, à 2: "0" è "1".

     Òàêîå ïðåäñòàâëåíèå âûçâàíî òåõíè÷åñêèìè ñîîáðàæåíèÿìè:

äâóõñòàáèëüíûé ýëåìåíò ñîçäàòü ëåã÷å, ÷åì 10-è. Ïðèìåðû  äâóñòàáèëüíûõ ýëåìåíòîâ: ÷¸ðíîå -  áåëîå; âûñîêèé - íèçêèé;  íàëè÷èå  -  îòñóòñòâèå,  èñòèííî - ëîæíî.

                           2.2. Îñíîâû àëãåáðû ëîãèêè.                                

                                                        

     Äâîè÷íàÿ ñèñòåìà îêàçàëàñü î÷åíü óäîáíîé äëÿ ïîñòðîåíèÿ  ýëåìåíòíîé áàçû ÖÂÌ, ïîñêîëüêó îêàçàëîñü âîçìîæíûì èñïîëüçîâàòü àïïàðàò ìàòåìàòè÷åñêîé ëîãèêè, áàçèðóþùåéñÿ íà òîì, ÷òî ëþáîå ñóæäåíèå (óòâåðæäåíèå)   ÿâëÿåòñÿ äâîè÷íûì:  èñòèííîå  è ëîæíîå.  Äâîè÷íàÿ àëãåáðà áûëà ñîçäàíà    Äæîíîì Áóëåì ("Ìàòåìàòè÷åñêèé àíàëèç ëîãèêè" 1847ã.), êîòîðàÿ ïîëó÷èëà    íàçâàíèå áóëåâîé àëãåáðû.                                                                         

     Äëÿ îïèñàíèÿ ôóíêöèîíèðîâàíèÿ öèôðîâûõ ñõåì èñïîëüçóåòñÿ  ìàòåìàòè÷åñêèé àïïàðàò áóëåâûõ ôóíêöèé (÷àñòè ôóíêöèé àëãåáðû ëîãèêè).   ÔÀË, êàê è åå ïåðåìåííûå, ìîãóò ïðèíèìàòü òîëüêî äâà çíà÷åíèÿ.        

     Îñîáûé èíòåðåñ ïðåäñòàâëÿþò áóëåâû ôóíêöèè îäíîé è äâóõ ïåðåìåí. Ôóíêöèè äëÿ áîëüøåãî ÷èñëà ïåðåìåííûõ ìîãóò áûòü ñâåäåíû  ê  ôóíêöèÿì îò äâóõ ïåðåìåííûõ.                                                 

 

 Êîëè÷åñòâî ôóíêöèé îäíîé ïåðåìåííîé ðàâíî 22 = 4 

 



Àðãóìåíò

Ôóíêöèÿ

Îáîçíà÷åíèå

Íàçâàíèå

         õ

Çíà÷åíèå

F(x

0

1

0

       0

F0(õ)

Êîíñòàíòà «0»

0

1

       0

       1

F1(x)

Ïåðåìåííàÿ «õ»

0

1

       1

       0

F2(x)

Îòðèöàíèå

(èíâåðñèÿ)  «/õ»

0

1

       1

       1

F3(x)

Êîíñòàíòà  «1»

<
  

 

                                                                      

      

  Êîëè÷åñòâî ôóíêöèé äâóõ ïåðåìåííûõ (22)2 = 16  

Àðãóìåíò

                                                      Ôóíêöèè

X

Y

F0

F1

F2

F3

F4

F5

F6

F7

F8

F9

F10

F11

F12

F13

F14

F15

0

0

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

1

0

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

1

1

0

1

0                                                                                                                                                                                                                                                                                                           

1

0

1

0

1

0

1

0

1

0

1

0

1

             

     f0 - êîíñòàíòà 0                                              

     F1 - x&y êîíúþíêöèÿ (*,  , /\)                                         

     F2 - õÌ`y çàïðåò ïî ó - îòðèöàíèå èìïëèêàöèè    õ`y                   

     F3 - õ       - ïåðåìåííàÿ õ                                                      

 

       F4     xÌy -  çàïðåò ïî õ - îòðèöàíèå èìïëèêàöèè `xy                   

     F5 - ó                                                              

     F6 -  x?y - íåýêâèâàëåíòíîñòü             x`y\/`xy                  

     F7 - x\/y -   äèçúþíêöèÿ  (+)                                                       

     F8 - x|y  - ñòðåëêà Ïèðñà                   x\/y -íå-èëè            

                                                                    _ _                

     F9 -  x=y ýêâèâàëåíòíîñòü                   xy\/xy                  

                                                                      _                       



     F10-  y - íå ó                                            y                       

                                                                    _                          

     F11 - yÌx èìïëèêàöèÿ îò ó ê õ            y\/x                       

                                                                         

