Арифметические основы ЦВМ

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A?EOIAOE*ANEEA INIIAU OeAI

1.1. Nenoaiu n/eneaiey

A iianaaeiaaiie i?aeoeea aeey i?aaenoaaeaiey /enae ethaee iieuecothony
ii/oe eneeth/eoaeueii aeanyoe/iie nenoaiie n/eneaiey. Eeoue a ?aaeeeo
neo/ayo ano?a/athony inoaoee ae?oaeo nenoai – ?eineee n/ao,
aeaaiaaeoeaoe?e/iay nenoaia (/anu), oanoeaeanyoe?e/iay (ieioou).

Iaeiaei nenoaia ecia?aaeaiey /enae, eioi?ay aaeaie neeaaeuaaeanue
i?eiaieoaeueii e ?o/iiio o?oaeo, ia iicaieyao iieo/eoue iaeaieaa
yooaeoeaiua iaoiaeu auiieiaiey au/eneaiee. Ii yoie i?e/eia a
au/eneeoaeueiie oaoieea i?eiaiythony ae?oaea nenoaiu n/eneaiey e /aua
anaai – aeaie/iay.

Aaaaeai ianeieueei ii?aaeaeaiee.

Cenoaia n/eneaiey – niaieoiiinoue neiaieia e i?aaee aeey
iaicia/aiey /enae.

?acaeaeytho nenoaiu n/eneaiey iiceoeeiiiua e iaiiceoeeiiiua.
Iaiiceoeeiiiay nenoaia n/eneaiey caaeaaony ia?a/eneaieai ecia?aaeaaiuo a
iae cia/aiee. Iiceoeeiiiay nenoaia n/eneaiey oa?aeoa?ecoaony iniiaaieai
e oai, /oi /enea, eae i?aaeei, i?aaenoaaeythony ianeieueeeie
?ac?yaeaie (yaeythony iiiai?ac?yaeiuie), a aan ethaiai ?ac?yaea
ii?aaeaeyaony aai iiceoeeae a /enea.

Oniiaaiea iiceoeeiiiie nenoaiu n/eneaiey ii?aaeaeyao eiee/anoai
?acee/iuo oeeo? (neiaieia), aeiionoeiia a nenoaia n/eneaiey. Yoi aea
/enei ii?aaeaeyao, ai neieueei ?ac aan oeeo?u aeaiiiai ?ac?yaea iaiueoa
aana oeeo?u ninaaeiaai noa?oaai ?ac?yaea.

Oae, a aeanyoe/iie nenoaia n/eneaiey, iniiaaiea eioi?ie ?aaii 10,
?acee/atho 10 a?aaneeo oeeo? – 0, 1, 2, …, 9. Neaaeiaaoaeueii, i?e
aa eniieueciaaiee aeey caiene /enea, ia i?aauoathuaai aeaayoe,
aeinoaoi/ii iaeiie oeeo?u, e oaeia /enei caienuaaaony eae
iaeii?ac?yaeiia. A a neo/aa caiene /enea, aieueoaai aeaayoe, iii
i?aaenoaaeyaony eae iiiai?ac?yaeiia. I?e yoii aan eaaeaeiai aieaa
noa?oaai (?aniieiaeaiiiai neaaa io oaeouaai) ?ac?yaea a aeanyoue
(iniiaaiea nenoaiu n/eneaiey) ?ac aieueoa oaeouaai.

Oae, iai?eia?, /enei 359 – o?ao?ac?yaeiia, e a iai 9 – oeeo?a ?ac?yaea
aaeeieoe, 5 – oeeo?a ?ac?yaea aeanyoeia, 3 – oeeo?a ?ac?yaea nioai (a
10 ?ac i?aauoaao aan ?ac?yaea aeanyoeia). I?e yoii cia/aiea
o?ao?ac?yaeiiai /enea 359 iieo/aaony noiie?iaaieai o?ao neaaaaiuo : 3
nioie + 5 aeanyoeia + 9 aaeeieoe.

Iauaa i?aaeei ii?aaeaeaiey aana ?ac?yaea iiiai?ac?yaeiiai /enea oaeiai:

Anee i?iioia?iaaoue ?ac?yaeu oeaeiai /enea ni?aaa iaeaai, ia/eiay
io 0 aeey ?ac?yaea aaeeieoe, oi aan ethaiai ?ac?yaea iieo/aaony
aicaaaeaieai iniiaaiey nenoaiu n/eneaiey a noaiaiue, cia/aiea
eioi?ie ?aaii iiia?o ?ac?yaea.

Oae, aan naiiai ieaaeoaai ?ac?yaea oeaeuo /enae ?aaai 1, iineieueeo
iiia? ?ac?yaea ?aaai 0, a ethaia /enei, a oii /enea e /enei 10,
aicaaaeaiiia a ioeaaoth noaiaiue, aeaao a ?acoeueoaoa aaeeieoeo. Aan
neaaeothuaai neaaa ?ac?yaea ?aaai 10 a noaiaie 1, o.a. ?aaai aeanyoe,
e o.ae.

Yoi aea i?aaeei ni?aaaaeeeai e aeey caiene ae?iaiuo /enae. I?e yoii
?ac?yaeai ni?aaa io ?ac?yaea aaeeieoe, eiathuaai iiia? 0,
i?enaaeaathony io?eoeaoaeueiua cia/aiey: -1, -2, e o.ae., a eo aana
iieo/athony oaeaea i?e aicaaaeaiee iniiaaiey 10 a niioaaonoaothuoth
noaiaiue. Oae, iai?eia?, aan o?aoueaai ?ac?yaea a ae?iaiie /anoe
/enea 42,9724 aoaeao ?aaai 10 a noaiaie (-3), o.a. ?aaai iaeiie
ouny/iie.

Oeacaiiia i?aaeei iiaeii i?ieeethno?e?iaaoue neaaeothuei ia?acii:

Eae aeaeii ec i?eia?a, a iiceoeeiiiie nenoaia n/eneaiey aeinoaoi/ii
ciaoue cia/aiea iniiaaiey nenoaiu n/eneaiey, neiaieu, ecia?aaeathuea
ioaeaeueiua oeeo?u, e oeacaiiia i?aaeei, /oiau i?aaenoaaeoue ethaia
/enei.

A au/eneeoaeueiie oaoieea oe?iei i?eiaiytho aeaie/ioth, ainueia?e/ioth e
oanoiaaeoeaoe?e/ioth nenoaio n/eneaiey.

Aeaie/iay nenoaia n/eneaiey eiaao iniiaaiea 2, e, neaaeiaaoaeueii,
aeaa ?aciuo oeeo?u – 0 e 1; ainueia?e/iay – ainaiue ?aciuo oeeo? – 0,
1, 2, 3, 4, 5, 6, 7, a oanoiaaeoeaoe?e/iay – oanoiaaeoeaoue oeeo? –
aeanyoue a?aaneeo oeeo? io 0 aei 9 e aua oanoue neiaieia –

A (oeeo?a, ecia?aaeathuay aeanyoue), D (oeeo?a o?eiaaeoeaoue),

A (oeeo?a iaeeiiaaeoeaoue), E (oeeo?a /aou?iaaeoeaoue),

N (oeeo?a aeaaiaaeoeaoue), F (oeeo?a
iyoiaaeoeaoue).

I?iua anaai niiinoaaeoue caienue iaeieo e oao aea /enae a yoeo nenoaiao
n/eneaiey iiaeii n eniieueciaaieai oaaeeoeu 1, i?eaaaeaiiie ia
neaaeothuae no?aieoea.

Iu oaea aiai?eee i oii, /oi nia?aiaiiua oeeo?iaua YAI ana eniieuecotho a
ea/anoaa iniiaiie aeaie/ioth nenoaio n/eneaiey. E aa aeinoieinoaai
ioiineony:

i?inoioa auiieiaiey a?eoiaoe/aneeo e eiae/aneeo iia?aoeee, /oi aea/ao
ca niaie i?inoioo ono?ienoa, ?aaeecothueo yoe iia?aoeee;

aiciiaeiinoue eniieueciaaiey aiia?aoa aeaaa?u eiaeee (aoeaaie aeaaa?u)
aeey aiaeeca e neioaca iia?aoeeiiiuo ono?ienoa YAI.

E iaoaeianoaai aeaie/iie nenoaiu n/eneaiey ioiineony iaiaoiaeeiinoue
ia?aaiaea /enae ec aeanyoe/iie a aeaie/ioth e iaiai?io, a oaeaea oi,
/oi caienue /enea a aeaie/iie nenoaia a?iiicaeea (o?aaoao aieueoaai
/enea ?ac?yaeia, /ai i?eau/iay aeey /aeiaaea aeanyoe/iay). Ii yoie e
?yaeo ae?oaeo i?e/ei, e?iia aeaie/iie i?eiaiythony ainueia?e/iay e
oanoiaaeoeaoe?e/iay nenoaiu n/eneaiey.

Oaaeeoea 1.1

N e n o a i a n / e n e a i e y

10 2 8 16

0 0 0 0

1 1 1 1

2 0 1 2 2

3 1 1 3 3

4 1 0 0 4 4

5 1 0 1 5 5

6 1 1 0 6 6

7 1 1 1 7 7

8 1 0 0 0 1 0 8

9 1 0 0 1 1 1 9

10 1 0 1 0 1 2 A

11 1 0 1 1 1 3 B

12 1 1 0 0 1 4 C

13 1 1 0 1 1 5 D

14 1 1 1 0 1 6 E

15 1 1 1 1 1 7 F

16 1 0 0 0 0 2 0 1 0

Niaianoiia eniieueciaaiea oeacaiiuo nenoai iaoneiaeaii aeaoiy i?e/eiaie:

a ainueia?e/iie e oanoiaaeoeaoe?e/iie nenoaiao ethaia /enei
caienuaaaony aieaa eiiiaeoii, iaaeaee aeaie/iia;

i?inoioie i?aia?aciaaiey ec aeaie/iie a ainueia?e/ioth
(oanoiaaeoeaoe?e/-ioth) nenoaio n/eneaiey e iaiai?io.

I?eaaaeai i?aaeea ia?aaiaea /enae ec aeaie/iie nenoaiu a ainueia?e/ioth
(oanoiaaeoeaoe?e/ioth) e iaiai?io.

I1 .I?aaeei ia?aaiaea “8n/n -> 2c/c”

I?e ia?aaiaea iiiai?ac?yaeiiai /enea eaaeaeoth oeeo?o enoiaeiiai
ainueia?e/iiai /enea i?aaenoaaeoue anaaaea oi/ii o?aiy aeaie/iuie
oeeo?aie, acyouie ec i?eaaaeaiiie auoa oaaeeoeu. I?e yoii, anee aeey
caiene niioaaonoaothuae ainueia?e/iie oeeo?u a aeaea aeaie/iie o?aaoaony
iaiaa o?ao aeaie/iuo oeeo?, aeaie/iue yeaeaaeaio aeiiieiyaony neaaa
ioeyie (iacia/auea ioee ia eneacyo cia/aiey /enea). Oaeei ia?acii,
iai?eia?, i?e caiene /aou?ao?ac?yaeiiai ainueia?e/iiai /enea aeieaeii
iieo/eoueny aeaaiaaeoeaoe?ac?yaeiia aeaie/iia. Iinea ieii/aiey
oaeiai i?aia?aciaaiey iiaeii ioa?ineoue noa?oea aeey anaai /enea
iacia/auea aeaie/iua oeeo?u.

Ioiaoei, /oi o?e oeeo?u i?eiyoi iacuaaoue o?eaaeie. Iiyoiio iiaeii
neacaoue, /oi i?e iienuaaaiii ia?aaiaea eaaeaeay ainueia?e/iay oeeo?a
caiaiyaony niioaaonoaothuae ae o?eaaeie aeaie/iuo oeeo?.

Anee enoiaeiia /enei ae?iaiia, o.a. eiaao oeaeoth e ae?iaioth
/anoue, oi a aeaie/iii /enea caiyoay noaaeony iaaeaeo o?eaaeaie,
i?aaenoaaeythueie niioaaonoaothuea oeeo?u enoiaeiiai /enea.

I?eia?.

I?aia?acoai ainueia?e/iia /enei 371,62.

Aeey yoiai caieoai aeey eaaeaeie oeeo?u niioaaonoaothuoth o?eaaeo:

3 –> 011

7 –> 111

1 –> 001

6 –> 110

2 –> 010

Oaia?ue iiaeii caienaoue /enei a aeaie/iie oi?ia (aeey iaaeyaeiinoe
iaaeaeo o?eaaeaie iiianoei i?iaaeu):

371,62 -> 011 111 001 , 110 010

E, iaeiiaoe, caieoai iieo/aiiia aeaie/iia /enei oae, eae yoi i?eiyoi a
iaoaiaoeea, aac iacia/aueo ioeae, a oaeaea ioa?inea i?aaua ioee a
ae?iaiie /anoe /enea:

371,62 -> 11111001,11001

I2. I?aaeei ia?aaiaea “2n/n -> 8c/c”

I?e ia?aaiaea iiiai?ac?yaeiiai aeaie/iiai /enea a ainueia?e/ioth oi?io
iinooiatho neaaeothuei ia?acii: Enoiaeiia /enei ?acaeaatho ia o?eaaeu.
I?e yoii aeey oeaeie /anoe /enea ?acaeaiea i?iaiaeyo io
ianoiiaoiaeaeaiey caiyoie aeaai, a aeey ae?iaiie /anoe – io yoiai aea
ianoa ai?aai. Caoai naiay eaaay a?oiia i?e iaiaoiaeeiinoe aeiiieiyaony
iacia/aueie ioeyie aei ia?aciaaiey o?eaaeu, a naiay i?aaay a?oiia
oieueei a ae?iaiie /anoe aeiiieiyaony ioeyie ni?aaa oaeaea aei
ia?aciaaiey iieiie o?eaaeu. Iinea yoiai eaaeaeay o?eaaea caiaiyaony
niioaaonoaothuae ainueia?e/iie oeeo?ie. Ianoiiieiaeaiea caiyoie
nio?aiyaony ii oai aea i?aaeeai, /oi e a i?aaeea I1.

I?eia?.

I?aaenoaaeoue aeaie/iia /enei 1101100,01111101 a oi?ia ainueia?e/iiai.

?aciaueai enoiaeiia /enei ia a?oiiu ii o?e oeeo?u, i?eiya a ea/anoaa
oi/ee ion/aoa ianoiiieiaeaiea caiyoie (aeey iaaeyaeiinoe iaaeaeo
o?eaaeaie iiianoei i?iaaeu):

1 101 100 , 011 111 01

Oaia?ue aeiiieiei aei o?ao oeeo? ioeyie naioth eaaoth a?oiio neaaa e
naioth i?aaoth a?oiio ni?aaa:

001 101 100 , 011 111 010

E, iaeiiaoe, caiaiei eaaeaeoth o?eaaeo niioaaonoaothuae ainueia?e/iie
oeeo?ie:

001 101 100 , 011 111 100 –> 154,372

I3. I?aaeei ia?aaiaea “16n/n -> 2c/c”

I?e ia?aaiaea iiiai?ac?yaeiiai oanoiaaeoeaoe?e/iiai /enea a
aeaie/ioth oi?io eaaeaeoth oeeo?o enoiaeiiai /enea caiaiytho a?oiiie
oi/ii ec /aou?ao aeaie/iuo oeeo? (caiaiytho oao?aaeie aeaie/iuo
oeeo?). Ianoiiieiaeaiea caiyoie nio?aiyaony ii oai aea i?aaeeai, /oi
e a i?aaeea I1. A ieii/aoaeueiie caiene iiaeii ioa?ineoue naiua eaaua
(iacia/auea) ioee e naiua i?aaua ioee ae?iaiie /anoe.

I?eia?. I?aia?aciaaoue oanoiaaeoeaoe?e/iia /enei “6C,7D” a
aeaie/ioth oi?io.

Aeey yoiai caieoai aeey eaaeaeie oeeo?u niioaaonoaothuoth oao?aaeo:

6 –> 0110

C –> 1100

7 –> 0111

D –> 1101

Oaia?ue iiaeii caienaoue /enei a aeaie/iie oi?ia (aeey iaaeyaeiinoe
iaaeaeo oao?aaeaie iiianoei i?iaaeu):

6C,7D -> 0110 1100 , 0111 1101

E, iaeiiaoe, caieoai iieo/aiiia aeaie/iia /enei oae, eae yoi i?eiyoi a
iaoaiaoeea, aac iacia/aueo ioeae:

6C,7D -> 1101100,01111101

I4. I?aaeei ia?aaiaea “2n/n -> 16c/c”

I?e ia?aaiaea iiiai?ac?yaeiiai aeaie/iiai /enea a oanoiaaeoeaoe?e/ioth
oi?io iinooiatho neaaeothuei ia?acii. Enoiaeiia /enei ?acaeaatho ia
oao?aaeu. I?e yoii aeey oeaeie /anoe /enea ?acaeaiea i?iaiaeyo io
ianoiiaoiaeaeaiey caiyoie aeaai, a aeey ae?iaiie /anoe io yoiai aea
ianoa ai?aai. Caoai naiay eaaay a?oiia i?e iaiaoiaeeiinoe aeiiieiyaony
iacia/aueie ioeyie aei ia?aciaaiey oao?aaeu, a naiay i?aaay a?oiia
oieueei a ae?iaiie /anoe aeiiieiyaony ioeyie ni?aaa oaeaea aei
ia?aciaaiey iieiie oao?aaeu. Iinea yoiai eaaeaeay oao?aaea caiaiyaony
niioaaonoaothuae oanoiaaeoeaoe?e/iie oeeo?ie. Ianoiiieiaeaiea caiyoie
nio?aiyaony ii oai aea i?aaeeai, /oi e a i?aaeea I1.

I?eia?. I?aaenoaaeoue aeaie/iia /enei 1101100,01111101 a oi?ia
oano-iaaeoeaoe?e/iiai.

?aciaueai enoiaeiia /enei ia a?oiiu ii /aou?a oeeo?u, i?eiya a ea/anoaa
oi/ee ion/aoa ianoiiieiaeaiea caiyoie (aeey iaaeyaeiinoe iaaeaeo
oao?aaeaie iiianoei i?iaaeu):

110 1100 , 0111 1101

Oaia?ue aeiiieiei aei /aou?ao oeeo? ioeyie neaaa naioth eaaoth
a?oiio:

0110 1100 , 0111 1101

E, iaeiiaoe, caiaiei eaaeaeoth oao?aaeo niioaaonoaothuae
oanoiaaeoeaoe?e/iie oeeo?ie:

0110 1100 , 0111 1101 -> 6N,7D.

Oanoiaaeoeaoe?e/iay e ainueia?e/iay nenoaiu n/eneaiey eniieuecothony
aeey aieaa eiiiaeoiie e oaeiaiie caiene aeaie/iuo /enae.