     F12 - x - íå õ                                                      

                                                                      _                         

     F13 - xÌy èìïëèêàöèÿ îò õ ê ó             x\/y                       

                                                                  ___                          

     F14 - x/y - øòðèõ Øåôôåðà               õy  - íå è                  

     F15 - 1                                                              

                                                                         

     Ñèñòåìà áóëåâûõ ôóíêöèé ÿâëÿåòñÿ ôóíêöèîíàëüíî ïîëíîé, åñëè  ëþáóþ  áóëåâó ôóíêöèþ ìîæíî ïðåäñòàâèòü ïîñðåäñòâîì ýòîé ñèñòåìû.              

     Òàê ìîæíî äîêàçàòü ÷òî ëþáîå ñëîæíîå âûñêàçûâàíèå ìîæåò áûòü âûðàæåíî â âèäå ôîðìóëû, â êîòîðîé  èñïîëüçóþòñÿ  òîëüêî  òðè  îïåðàöèè:   

êîíúþíêöèÿ, äèçúþíêöèÿ è îòðèöàíèå. Áóäåì èõ îáîçíà÷àòü ñèìâîëàìè: îòñóòñòâèå ñèìâîëà, «+» è «`   »    

 

Àêñèîìû àëãåáðû ëîãèêè.  

                                                _               _        

     00 = 0 ;      1+1 = 1;           0  = 1:       1 = 0;                                                  

                           

     À+0 = À:    À1 = À;           À+1 = 1    À0 = 0        À+À = À   ÀÀ = À                                                    

    ___    _                             _           _                                                         

    (À) = À;   (À) = À;     À+À = 1;   ÀÀ = 0;                                                                                                      

   

               Òåîðåìà äå Ìîðãàíà.                         



       ___      _ _      __      _    _                                              

      À+ = À Â;    À = À +   

               

                   Çàêîíû àëãåáðû ëîãèêè.

                                                                      

     Äëÿ òàêîé àëãåáðû ñïðàâåäëèâû çàêîíû                                                          

       à) êîììóòàòèâíîñòè:     ÀÂ=ÂÀ          À+Â=Â+À                                              

       á) àññîöèàòèâíîñòè:     À(ÂÑ)=(ÀÂ)Ñ ;      À+(Â+Ñ) = (À+Â)+Ñ                                                                                     

       â) äèñòðèáóòèâíîñòè:   À(Â+Ñ) = ÀÂ+ÀÑ;     À+ÂÑ = (À+Â)(À+Ñ) 

       ã) ïîãëîùåíèÿ:             À(À+Â) = À;    À + ÀÂ = À ;

                                             

      Òàáëèöû áóëåâûõ îïåðàöèé   äâóõ ïåðåìåííûõ  

                               

Äèçüþíêöèÿ                                                 Êîíúþíêöèÿ                    

                  _         _



Õ



Ó



Õ+Ó



0



0



  0



0



1



  1



1



0



  1



1



1



  1



Õ



Ó



ÕÓ



0



0



0



0



1



0



1



0



0



1



1



1

F=ÕÓ+ÕÓ+ÕÓ=Õ+Ó      F= ÕÓ

 _       _    _  _       ____

F=`ÕÓ = ÕÓ  =  Õ+Ó                          

                  

                                                            _        _   _         _   ___

F=`ÕÓ+ÕÓ+ÕÓ=ÕÓ

        

                                                                                               

Ïðè ýòîì, êàê ìû âèäèì, ñóùåñòâóåò äâå íîðìàëüíûå ôîðìû ïðåäñòàâëåíèÿ: äèçúþíêòèâíàÿ (äèçúþíêöèÿ êîíúþíêöèé) è êîíúþíêòèâíàÿ (êîíúþíêöèÿ äèçúþíêöèé).                                                              

Ìîæíî ïîêàçàòü, ÷òî ôóíêöèîíàëüíî ïîëíîé ÿâëÿþòñÿ ñèñòåìû, ñîñòîÿùèå èç äèçúþíêöèè è îòðèöàíèÿ, èç êîíúþíêöèè è îòðèöàíèÿ, ñòðåëêà Ïèðñà è øòðèõ Øåôôåðà.

2.3.  Ìåòîäû ôèçè÷åñêîãî ïðåäñòàâëåíèÿ äâîè÷íûõ êîäîâ.