Oae, ecaanoiinoue oanoiaaeoeaoe?e/iie nenoaia i?eianei oi, /oi n aa
eniieueciaaieai oaeiaii i?aaenoaaeyoue i?ia?aiiu a eiaeao aieueoeinoaa
nia?aiaiiuo YAI.

1.2. Ia?aaiae /enae ec iaeiie nenoaiu n/eneaiey

a ae?oaoth

Iineieueeo a i?aeoe/aneie aeayoaeueiinoe ethaee i?eaueee iia?e?iaaoue
aeanyoe/iie nenoaiie n/eneaiey, a a YAI /enea i?aaenoaaeythony a
aeaie/iie, iaiaoiaeeii iao/eoueny i?aia?aciauaaoue /enea ec iaeiie
nenoaiu n/eneaiey a ae?oaoth. ?anniio?aiiua auoa i?aaeea ia?aaiaea ec
aeaie/iie nenoaiu n/eneaiey a ainueia?e/ioth e oanoiaaeoeaoe?e/ioth e
iaiai?io iinyo /anoiue oa?aeoa? e ia iiaoo auoue ?ani?ino?aiaiu ia
ae?oaea nenoaiu. Caeanue aea iu ?anniio?ei iauea i?aaeea ia?aaiaea,
ni?aaaaeeeaua aeey ethaie ia?u nenoai n/eneaiey, oioy e aieaa
a?iiicaeeea e o?oaeiaieea ii n?aaiaieth n ?anniio?aiiuie auoa.

I?aaeea ia?aaiaea oeaeuo e ae?iaiuo /enae ia niaiaaeatho, iiyoiio
i?eaaaeai o?e i?aaeea ia?aaiaea /enae ec nenoaiu n/eneaiey n
iniiaaieai R a nenoaio n/eneaiey n iniiaaieai Q.

I?aaeei 1. Ia?aaiae oeaeuo /enae

Aeey ia?aaiaea oeaeiai /enea N, i?aaenoaaeaiiiai a nenoaia
n/eneaiey (n/n) n iniiaaieai R, a n/n n iniiaaieai Q iaiaoiaeeii
aeaiiia /enei aeaeeoue ia iniiaaiea Q ii i?aaeeai n/n n
iniiaaieai R aei iieo/aiey oeaeiai inoaoea, iaiueoaai Q. Iieo/aiiia
/anoiia niiaa iaiaoiaeeii aeaeeoue ia iniiaaiea Q aei iieo/aiey iiaiai
oeaeiai inoaoea, iaiueoaai Q, e o.ae., aei oao ii?, iiea
iineaaeiaa /anoiia aoaeao iaiueoa Q. *enei N a n/n n iniiaaieai Q
i?aaenoaaeony a aeaea ia oii?yaei/aiiie iineaaeiaaoaeueiinoe
inoaoeia aeaeaiey a ii?yaeea, ia?aoiii eo iieo/aieth (eiuie
neiaaie, noa?ooth oeeo?o /enea N aeaao iineaaeiaa /anoiia).

I?eia?. I?aia?aciaaoue aeanyoe/iia /enei 67 a aeaie/ioth oi?io.

Iniiaaiea enoiaeiie nenoaiu n/eneaiey R=107. Iniiaaiea iiaie nenoaiu
n/eneaiey Q=2.

Niaeanii i?eaaaeaiiiio i?aaeeo iaaei enoiaeiia /enei 67 aeaeeoue ia
iniiaaiea iiaie nenoaiu (ia 2) ii i?aaeeai aeanyoe/iie nenoaiu n/eneaiey
(enoiaeiay n/n).

Iineieueeo i?ioeann aeaeaiey ia 2 i/aiue i?ino, ainiieuecoainy
neaaeothuei i?eaiii: a eaaii noieaoea aoaeai ienaoue oaeouea /anoiua, a
a i?aaii – oaeouea inoaoee io eo aeaeaiey ia 2 (yoi iiaeao auoue eeai
0, eeai 1):

67 1 I?e aeaeaiee 67 ia 2 iieo/aaony /anoiia 33 e inoaoie 1;

33 1 i?e aeaeaiee 33 – /anoiia 16 e inoaoie 1 e o.ae.

16 0

8 0

4 0

2 0

1 1 <- Noa?oay oeeo?a /enea.0Oaia?ue iiaeii caienaoue /enei 67 a iiaie nenoaia n/eneaiey. Iii ?aaii 1000011.I?aaeei 2. Ia?aaiae i?aaeeueiie ae?iaeIa?aaiae i?aaeeueiie ae?iae, i?aaenoaaeaiiie a n/n n iniiaaieai R, a n/n n iniiaaieai Q caeeth/aaony a iineaaeiaaoaeueiii oiiiaeaiee yoie ae?iae ia iniiaaiea Q ii i?aaeeai nenoaiu n/eneaiey n iniiaaieai R, i?e/ai ia?aiiiaeatho oieueei ae?iaiua /anoe. Ae?iaue N a n/n n iniiaaieai Q i?aaenoaaeyaony a aeaea oii?yaei/aiiie iineaaeiaaoaeueiinoe oeaeuo /anoae i?iecaaaeaiee a ii?yaeea eo iieo/aiey. (Eiuie neiaaie, noa?oee ?ac?yae yaeyaony ia?aie oeeo?ie i?iecaaaeaiey). Eiee/anoai iineaaeiaaoaeueiuo i?iecaaaeaiee ii?aaeaeyao eiee/anoai oeeo? a iieo/aiiii /enea.Aeey iiiaeo /enae oeacaiiue i?ioeann oiiiaeaiey iioaioeeaeueii ieeiaaea ia eii/aaony. Iiyoiio ii i?iaeieaeaaony aei oao ii?, iiea ia aoaeao iieo/aii iaiaoiaeeiia /enei oeeo? ae?iaiie /anoe. I?e ia?aaiaea /enea n oeaeueth i?aaenoaaeaiey aa a “iaoeiiie” oi?ia iiaeii oi/ii oeacaoue o?aaoaiia eiee/anoai oeeo?. (Yoi aoaeao ?anniao?eaaoueny iicaea, a ?acaeaea 1.5).I?eia?. Ia?aaanoe a aeaie/ioth nenoaio n/eneaiey aeanyoe/ioth ae?iaue 0,7243.Iniiaaiea enoiaeiie nenoaiu n/eneaiey R=10. Iniiaaiea iiaie nenoaiu n/eneaiey Q=2.Niaeanii i?eaaaeaiiiai i?aaeea enoiaeiia /enei 0,7243 iaaei oiiiaeaoue ia iniiaaiea iiaie nenoaiu (ia 2) ii i?aaeeai aeanyoe/iie nenoaiu n/eneaiey (enoiaeiay n/n). Auiieiei na?eth oiiiaeaiee aei iieo/aiey, iai?eia?, oanoe oeeo? a aeaie/iii /enea:Eneiiua oeeo?u ae?iae:0,7243 * 2 = 1,4486 1 -> noa?oay oeeo?a

0,4486 * 2 = 0,8972 0

0,8942 * 2 = 1,7944 1

0,7944 * 2 = 1,5888 1

0,5888 * 2 = 1,1776 1

0,1776 * 2 = 0,3552 0

0,3552 * 2 = 0,7104 0

Eneiiia i?aaenoaaeaiea /enei 0,7243 a aeaie/iie nenoaia
n/eneaiey -> 0,101110.

Ia?aoeoa aieiaiea, /oi aeey iieo/aiey oanoe oeeo? ae?iae auiieiaii
naiue oiiiaeaiee

Yoi naycaii n iaiaoiaeeiinoueth auiieieoue ie?oaeaiea, /oiau
i?aaenoaaeoue ae?iaue caaeaiiie aeeeiu aieaa oi/ii.

Ec iineaaeiaai i?eia?a, eiia/iay ae?iaue a iaeiie nenoaia n/eneaiey
iiaeao noaoue aaneiia/iie a ae?oaie. Yoi ooaa?aeaeaiea ni?aaaaeeeai
aeey anao neo/aaa, eiaaea iaeia nenoaia n/eneaiey ia iiaeao auoue
iieo/aia aicaaaeaieai a oeaeoth noaiaiue iniiaaiey ae?oaie.

I?eia?u.

Aeanyoe/iay ae?iaue 0,2 i?aaenoaaeyaony aaneiia/iie ae?iaueth
0,33333… a oanoiaaeoeaoe?e/iie nenoaia n/eneaiey (iniiaaiey n/n
10 e 16).

Oanoiaaeoeaoe?e/iay ae?iaue 0,A1 i?aaenoaaeyaony eiia/iie ae?iaueth
0,10110001 a aeaie/iie nenoaia n/eneaiey (iniiaaiey n/n 16 e 2).

I?aaeei 3. Ia?aaiae iai?aaeeueiie ae?iae

Ia?aaiae iai?aaeeueiie ae?iae ec iaeiie nenoaiu n/eneaiey a ae?oaoth
inouanoaeyaony ioaeaeueii aeey oeaeie e ae?iaiie /anoe ii i?aaeeai,
eceiaeaiiui auoa.

1.3. Aeaie/iua eiaeu aeey aeanyoe/iuo oeeo?

A ?yaea neo/aaa a au/eneeoaeueiie oaoieea i?eiaiyaony ia oieueei
aeaie/iay, ii e aeanyoe/iay nenoaia n/eneaiey. Iaeiaei e a yoii
neo/aa aeey i?aaenoaaeaiey aeanyoe/iuo oeeo? eniieuecoaony
iai?oaeiaaiea, ?ac?aaioaiiia aeey i?aaenoaaeaiey aeaie/iuo oeeo?. A yoii
neo/aa aiai?yo i aeaie/ii-aeanyoe/iuo eiaeao aeanyoe/iuo oeeo?.

Niaeanii oi?ioeu Oa?oee aeey i?aaenoaaeaiey 10 ?acee/iuo oeeo? o?aaoaony
/aou?a aeoa eioi?iaoeee:

3 aeoa < I = log(10) < 4 aeoa.Oaeei ia?acii, i?e iaiaoiaeeiinoe i?aaenoaaeoue aeanyoue ?aciuo aeanyoe/iuo oeeo? eiiaeiaoeeyie aeaie/iuo oeeo?, eaaeaeoth ec ieo iiaeii i?aaenoaaeoue ieieioi oao?aaeie aeaie/iuo /enae. Aieueoeinoai eiaeia aeanyoe/iuo oeeo? eniieuecoao oao?aaeu, oioy anoue e eiaeu, a eioi?uo aeey eiaee?iaaiey eniieuecoaony aieueoaa /enei aeoia.Iaeaieaa ?ani?ino?aiaiu aeaie/ii-aeanyoe/iua eiaeu, a eioi?uo aeey i?aaenoaaeaiey aeanyoe/iuo oeeo? eniieuecothony iiceoeeiiiua iaoiaeu eiaee?iaaiey. Oae, anee ?anniao?eaaoue /aou?a aeaie/iuo ?ac?yaea oao?aaeu eae /aou?ao?ac?yaeiia aeaie/iia /enei, oi aana aa ioaeaeueiuo ?ac?yaeia neaaa iai?aai aoaeoo ?aaiu niioaaonoaaiii 8, 4, 2 e 1.Iiyoiio ia?aue aeaie/ii-aeanyoe/iue eiae, eioi?ue iu ?anniio?ei, iaicia/aaony eae eiae “8421”. Aai iiaeii iacaaoue eiaeii n anoanoaaiiuie aanaie.A yoii eiaea eaaeaeay aeanyoe/iay oeeo?a i?aaenoaaeyaony aa aeaie/iui yeaeaaeaioii :oeeo?a 0 eae 0000,oeeo?a 1 eae 0001,oeeo?a 2 eae 0010,oeeo?a 5 eae 0101,oeeo?a 8 eae 1000,oeeo?a 9 eae 1001.A oi aea a?aiy, eiay /aou?a aeaie/iuo oeeo?u, iiaeii i?aaenoaaeoue ia 10, a 16 ?acee/iuo eiiaeiaoeee. Oaeei ia?acii, i?e eniieueciaaiee eiaea “8421” oanoue eiiaeiaoeee : 1010, 1011, ..., 1111 inoaioony iaeniieueciaaiiuie, o.a. ia aoaeoo ecia?aaeaoue ie iaeiie ec aeanyoe/iuo oeeo?. Yoe eiiaeiaoeee n/eoathony cai?auaiiuie.a) Eiaeu n ecauoeiiE?iia ?anniio?aiiie nenoaiu eiaee?iaaiey aeinoaoi/ii oe?iei eniieuecothony oaeaea oae iacuaaaiua eiaeu n ecauoeii. ?anniio?ei a?oiio eiaeia “8421” n ecauoeii”.Eiae “8421” n ecauoeii W” no?ieony ii neaaeothuei i?aaeeai:I?e eiaee?iaaiee aeanyoe/iie oeeo?u, e iae aia/aea i?eaaaeytho W, e caoai iieo/aiiia /enei i?aaenoaaeytho eae aeaie/iia a eiaea “8421”.Cia/aiea W iiaeao auoue ?aaiui 1, 2, 3, 4, 5 eee 6. I?e ethaii cia/aiee ecauoea W oanoue ec oanoiaaeoeaoe eiiaeiaoeee inoaioony iaeniieueciaaiiuie. Oieueei aeey ?aciuo ecauoeia yoe cia/aiey aoaeoo ?aciuie.I?eia?. ?anniio?ei eiae “8421” n ecauoeii 3”.a)I?aaenoaaei oeeo?o 8 a aeaiiii eiaea.Aia/aea oaaee/ei 8 ia 3. Iieo/eony 11.Caoai caieoai 11 a eiaea “8421”. Iieo/eony 1011.*enei 1011 e anoue i?aaenoaaeaiea oeeo?u 8 a aeaiiii eiaea.a)Ainnoaiiaei oeeo?o, eioi?ay ecia?aaeaaony eiiaeiaoeeae 0101.Aia/aea i?aaenoaaei aeanyoe/iia /enei, ?anniao?eaay eiiaeiaoeeth 0101, eae aai ecia?aaeaiea a eiaea “8421”. Iieo/eony /enei 5.Caoai au/oai ec iaai (ec 5) ecauoie 3. Iieo/eony 2.Yoi e anoue eneiiue ioaao: Eiiaeiaoeey 0101 ecia?aaeaao aeanyoe/ioth oeeo?o 2 a eiaea “8421” n ecauoeii 3”.a)Ainnoaiiaei oeeo?o, eioi?ay ecia?aaeaaony eiiaeiaoeeae 1110.Ainnoaiiaei aeanyoe/iia /enei. Iieo/eony 14.Au/oai ec iaai ecauoie 3. Iieo/eony 11.Iineieueeo 11 ia yaeyaony aeanyoe/iie oeeo?ie (yoi aeaoo?ac?yaeiia aeanyoe/iia /enei), aeaeaai auaiae, /oi eiiaeiaoeey 1110 ia ecia?aaeaao ieeaeie aeanyoe/iie oeeo?u e yaeyaony cai?auaiiie.a) Eiae “2421”E?iia eiaeia n anoanoaaiiuie aanaie ?ac?yaeia i?eiaiythony e ae?oaea. Iaeiei ec oe?iei ecaanoiuo eiaeia yaeyaony iiceoeeiiiue eiae, iino?iaiiue n eniieueciaaieai oao?aaeu aeaie/iuo oeeo?, aana eioi?uo neaaa iai?aai ?aaiu niioaaonoaaiii : 2, 4, 2 e 1.I?aaenoaaei eiaeu oeeo? a oaaeeoea:Oeeo?a Eiae “2421” Oeeo?a Eiae “2421”0 0000 5 0101 eee 10111 0001 6 0110 eee 11002 0010 eee 1000 7 0111 eee 11013 0011 eee 1001 8 11104 0100 eee 1010 9 1111Eae aeaeii ec oaaeeoeu, ?yae aeanyoe/iuo oeeo? iiaoo auoue i?aaenoaaeaiu aeaoiy ia niaiaaeathueie aeaie/iuie eiiaeiaoeeyie.Iai?eia?, eiiaeiaoeee 0100 e 0010 ecia?aaeatho oeeo?o 2, eiiaeiaoeee 1010 e 0100 ecia?aaeatho oeeo?o 4 e o.ae. Ioee/eoaeueiie iniaaiiinoueth aeaiiiai eiaea yaeyaony oi, /oi a iai iao iaeniieueciaaiiuo (cai?auaiiuo) eiiaeiaoeee.a) Eiae “2 ec 5”Aeaiiue eiae i?eiaaeeaaeeo e iaiiceoeeiiiui eiaeai. Eae e ana iaiiceoeeiiiua eiaeu ii ii?aaeaeyaony oaaee/iui niiniaii. Aai iacaaiea io?aaeaao i?eioeei iino?iaiey eiaea: ethaay aeanyoe/iay oeeo?a i?aaenoaaeyaony eiiaeiaoeeae ec 5 aeaie/iuo oeeo?, a eioi?ie oi/ii aeaa oeeo?u 1 e, neaaeiaaoaeueii, o?e oeeo?u 0.I?aaenoaaei oaaeeoeo iaeiiai ec aiciiaeiuo aa?eaioia aeey aeaiiiai eiaea:Oeeo?a Eiae Oeeo?a Eiae0 11000 5 010101 00011 6 011002 00101 7 100013 00110 8 100104 01001 9 10100Ana inoaeueiua aiciiaeiua eiiaeiaoeee, a eioi?uo /enei aaeeieoe ia ?aaii aeaoi, yaeythony cai?auaiiuie.Oaeaea eae e ana eiaeu ia iniiaa oao?aaeu “8421”, iineaaeiee eiae i?eiaaeeaaeeo e a?oiia eiaeia, iaeaaeathueo oae iacuaaaiuie aeeaaiinoe/aneeie aiciiaeiinoyie: Anee ecaanoii, /oi iaeioi?ay eiiaeiaoeey aeieaeia ecia?aaeaoue aeanyoe/ioth oeeo?o, ii iiiaaeaao a iaeanoue cai?auaiiuo, cia/eo i?iecioei eneaaeaiea eioi?iaoeee. Yoi naienoai eiaeia aeoeaii eniieuecoaony a aiia?aoo?a YAI.Aeey cae?aieaiey iaoa?eaea ii ia?aaiaeo /enae ec iaeiie nenoaiu n/eneaiey a ae?oaoth auiieiei ianeieueei i?eia?ia.I?eia? 1. I?aaenoaaeoue aeanyoe/iia /enei 581 a aeaie/iie, ainueia?e/iie e oanoiaaeoeaoe?e/iie nenoaiao n/eneaiey.Caaea/o iiaeii ?aoeoue n ieieiaeueiuie cao?aoaie oneeee, auiieiea, iai?eia?, ia?aaiae a aeaie/ioth n/n ii iauaio i?aaeeo (o. a. aeaeaieai ia iniiaaiea 2 ii i?aaeeai aeanyoe/iie nenoaiu n/eneaiey), a caoai ec aeaie/iie a ainueie- e oanoiaaeoeaoe?e/ioth nenoaiu n/eneaiey, eniieuecoy oi?iuaiiua i?aaeea (eiaee?iaaieai niioaaonoaaiii oao?aae e o?eaae).I?eia? 2. I?aaenoaaeoue aeanyoe/iia /enei 993,761 a aeaie/iie e oanoiaaeoeaoe?e/iie nenoaiao n/eneaiey.Caaea/o iiaeii ?aoeoue oaeei aea ia?acii, eae e i?aaeuaeouoth.I?eia? 3. I?aaenoaaeoue oanoiaaeoeaoe?e/iia /enei 8363 a aeanyoe/iie nenoaia n/eneaiey.Ainiieuecoainy iauei i?aaeeii. Aeey yoiai iaaei enoiaeiia /enei aeaeeoue ia 10 ii i?aaeeai oanoiaaeoeaoe?e/iie nenoaiu n/eneaiey.