     Ðàçëè÷àþò äâà îñíîâíûõ ñïîñîáà ïðåäñòàâëåíèÿ êîäèðîâàííîé èíôîðìàöèè;  ïàðàëëåëüíûé êîä, (êîãäà âñå áèòû ïðåäàþòñÿ îäíîâðåìåííî) è ïîñëåäîâàòåëüíûé  (êîãäà áèòû ïåðåäàþòñÿ ïîî÷åð¸äíî).



     Ïîñêîëüêó ýòè ñïîñîáû èìåþò ïðîòèâîïîëîæíûå òðåáîâàíèÿ ê  áûñòðîäåéñòâèþ è çàòðàòàì îáîðóäîâàíèÿ, òî ïðèìåíÿþò  ïàðàëëåëüíî-ïîñëåäîâàòåëüíûé ñïîñîá.

     Íàïîìíèì, ÷òî â ÖÂÒ èíôîðìàöèÿ ïîäðàçäåëÿåòñÿ íà  áèòû,  ñîâîêóïíîñòè áèòîâ(áàéòû, ñëîâà, è ò.ä.) è ìàññèâû (ôàéëû, çàïèñè).

     Äëÿ èäåíòèôèêàöèè îòäåëüíûõ ýëåìåíòîâ èíôîðìàöèè  ïðèìåíÿþò  ñïåöèàëüíûå ñèíõðîíèçèðóþùèå ñèãíàëû èëè ñòðîáû.   Ïî âèäó ïðåäñòàâëåíèÿ ðàçëè÷àþò ïîòåíöèàëüíûé âèä è èìïóëüñíûé.

     Ïðè ëþáûõ ïåðåäà÷àõ ïàðàëëåëüíûì êîäîì  îáû÷íî  ïðèìåíÿþò  ïîòåíöèàëüíûé ñïîñîá ïðåäñòàâëåíèÿ èíôîðìàöèè, ïðè ýòîì  ñòðîáèðîâàíèå  îñóùåñòâëÿåòñÿ ëèáî èìïóëüñîì, ëèáî ôðîíòîì, ëèáî ñïàäîì.

  Ïåðåäà÷è ïîñëåäîâàòåëüíûì êîäîì îòëè÷àþòñÿ áîëüøèì  ðàçíîîáðàçèåì ñïîñîáîâ êîäèðîâàíèÿ: ïîòåíöèàëüíûé, èìïóëüñíûé, êîäèðîâàíèå íàïðàâëåíèåì ïåðåïàäà (ôàçîìàíèïóëèðîâàííûé êîä), áåç ñòðîáèðîâàíèÿ (íà  ôèêñèðîâàííîé ÷àñòîòå).

Ñèíõðîñèãíàëû 

Äâîè÷íûé êîä                   0    0    1     1     1     0     0     0 

Ïîòåíöèàëüíûé êîä   

 (áåç âîçâðàòà ê íóëþ

 Èìïóëüñíûé êîä            

 

Áèïîëÿðíûé êîä      

Ôàçîìàíèïóëèð.

 

"Ìàí÷åñòåð 2"  - íóëè è åäèíèöû ïåðåäàþòñÿ ðàçíûìè ôðîíòàìè

     Ïðè ïàðàëëåëüíîé ïåðåäà÷å äëÿ èäåíòèôèêàöèè îòäåëüíûõ ýëåìåíòîâ (áàéòîâ, ñëîâ) èíôîðìàöèè  ïðèìåíÿþò  ñïåöèàëüíûå ñèíõðîíèçèðóþùèå ñèãíàëû èëè ñòðîáû.  Ïðè ýòîì ðàçëè÷àþò ñèíõðîííóþ è àñèíõðîííóþ

      

Ñèíõðîííàÿ ïåðåäà÷à



ÒÈ
 
 

Ñòðîá

ïîäòâåðæäåíèÿ
 
                                                                                                                                                                                                                                                                       



Âðåìÿ óäåðæàíèÿ

ñòðîáà äàííûõ
 


 




Âðåìÿ îïåðåæåíèÿ

äàííûìè ñòðîáà
 


Äàííûå
 


Ñòðîá

äàííûõ
 
Àñèíõðîííàÿ ïåðåäà÷à
 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    

Îòìå÷åííûå âûøå ñðåäñòâà êîäèðîâàíèÿ  öèôðîâîé  èíôîðìàöèè ÿâëÿþòñÿ ñðåäñòâàìè àìïëèòóäíîé ìîäóëÿöèè (ïîòåíöèàëû, èìïóëüñû è ôðîíòû èìïóëüñîâ). Õîòÿ ñðåäñòâ êîäèðîâàíèÿ ñóùåñòâóåò áåñêîíå÷íîå ìíîæåñòâî, îòìåòèì çäåñü ñðåäñòâà êîäèðîâàíèÿ ïîñðåäñòâîì  ìîäóëÿöèè ñèãíàëà.