*oi aea yoi ca i?aaeea? Yoi oaeea aea i?aaeea neiaeaiey, au/eoaiey, oiiiaeaiey e aeaeaiey, /oi e a aeanyoe/iie n/n, ii iaae /eneaie a iiceoeeiiiie oanoiaaeoeaoe?e/iie n/n.Auiieiei ia?aaiae:8 3 6 3 A_(131)(130) D 2 3 A------- A1 6 ---- 1 5 0 A_ (22) 3 2 _(21)(20) _(50) (20) 2 1 A----- (50) ----- _(33)2 3 ----- 1 0 (30) 3_(35) 0 3 _ (16) -----(30) (10) 3----- -----5 6Eneiiia /enei a aeanyoe/iie nenoaia ?aaii 33635.I?eia/aiea. A e?oaeuo neiaeao caienaiu aeanyoe/iua yeaeaaeaiou niioaaonoaothueo oanoiaaeoeaoe?e/iuo /enae. I?e yoii a eaaeaeie ia?a /enae, ?aniieiaeaiiuo ae?oa iiae ae?oaii, ia?aia /enei - /anoe/iia aeaeeiia, a aoi?ia - i?iecaaaeaiea aeaeeoaey ia /anoe/iia /anoiia. Oae caienue (131) - yeaeaaeaio oanoiaaeoeaoe?e/iiai aeaeeiiai 83, a (130) - ?acoeueoao oiiiaeaiey aeaeeoaey A (=10) ia D (13).1.4. A?eoiaoeea oeeo?iauo au/eneeoaeueiuo iaoeiEae oaea aiai?eeinue auoa, i?aeoe/anee ana nia?aiaiiua oeeo?iaua YAI a ea/anoaa iniiaiie eniieuecotho aeaie/ioth nenoaio n/eneaiey. A ana a?eoiaoe/aneea iia?aoeee iaae aeaie/iuie /eneaie iiaeii naanoe e aeaoi yeaiaioa?iui - neiaeaieth e naeaeao aeaie/iuo eiaeia, ecia?aaeathueo /enea. Yoi iicaieeo oaoie/anee ?aaeeciaaoue /aou?a aeaenoaey a?eoiaoeee a iaeiii ono?ienoaa, iacuaaaiii a?eoiaoeei-eiae/aneii (AEO), eniieuecoy iaeie e oa aea yeaeo?e/aneea noaiu.1.4.1. I?aaenoaaeaiea /enae ni ciaeaieI?e auiieiaiee a?eoiaoe/aneeo iia?aoeee a YAI i?eiaiytho i?yiie, ia?aoiue e aeiiieieoaeueiue eiaeu.Eae oaea aiai?eeinue auoa, eiaeii iacuaatho oaeoth caienue /enea, eioi?ay ioee/aaony io anoanoaaiiie e iauai?eiyoie. Oae aio, a iaoaiaoeea anoanoaaiiie oi?iie caiene /enea yaeyaony caienue, i?e eioi?ie iaiin?aaenoaaiii ia?aae noa?oae cia/auae oeeo?ie /enea iiiauaaony ciae iethn(+) eee ieion(-), a aeeeia caiene ii?aaeaeyaony aaee/eiie /enea (eia/a, eiee/anoai neiaieia, eniieueciaaiiuo aeey caiene ?aciuo /enae, eae i?aaeei, ia niaiaaeaao). A YAI yoi ia oae. Iaeiie ec aaaeiaeoeo oa?aeoa?enoee ethaie YAI yaeyaony aeeeia neiaa a iae. Aeeeia neiaa ii?aaeaeyaony eiee/anoaii aeaie/iuo ?ac?yaeia neiaa.Iiyoiio a YAI, aia caaeneiinoe io aaee/eiu /enea, aai eiae anaaaea eiaao oeene?iaaiiia eiee/anoai aeaie/iuo oeeo?.E?iia yoiai, a aeaie/iii aeoaaeoa iao ieeaeeo neiaieia, e?iia oeeo? 0 e 1, e iaiaoiaeeiu iiaua i?aaeea aeey oeacaiey ciaea /enea. Nooue yoeo i?aaee naiaeeony e oiio, /oi ciae iethn ecia?aaeaaony oeeo?ie 0, ciae ieion - oeeo?ie 1, a oeeo?a, ecia?aaeathuay ciae anaaaea caienuaaaony naiie ia?aie a caiene /enea.Ia?aoeoa aieiaiea, /oi eiae /enea anaaaea niaea?aeeo ecia?aaeaiea aai ciaea, a ioee/ea io iaoaiaoe/aneie caiene, eioi?ay iicaieyao iioneaoue ciae iethn i?e ecia?aaeaiee iieiaeeoaeueiiai /enea.Oae, eiae 011101, niaeanii yoei i?aaeeai, ecia?aaeaao iieiaeeoaeueiia (naiay eaaay oeeo?a - 0) aeaie/iia /enei 11101.Aeey oiai, /oiau aieaa i?inoi, e, neaaeiaaoaeueii, aieaa yeiiiie/ii ?aaeeciaaoue ono?ienoai AEO i?eiaiytho ianeieueei ?aciuo eiaeia /enae. Yoi naycaii n oai, /oi ?aciua iia?aoeee a YAI aieaa i?inoi ?aaeecothony a ?aciuo eiaeao.I?e auiieiaiee a?eoiaoe/aneeo iia?aoeee a YAI i?eiaiytho i?yiie, ia?aoiue e aeiiieieoaeueiue eiaeu /enae.I?yiie eiae aeaie/iiai /enea - yoi naii aeaie/iia /enei, a eioi?ii ana oeeo?u, ecia?aaeathuea aai cia/aiea, caienuaathony eae a iaoaiaoe/aneie caiene, a ciae /enea caienuaaaony aeaie/iie oeeo?ie.I?e yoii ieeaeiai neiaiea, ioaeaeythuaai yoo oeeo?o io noa?oae oeeo?u, eniieuecoaiie i?e ecia?aaeaiee aai aaee/eiu, ia aeiioneaaony. A oaeeo neo/ayo aiai?yo i oii, /oi iacia/aiea oeeo?u a eiaea ii?aaeaeyaony aai iiceoeeae.I?eia?u.Ecia?aaeaaiia /enei Eiae+1101 (+13) 0000 1101 ( A i?eia?ao eiaeu )+1011101 (+93) 0101 1101 ( ecia?aaeathony )1101 (-13) 1000 1101 ( ainaiueth oeeo?aie )Eoae, i?yiie eiae ii/oe ia ioee/aaony io i?eiyoiai a iaoaiaoeea: aeey auyaeaiey aaniethoiie aaee/eiu (iiaeoey) /enea, iaaei ioa?ineoue oeeo?o, iaicia/athuoth aai ciae.Iaeiaei i?eiaieoaeueii e iia?aoeeyi neiaeaiey e au/eoaiey oaeie eiae iaoaeiaai: i?aaeea n/aoa aeey iieiaeeoaeueiuo e io?eoeaoaeueiuo /enae ?acee/athony. *oiau i?iynieoue yoi ianoiyoaeuenoai, i?aaenoaaei /oi aeeeia eiaea (neiaa) ?aaia 5 aeaie/iui ?ac?yaeai e caieoai ianeieueei /enae a iai:*enei -2 -1 0 +1 +2Eiae 10010 10001 00000 00001 00010Eae aeaeii ec i?eia?a, i?e eniieueciaaiee i?yiiai eiaea i?e ia?aoiaea cia/aiey /enei /a?ac iieue, i?ienoiaeeo nea/eiia?aciia eciaiaiea eiaea! Iiyoiio iino?iaiea ono?ienoaa, a eioi?ii aeieaeiu auiieiyoueny oaeea aeaenoaey a?eoiaoeee, eae neiaeaiea /enae n ?aciuie ciaeaie e au/eoaiea, noaiiaeony neiaeiie caaea/ae.I?yiie eiae eniieuecoaony i?e o?aiaiee /enae a iaiyoe YAI, a oaeaea i?e auiieiaiee iia?aoeee oiiiaeaiey e aeaeaiey.*oiau iino?ieoue aieaa i?inoua noaiu AEO i?aaeeiaeaiu e aeoeaii i?eiaiythony ia?aoiue e aeiiieieoaeueiue eiaeu.Ia?aoiue eiae iieiaeeoaeueiiai /enea niaiaaeaao n i?yiui, a i?e caiene io?eoeaoaeueiiai /enea ana aai oeeo?u, e?iia oeeo?u, ecia?aaeathuae ciae /enea, caiaiythony ia i?ioeaiiieiaeiua ( 0 caiaiyaony ia 1, a 1 - ia 0).I?eia?u caiene.Ecia?aaeaaiia /enei Eiae+1101 (+13) 0000 1101 ( A i?eia?ao eiaeu )+1011101 (+93) 0101 1101 ( ecia?aaeathony )1101 (-13) 1111 0010 ( ainaiueth oeeo?aie )Niiinoaaeaiea yoie caiene n i?yiui eiaeii iieacuaaao, /oi iaiin?aaenoaaiii ainnoaiiaeoue aaniethoioth aaee/eio (iiaeoeue) io?eoeaoaeueiiai /enea iai?inoi. Iaeiaei, a yoii eiaea eae e iieiaeeoaeueiui, oae e e io?eoeaoaeueiui /eneai iiaeii i?eiaiyoue iaeie e oa aea i?aaeea, a iia?aoeeth A-A iiaeii caiaieoue iia?aoeeae neiaeaiey /enae A e “ieion A”.Iiniio?ei, eae i?aaenoaaeyaony iineaaeiaaoaeueiua /enea i?e ia?aoiaea /a?ac iieue:*enei -2 -1 0 +1 +2Eiae 11101 11110 00000 00001 00010Ec i?eia?a aeaeii, /oi ia?aoiae /a?ac iieue oaeaea ia auaeyaeeo anoanoaaiiui. Ioia/aiiay iniaaiiinoue aea/ao ca niaie e neaaeothuaa - a ia?aoiii eiaea iieue ecia?aaeatho aeaa ?acee/athueany eiiaeiaoeee: 00000 (+0) e 11111 (-0), /oi oneiaeiyao aiia?aoioth ?aaeecaoeeth iia?aoeee.Aeey ainnoaiiaeaiey i?yiiai eiaea io?eoeaoaeueiiai /enea ec ia?aoiiai eiaea iaaei ana oeeo?u, e?iia oeeo?u, ecia?aaeathuae ciae /enea, caiaieoue ia i?ioeaiiieiaeiua.Aeiiieieoaeueiue eiae iieiaeeoaeueiiai /enea niaiaaeaao n i?yiui, a eiae io?eoeaoaeueiiai /enea ia?acoaony eae ?acoeueoao oaaee/aiey ia 1 aai ia?aoiiai eiaea.Eiuie neiaaie, i?ioeann iino?iaiey aeiiieieoaeueiiai eiaea io?eoeaoaeueiiai /enea iiaeii ?acaeoue ia aeaa yoaia - iino?ieoue ia?aoiue eiae, a caoai ec iaai iino?ieoue aeiiieieoaeueiue.I?ieeethno?e?oai yoi ia i?eia?a.*enei -> – 101101

I?yiie eiae -> 1101101

Ia?aoiue eiae -> 1010010

+1

Aeiiieieoaeueiue -> 1010011

I?eia?u caiene.

Ecia?aaeaaiia /enei Eiae

+1101 (+13) 0000 1101 ( A i?eia?ao eiaeu )

+1011101 (+93) 0101 1101 ( ecia?aaeathony )

1101 (-13) 1111 0011 ( ainaiueth oeeo?aie )

A aeiiieieoaeueiii eiaea, a ioee/ea io ia?aoiiai, iieue ecia?aaeaaony
oieueei iaeiie eiiaeiaoeeae, e e?iia yoiai, aeinoaoi/ii anoanoaaiii
iieo/aaony ia?aoiae /a?ac iieue, anee eiaoue a aeaeo, /oi ethaia /enei,
aieueoaa ae?oaiai ia 1, iieo/aaony i?e i?eaaaeaiee e yoiio ae?oaiio 1
ii i?aaeeai neiaeaiey. I?eiaieoaeueii e aeiiieieoaeueiiio eiaeo yoi
eiaiii oae, anee i?eiyoue e naaaeaieth, /oi ?ac?yaeiinoue neiaa
oeene?iaaia, e aaeeieoea ia?aiina ec noa?oaai ?ac?yaea oa?yaony,
iineieueeo aa iaeoaea caienaoue:

2 -> 11101 + 1 = 11110

1 -> 11110 + 1 = 11111

0 -> 11111 + 1 = (1)00000 (ia?aiin ioa?anuaaaony)

+1 -> 00000 + 1 = 00001

+2 -> 00001 + 1 = 00010

Aeey ainnoaiiaeaiey i?yiiai eiaea /enea ec aeiiieieoaeueiiai ioaeii
iieiinoueth iiaoi?eoue (e eiaiii a oii aea ii?yaeea!) aeaenoaey, eioi?ua
eniieueciaaeenue i?e ia?aaiaea ec i?yiiai a aeiiieieoaeueiue eiae:
nia/aea ana oeeo?u, e?iia oeeo?u, ecia?aaeathuae ciae, caiaieoue ia
i?ioeaiiieiaeiua, a caoai i?eaaaeoue 1.

Iniiaiui aeinoieinoaii aeiiieieoaeueiiai eiaea yaeyaony oi, /oi a iai
aaeeiiia?acii ?aaeecothony iia?aoeee neiaeaiey /enae ?aciuo ciaeia
(aeaaa?ae/aneia neiaeaiea), a iia?aoeeth au/eoaiey iiaeii naanoe e
iia?aoeee neiaeaiey caiaiie ciaea au/eoaaiiai ia ia?aoiue. Aniiiiea,
/oi a iaiyoe YAI /enea o?aiyony a i?yiii eiaea, noaiao ynii, /oi
caiaia ciaea au/eoaaiiai iiaeao auoue auiieiaia /?acau/aeii i?inoi
(caiaiie ciaea /enea a i?yiii eiaea ia ia?aoiue). Eiaiii ii oeacaiiie
i?e/eia aeiiieieoaeueiue eiae i?eiaiyaony /aua ia?aoiiai.

1.4.2. Neiaeaiea e au/eoaiea /enae

Neiaeaiea e au/eoaiea /enae a ia?aoiii e aeiiieieoaeueiii eiaeao
auiieiyaony n eniieueciaaieai iau/iiai i?aaeea a?eoiaoe/aneiai neiaeaiey
iiiai?ac?yaeiuo /enae. Iauae aeey yoeo eiaeia iniaaiiinoueth (e i/aiue
oaeiaiie iniaaiiinoueth) yaeyaony eeoue oi, /oi i?e ii?ac?yaeiii
neiaeaiee /enae ?ac?yaeu, ecia?aaeathuea ciaee /enae
?anniao?eaathony eae ?aaiii?aaiua ?ac?yaeu aeaie/iiai /enea, eioi?ua
neeaaeuaathony ae?oa n ae?oaii e n aaeeieoeae ia?aiina ec i?aaeuaeouaai
?ac?yaea /enea ii iau/iui i?aaeeai a?eoiaoeee. ?acee/ey aea ia?aoiiai e
aeiiieieoaeueiiai eiaeia naycaiu n oai, /oi aeaeaaony n aaeeieoeae
ia?aiina ec noa?oaai ?ac?yaea (ecia?aaeathuaai, eae iaiaeiie?aoii
aiai?eeinue, ciae /enea).

I?e neiaeaiee /enae a aeiiieieoaeueiii eiaea aaeeieoea ia?aiina ec
noa?oaai ?ac?yaea eaii?e?oaony (oa?yaony), a a ia?aoiii eiaea yoo
aaeeieoeo iaaei i?eaaaeoue e ieaaeoaio ?ac?yaeo ?acoeueoaoa.

I?eia? 1. Neiaeeoue /enea +12 e -5.

a) A ia?aoiii eiaea

Aeanyoe/iay oi?ia -> +12 -5

Aeaie/iay oi?ia -> +1100 -101

I?yiie eiae -> 00001100 10000101

Ia?aoiue eiae -> 00001100 11111010

Auiieiei neiaeaiea a noieaee:

0 0 0 0 1 1 0 0

1 1 1 1 1 0 1 0

===============

(1) 0 0 0 0 0 1 1 0

+ 1 (Aeiaaaeaiea 1 ia?aiina)

==============

0 0 0 0 0 1 1 1

Eoae, ?acoeueoao a ia?aoiii eiaea = 00000111.

Iineieueeo ciaeiaue ?ac?yae ?aaai 0, ?acoeueoao iieiaeeoaeueiue, e,
neaaeiaaoaeueii, caienue eiaea /enea niaiaaeaao n caienueth i?yiiai
eiaea. Oaia?ue iiaeii ainnoaiiaeoue aeaaa?ae/aneoth caienue
?acoeueoaoa. Ii ?aaai +111 (iacia/auea ioee ioa?ioaiu), eee a
aeanyoe/iie oi?ia +7.

I?iaa?ea (+12-5=+7) iieacuaaao, /oi ?acoeueoao aa?iue.

a) A aeiiieieoaeueiii eiaea

Aeanyoe/iay oi?ia -> +12 -5

Aeaie/iay oi?ia -> +1100 -101

I?yiie eiae -> 00001100 10000101

Ia?aoiue eiae -> 00001100 11111010

+1

Aeiiieieoaeueiue eiae -> 00001100 11111011

Auiieiei neiaeaiea a noieaee:

0 0 0 0 1 1 0 0

1 1 1 1 1 0 1 1

============

(1) 0 0 0 0 0 1 1 1

(Ia?aiin eaii?e?oaony)

Eoae, ?acoeueoao a aeiiieieoaeueiii eiaea = 00000111.

Iineieueeo ciaeiaue ?ac?yae ?aaai 0, ?acoeueoao iieiaeeoaeueiue, e,
neaaeiaaoaeueii, caienue eiaea /enea niaiaaeaao n caienueth i?yiiai
eiaea. Oaia?ue iiaeii ainnoaiiaeoue aeaaa?ae/aneoth caienue
?acoeueoaoa. Ii ?aaai +111 (iacia/auea ioee ioa?ioaiu), eee a
aeanyoe/iie oi?ia +7.