-       ÷àñòîòíàÿ: 0 è 1 – ðàçíûìè ÷àñòîòàìè;

-       ôàçîâàÿ: ÷àñòîòà ïîñòîÿííàÿ, íî  ïðè ïåðåõîäå ñ 0 íà 1 ìåíÿåòñÿ ôàçà ñèãíàëà.



 

 

  .

2.4. Ñõåìíàÿ (ôèçè÷åñêàÿ) ðåàëèçàöèÿ ëîãè÷åñêèõ ôóíêöèé.

Îñíîâíûå ïàðàìåòðû ëîãè÷åñêèõ ýëåìåíòîâ.

     - òåõíîëîãèÿ èçãîòîâëåíèÿ

     - çàäåðæêà ðàñïðîñòðàíåíèÿ (÷àñòîòà ïåðåêëþ÷åíèÿ)

     - ìîùíîñòü ïîòðåáëåíèÿ

     - íàãðóçî÷íàÿ ñïîñîáíîñòü (êîëè÷åñòâî ñåáå ïîäîáíûõ)

Íàèáîëåå ïðîñòî ïðîèëëþñòðèðîâàòü ðåàëèçàöèþ ëîãè÷åñêèõ ôóíêöèé íà îñíîâå òðàíçèñòîðíîé ëîãèêè.

+                                             +                                   +                                            

                                                                  xy                                  xy

                            `õ                       

õ                                                 õ

ÍÅ
 
è-íå
 
Âðåìÿ óäåðæàíèÿ

äàííûõ
 
è
 
 
                                                       

                                               `                                             

                                     

        

          +                                          +

                              x+y                                       x+y

x

                                                       

èëè
 

                                                                          

y

èëè-íå
 

 

    Ïðèâåäåííûå ñõåìû ÿâëÿþòñÿ êîìáèíàöèîííûìè, òî åñòü çíà÷åíèå âûõîäíîãî ñèãíàëà îäíîçíà÷íî îïðåäåëÿåòñÿ  âõîäíûìè ñèãíàëàìè.   Êñòàòè, ïðèâåäåííûå ñõåìû ðåàëèçóþò ïîëîæèòåëüíóþ ëîãèêó,  êîãäà  ëîãè÷åñêîé åäèíèöå ñîîòâåòñòâóåò áîëåå âûñîêèé óðîâåíü, åñëè  æå  ïðèíÿòü  çà  ëîãè÷åñêóþ åäèíèöó áîëåå íèçêèé óðîâåíü, òî îïåðàöèè "è" è "èëè" ïîìåíÿþòñÿ ìåñòàìè.



                                                         

2.4.3.  Êîìáèíàöèîííûå ñõåìû

              Òàáëèöà èñòèííîñòè îäíîãî ðàçðÿäà äâîè÷íîãî ñóììàòîðà.

x

y

c

S

Co

0

0

0

0

0

1

0

0

1

0

0

1

0

1

0

1

1

0

0

1

0

0

1

1

0

1

0

1

0

1

0

1

1

0

1

1

1

1

1

1

S = x`y`c+ `xy`c+xy`c+xyc

Co= xy`c + x`yc +`xyc +xyc

                                                      

      

2.6. Ýëåìåíòû ñ ïàìÿòüþ.

Ýëåìåíò äâîè÷íîãî õðàíåíèÿ (òðèããåð) íà ýëåìåíòàõ «èëè-íå». . Ýòî óæå íå êîìáèíàöèîííàÿ ñõåìà, à ïîñëåäîâàòåëüíîñòíàÿ (êîíå÷íûé àâòîìàò) – ñõåìà ñ ïàìÿòüþ.

Ðàáîòà ëîãè÷åñêèõ ýëåìåíòîâ îïèñûâàåòñÿ è ñ ïîìîùüþ âðåìåííûõ äèàãðàìì.          

                                                                                                       Q

                    S                         `Qn+1                                      

         Qn                                          

         _                                                                                            `Q

         Qn                                          

                   R                          Qn+1

 

1    2           3       4         5             6     7      8    9

S

R

_

Q

Q   

         

             Òàáëèöà ïåðåõîäîâ  àñèíõðîííîãî R-S òðèããåðà.

Çíà÷åíèå åãî âûõîäíîãî ñèãíàëà çàâèñèò íå òîëüêî îò çíà÷åíèé âõîäíûõ ñèãíàëîâ, íî è îò åãî âíóòðåííåãî ñîñòîÿíèÿ.