I?iaa?ea (+12-5=+7) iieacuaaao, /oi ?acoeueoao aa?iue.

Oiiiaeaiea e aeaeaiea aeaie/iuo /enae i?iecaiaeeony a YAI a i?yiii
eiaea, a ciaee eo eniieuecothony eeoue aeey ii?aaeaeaiey ciaea
?acoeueoaoa. Oaeaea eae e a iaoaiaoeea, oiiiaeaiea naiaeeony e
iia?aoeeyi neiaeaiey e naeaeaa. Aeaeaiea auiieiyaony ca n/ao
eiiaeie?iaaiey naeaeaia, au/eoaiee (a yoio iiiaio iiaoo
eniieueciaaoueny ia?aoiue eee aeiiieieoaeueiue eiaeu) e neiaeaiee.

1.5. Eiaee?iaaiea /enae a YAI

A YAI i?eiaiyaony /aua anaai iaeia ec aeaoo oi?i i?aaenoaaeaiey /enae:

n oeene?iaaiiie caiyoie;

n ieaaathuae caiyoie.

*enea i?aaenoaaeythony a iaoeiiii neiaa, eiathuai aeey eiie?aoiie YAI
anaaaea oeene?iaaiiia /enei ?ac?yaeia (aeoia). Yoi /enei yaeyaony
iaeiie ec aaaeiaeoeo oa?aeoa?enoee ethaie YAI e iacuaaaony
?ac?yaeiinoueth iaoeiu. ?aciua ?ac?yaeu neiaa i?e eiaee?iaaiee eiiaiae e
aeaiiuo eiatho ianiaiaaeathuea ooieoeeiiaeueiua iacia/aiey. I?e
?anniio?aiee eo ooieoeee eniieuecotho oaeaea oa?iei “?ac?yaeiay naoea
iaoeiu”.

1.5.1. *enea n oeene?iaaiiie caiyoie

A /eneao n oeene?iaaiiie caiyoie iieiaeaiea caiyoie a ?ac?yaeiie naoea
iaoeiu ca?aiaa iaoneiaeaii aeey anao /enae ?ac e iaanaaaea. Iiyoiio
a eiaea /enea caiyoay ieeae ia iaicia/aaony. A aieueoeinoaa iaoei ianoi
caiyoie iiae?acoiaaaaony iinea iineaaeiae oeeo?u (ni?aaa io iaa). A
oaeea /enea – oeaeua. I?e iaiaoiaeeiinoe i?aaenoaaeyoue ae?iaiua /enea n
eniieueciaaieai oi?iu n oeene?iaaiiie caiyoie i?ia?aiieno aeieaeai
aeai?eoie/aneeie n?aaenoaaie iaania/eoue eniieueciaaiea iiiaeeoaey,
auiieiythuaai ooieoeeth ianooaae?iaaiey (ianooaaiiai iiiaeeoaey).

Ii?aaeaeei aeeaiacii i?aaenoaaeiuo /enae.

Aia/aea ?anniio?ei i?eia?, a eioi?ii iieiaeei, /oi iu eiaai aeaei n
aeanyoe/iie (a ia aeaie/iie) nenoaiie n/eneaiey, e /oi aeey caiene
aaniethoiie aaee/eiu /enea (aac o/aoa aai ciaea) a iaoai ?anii?yaeaiee
eiaaony oanoue ?ac?yaeia.

Oiaaea iaeneiaeueiia (ii aaniethoiie aaee/eia) oeaeia aoaeao ?aaii
999999 eee eia/a 10**6-1. A iineieueeo a ?ac?yaeiie naoea iaoeiu aeey
caiene ciaea /enea anaaaea i?aaeoniao?eaaaony iaeei ?ac?yae, oi aeey
iaoaai neo/ay aeeaiacii i?aaenoaaeiuo /enae ninoaaeo ana oeaeua
/enea, ia/eiay io

-999999 aei +999999, a eiee/anoai ?acee/iuo oeaeuo – 2*10**6-1.

A aeaie/iuo YAI eo ?ac?yaeiinoue ii?aaeaeyaony /eneii ?ac?yaeia a
neiaa. Oae, anee ?ac?yaeiinoue iaeioi?ie YAI ?aaia 16, oi iaeei
?ac?yae ioaiaeeony aeey eiaee?iaaiey ciaea /enea, a inoaeueiua 15 –
aeey caiene aai aaee/eiu. I?e yoii iaeneiaeueiia ii iiaeoeth oeaeia
cia/aiea a iaoeiiii neiaa aoaeao ?aaii 2**15-1, /oi ninoaaeo 32767.
(Iiniio?eoa aeeaiacii oeaeuo (integer) /enae a ycuea i?ia?aiie?iaaiey
Ianeaeue aeey IYAI oeia IMB PC).

A iauai neo/aa, anee ?ac?yaeiinoue iaoeiu ninoaaeyao N aeoia. Oiaaea
iaeneiaeueiia ii aaniethoiie aaee/eia oeaeia /enei, eioi?ia iiaeii a
iae caienaoue, aoaeao ?aaii 2**(N-1)-1.

Iniaaiiinoe a?eoiaoe/aneeo iia?aoeee iaae /eneaie

Iineieueeo (anee iieiaeaiea caiyoie oeene?iaaii iinea iineaaeiae oeeo?u
/enea) /enea n oeene?iaaiiie caiyoie – oeaeua, iie i?aaenoaaeythony
a iaoeia oi/ii. A iioiio iia?aoeee neiaeaiey, au/eoaiey e oiiiaeaiey
ei??aeoiu anaaaea: eae iia?aiaeu, oae e ?acoeueoao – oeaeua /enea.

Aaeeinoaaiiie iniaaiiinoueth, i eioi?ie iaiaoiaeeii oiiiyiooue, yaeyaony
neooaoeey, eioi?ay iineo iacaaiea “ia?aiieiaiea ?ac?yaeiie naoee”
(FixedOverflow – ia?aiieiaiea n oeene?iaaiiie caiyoie) e eioi?ay
aicieeaao, eiaaea ?acoeueoao oiiiaeaiey i?aauoaao iaeneiaeueii
aiciiaeiia aeey aeaiiie ?ac?yaeiinoe cia/aiea. Yoa neooaoeey n/eoaaony a
YAI eneeth/eoaeueiie. I?e aa aicieeiiaaiee caienaoue iieo/eaoaany
cia/aiea iaaiciiaeii. A yoii neo/aa onoaiaaeeaaaony a “1” niaoeeaeueiue
oeaa ia?aiieiaiey, noa?oee aeo ?acoeueoaoa (aeo ia?aiina ec noa?oaai
?ac?yaea neiaa) oa?yaony, a a ea/anoaa ?acoeueoaoa auaeaaony
eneaaeaiiia /enei. Iienuaaaiay neooaoeey ia n/eoaaony e?eoe/aneie, e
iinea ieii/aiey aeaiiie iia?aoeee au/eneaiey i?iaeieaeathony. Oaeei
ia?acii, i?ia?aiieno nai aeieaeai iicaaioeoueny i ei??aeoiie ?aaeoeee ia
aicieeiiaaiea ia?aiieiaiey, eniieuecoy aeey iaia?oaeaiey oeacaiiie
neooaoeee niaea?aeeiia oeaaa ia?aiieiaiey.

Eia/a ianoieo aeaei n iia?aoeeae aeaeaiey. I?e aeaeaiee oeaeiai /enea
ia ae?oaia oeaeia ?acoeueoao nianai ia iaycaoaeueii aeieaeai auoue
oeaeui. A iineieueeo e ?acoeueoao aeieaeai auoue i?aaenoaaeai oeaeui
/eneii, aicieeaao eieeecey, eioi?oth i?ieeethno?e?oai i?eia?ii:

5 / 2 = 2

5 / 3 = 1

5 / 4 = 1

5 / 5 = 1

5 / 6 = 0

E a ioee/ea io oiiiaeaiey, n iiceoeee YAI ieeaeeo ioeaie i?e yoii iao,
e ieeaeea oeaae ia onoaiaaeeaathony, a oeacaiiua iniaaiiinoe aeaeaiey
oeaeuo aeieaeiu o/eouaaoueny i?ia?aiienoii naiinoiyoaeueii. A ?yaea
ycueia i?ia?aiie?iaaiey yoe iniaaiiinoe io?aaeathony iaai?ii aeiionoeiuo
a?eoiaoe/aneeo iia?aoeee. Oae, iai?eia?, a ycuea Ianeaeue aeey oeaeuo
(integer) ii?aaeaeaiu aeaa iia?aoeee:

div – oeaei/eneaiiia aeaeaiea, i?e eioi?ii a ea/anoaa
?acoeueoaoa i?aaenoaaeyaony oeaeay /anoue /anoiiai,

mod – inoaoie io aeaeaiey oeaeuo (aeaeaiea ii iiaeoeth), i?e
eioi?ii a ea/anoaa ?acoeueoaoa i?aaenoaaeyaony oeaeue inoaoie io
aeaeaiey, ii aaniethoiie aaee/eia iaiueoee aeaeeoaey.

I?eia?u:

5 div 3 = 1

5 mod 3 = 2

1.5.2. *enea n ieaaathuae caiyoie

A oi?ia n ieaaathuae caiyoie /enei i?aaenoaaeyaony aeaoiy eiiiiiaioaie :
iaioennie e ii?yaeeii. Iaioenna eniieuecoaony aeey caiene oeeo?
/enea, a ii?yaeie – aeey oeacaiey iieiaeaiey caiyoie.