¹

  R

S

Qn

Q(n+1)

Ñîñòîÿíèå

1

0

0

0

0

õðàíåíèå "0"

2

0

1

0

1

óñòàíîâêà â "1"

3

0

0

1

1

õðàíåíèå "1"

4

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1

1

1

õðàíåíèå "1"

5

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6

1

0

1

0

óñòàíîâêà â "0"

7

0

0

0

0

õðàíåíèå "0"

8

1

0

0

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õðàíåíèå "0"

9

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1

0

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10

1

1

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             Ñèíõðîííûé R-S òðèããåð

   Ñèíõðîííûé R- S òðèããåð ïîëó÷àåòñÿ èç àñèíõðîííîãî òðèããåðà ïóòåì äîáàâëåíèÿ ïî È êî âõîäàì R è S äîïîëíèòåëüíîãî âõîäà Ñ.

                           



s     T  

c

R
 
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                                                                  Q

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                   D –òðèããåð                             

                   Ìû óæå îáðàòèëè âíèìàíèå, ÷òî îäíîâðåìåííàÿ  ïîäà÷à  ñèãíàëîâ  íà âõîäû S è R íåäîïóñòèìà. ×òîáû ýòî èñêëþ÷èòü ìîæíî äîãîâîðèòüñÿ, ÷òîáû ýòè ñèãíàëû áûëè èíâåðñíûå äðóã äðóãó, ò.å. çàìåíèòü èõ îäíèì ñèãíàëîì òîãäà ïîëó÷àåì cñèíõðîííûé  D  òðèããåð

         

   Ñèíõðîííûé  D  òðèããåð

C

D

Qn

Qn+1

Ôóíêöèÿ

0

0

0

0

õðàíåíèå "0"

0

0

1

1

õðàíåíèå "1"      

0

1

0

0

õðàíåíèå "0"

0

1

1

1

õðàíåíèå "1"

1

0

0

0

õðàíåíèå "0"

1

0

1

0

óñòàíîâêà â"0"

1

1

0

1

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1

1

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1

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   Ðàçëè÷àþò D òðèããåðû, çàïèñü â êîòîðûå ïðîèñõîäèò ïî óðîâíþ, ò.å.

â ìîìåíò äåéñòâèÿ ñèíõðîèìïóëüñà òðèããåð ïðåäcòàâëÿåò  ñîáîé  êîìáèíà-

öèîííóþ ñõåìó (òðèããåðû òèïà çàùåëêè) è D-òðèããåðû, çàïèñü  â  êîòîðûå

ïðîèñõîäèò ïî ôðîíòó ñèãíàëà (ïåðåäíåìó èëè çàäíåìó).

             

 Cèíõðîííûé  T  òðèããåð

     Åñëè â êà÷åñòâå D-âõîäà èñïîëüçîâàòü èíâåðñíûé âûõîä ñàìîãî òðèããåðà.

C

Qn

Qn+1

Ôóíêöèÿ

0

0

0

õðàíåíèå "0"

1

0

1

óñòàíîâêà "1"

0

1

1

õðàíåíèå "1"

1

1

0

óñòàíîâêà "0"

          

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Èç âðåìåííîé äèàãðàììû ìîæíî ñäåëàòü ñëåäóþùèå âûâîäû:

- ÷àñòîòà íà âûõîäå â äâîå íèæå ÷àñòîòû íà âõîäå

- ýëåìåíò ÿâëÿåòñÿ ñóììàòîðîì ïî ìîäóëþ 2, ò.å. ñ÷åòíûì ýëåìåíòîì.

Ñîâîêóïíîñòü ñèíõðîííûõ òðèããåðîâ, ñîåäèí¸ííûõ ïîñëåäîâàòåëüíî (âûõîäû ïðåäøåñòâóþùèõ íà âõîäû ïîñëåäóþùèõ, â òîì ÷èñëå ïîñëåäíåãî ñ ïåðâûì ) è îáùèì ñèãíàëîì íà âõîäàõ «Ñ» îáðàçóåò ðåãèñòð ïîñëåäîâàòåëüíîãî õðàíåíèÿ (ñäâèãà). Åñëè æå èìååòñÿ ñîåäèíåíèå ïî òîëüêî ïî âõîäàì «Ñ», òî ïîëó÷àåì ðåãèñòð ïàðàëëåëüíîãî õðàíåíèÿ è ïàðàëëåëüíîé ïåðåäà÷è. Ïîñëåäîâàòåëüíîå ñîåäèíåíèå Ò-òðèããåðîâ îáðàçóåò ñ÷¸ò÷èê.


Ñîäåðæàíèå ðàçäåëà