?ac?yaeiay naoea iaoeiu a yoii neo/aa aeaeeony ia ianeieueei /anoae:

iaeei ?ac?yae – aeey eiaee?iaaiey ciaea /enea (yoi anaaaea naiue
noa?oee, eaaue, ?ac?yae neiaa);

M ?ac?yaeia – aeey caiene iaioennu;

? ?ac?yaeia – aeey caiene ii?yaeea (n o/aoii aai ciaea).

Ianoiiieiaeaiea caiyoie i?e yoii oiaea no?iai oeene?oaony: n/eoaaony,
/oi iaioenna anaaaea i?aaenoaaeyaony eae /enei, iaiueoaa aaeeieoeu, ii
oaeia, a eioi?ii ia?aay oeeo?a iinea caiyoie aeey anao aaniethoii /enae
ioee/ia io ioey (aaeeinoaaiiia eneeth/aiea ninoaaeyao /enei 0). Oaeay
oi?ia i?aaenoaaeaiey iaioennu iacuaaaony ii?iaeeciaaiiie. Eia/a
aiai?yo, /oi iaioenna ii?iaeeciaaia (i?eaaaeaia e aeaeo: 1 < M <= 0,1).Io, a anee ecaanoii, /oi iaioenna eiaao aeae “0,oeoeoeoe..”, oi aa eiae a iaoeiiii neiaa iiaeao ia niaea?aeaoue neiaieia “0,”, a ianoiiieiaeaiea caiyoie i?aaeiieaaaaony ia?aae noa?oae cia/auae oeeo?ie iaioennu.Ii?yaeie ? anaaaea i?aaenoaaeyaony oeaeui /eneii ni ciaeii + eee -. A aeey eiaee?iaaiey aaniethoiie aaee/eiu ii?yaeea inoaaony (?-1) oeeo?.Oaia?ue iiaeii ?anniio?aoue aeeaiacii i?aaenoaaeiuo /enae.Aia/aea ?anniio?ei i?eia? i?eiaieoaeueii e aeaie/iie nenoaia n/eneaiey.Ionoue m - eiee/anoai ?ac?yaeia iaioennu,? - eiee/anoai ?ac?yaeia ii?yaeea, aeeth/ay ciaeiaue.Oiaaea iaeneiaeueiia ii aaniethoiie aaee/eia /enei aoaeao ?aaii0,1111..1 * 2**(+111..1) = (1-2**(-i))*2**(2**(?-1)-1),m oeeo? (p-1) oeeo?eee i?eaeeceoaeueii 2**(2**(?-1)-1),a ieieiaeueiia ii aaniethoiie aaee/eia /enei0,1000..0 * 2**(-111..1) = 2**(-2**(?-1)).m oeeo? (p-1) oeeo?Eoae, /enei a oi?ia n ieaaathuae caiyoie i?aaenoaaeyaony iineaaeiaaoaeueiinoueth aeoia aac eaeeo eeai yaii oeacaiiuo ?acaeaeeoaeae, ii ooieoeeiiaeueii ?acaeoie ia o?e a?oiiu {(ciae /enea, iaioenna /enea, ii?yaeie /enea) eee (ciae /enea, ii?yaeie /enea, iaioenna /enea)}.?anniio?aiiay oi?ia eiaee?iaaiey /enea i?eaiaeeo e neaaeothuei iineaaenoaeyi:Aeeaiacii /enae, i?aaenoaaeiuo a oi?ia n ieaaathuae caiyoie, ii?aaeaeyaony aeaaiui ia?acii ?ac?yaeiinoueth ii?yaeea (?).?ac?yaeiinoue iaioennu (I) ii?aaeaeyao oi/iia eiee/anoai cia/aueo oeeo? a ecia?aaeaiee /enea.Neaaeiaaoaeueii, aieueoeinoai /enae a oi?ia n ieaaathuae caiyoie i?aaenoaaeyaony i?eaeeaeaiii e i?e/eiie yoiai yaeyaony ia?aie/aiiia /enei ?ac?yaeia iaioennu. Aaee/eia aea aaniethoiie iia?aoiinoe i?e i?eaeeaeaiiii i?aaenoaaeaiee /enea caaeneo eae io aaniethoiie aaee/eiu /enea, oae e io ?ac?yaeiinoe iaioennu e ii?yaeea.?anniio?ei i?eia?u. I?e yoii aeey i?inoiou iieiaeei, /oi /enea i?aaenoaaeythony a aeanyoe/iie nenoaia n/eneaiey, eiee/anoai oeeo? iaioennu ?aaii 4, eiee/anoai oeeo? ii?yaeea - 2, ciae ii?yaeea caienuaaaony eae a iaoaiaoeea, a ciae /enea iu ia ecia?aaeaai, iieaaay ana /enea iieiaeeoaeueiuie.I?eia? 1. Ionoue eiaaony /enei 12,42=0,1242*10**(+2).A caaeaiiii oi?iaoa iii i?aaenoaaeyaony oeaii/eie neiaieia1 2 4 2 + 0 2I?e yoiioeaii/ea “1 2 4 2” i?aaenoaaeyao iaioenno, o.a. a iaoaiaoe/aneii niunea /enei 0,1242 ,a oeaii/ea “+ 0 2” - ii?yaeie - oeaeia iieiaeeoaeueiia /enei 2.Oiaaea aeeaeaeoaa aieueoaa yoiai /enei iiaeao auoue caaeaii oeaii/eie1 2 4 3 + 0 2e iii ?aaii 0,1243*10**(+2)= 12,43.Oaeei ia?acii, aeeaeaeoea /enea ia /eneiaie ine, eioi?ua ?acee/eiu i?e eiaee?iaaiee eo a oi?ia n ieaaathuae caiyoie aeey aeaiiiai i?eia?a ?acee/athony ia 0,01 (aaniethoiay iia?aoiinoue i?aaenoaaeaiey anao /enae iaaeaeo 12,42 e 12,43 eiaao aa?oithth ioeaieo 0,01).I?eia? 2. Ionoue eiaaony /enei 0,001242=0,1242*10**(-2).A caaeaiiii oi?iaoa iii i?aaenoaaeyaony oeaii/eie neiaieia1 2 4 2 - 0 2,a aeeaeaeoaa aieueoaa yoiai /enei i?aaenoaaeyaony oeaii/eie1 2 4 3 - 0 2e ?aaii 0,1243*10**(-2)= 0,001243.Oaeei ia?acii, aaniethoiay iia?aoiinoue i?aaenoaaeaiey anao /enae iaaeaeo 0,001242 e 0,001243 eiaao aa?oithth ioeaieo 0,000001.I?eia? 3. Ionoue eiaaony /enei 0,1242*10**(+12).A anoanoaaiiie oi?ia caiene yoi /enei 124 200 000 000, a a caaeaiiii oi?iaoa iii i?aaenoaaeyaony oeaii/eie neiaieia1 2 4 2 + 1 2,a aeeaeaeoaa aieueoaa yoiai /enei i?aaenoaaeyaony oeaii/eie1 2 4 3 + 1 2e ?aaii 0,1243*10**(+12)= 124 300 000 000.Oaeei ia?acii, aaniethoiay iia?aoiinoue i?aaenoaaeaiey anao /enae iaaeaeo 124 200 000 000 e 124 300 000 000 eiaao aa?oithth ioeaieo 100 000 000 = 10**8.Ia?aoeoa aieiaiea, /oi a iineaaeiai i?eia?a iaaiciiaeii caienaoue ie iaeiiai /enea a eioa?aaea ?acia?ii 10**8.Aaaeiue auaiae, eioi?ue neaaeoao ec aiaeeca oi?iu eiaee?iaaiey /enae n ieaaathuae caiyoie e eeethno?e?oaony a ?anniio?aiiuo i?eia?ao: /enea a oi?ia n ieaaathuae caiyoie, ianiio?y ia oi /oi, yoa oi?ia i?aaeeiaeaia aeey i?aaenoaaeaiey a YAI iai?a?uaiuo aaee/ei, i?aaenoaaeythony aeene?aoiui iiiaeanoaii ia /eneiaie ine e ?aniieaaathony ia iae ia?aaiiia?ii.Anee ecia?aceoue ia (aaneiia/iie) /eneiaie ine iaeanoe nouanoaiaaiey /enae, oi iiaeii auaeaeeoue neaaeothuea iaeanoe (ni. ?en.):1 2 3 4 5 6RIaenAau -IeiAau 0 +IeiAau +IaenAauiaeanoue 1: O<-IaenAau - ie iaeiiai cia/aiey ec iaeanoe iaeuecy i?aaenoaaeoue a iaoeiiii neiaa (IaenAau - iaeneiaeueiia ii aaniethoiie aaee/eia /enei, eioi?ia iiaeii caeiaee?iaaoue);iaeanoue 2: -IaenAau<=X<=-IeiAau - a aeaiiii eioa?aaea iiaeao auoue i?aaenoaaeaii noieueei ?acee/iuo /enae, neieueei eo iiaeii caienaoue ii caaeaiiie ?ac?yaeiinoe iaioennu e ii?yaeea;iaeanoue 3: -IeiAau=X>=+IaenAau – a aeaiiii eioa?aaea iiaeao auoue
i?aaenoaaeaii noieueei ?acee/iuo /enae, neieueei eo iiaeii caienaoue ii
caaeaiiie ?ac?yaeiinoe iaioennu e ii?yaeea;

iaeanoue 6: X>+IaenAau – ie iaeiiai cia/aiey ec iaeanoe iaeuecy
i?aaenoaaeoue a iaoeiiii neiaa (IaenAau – iaeneiaeueiia ii aaniethoiie
aaee/eia /enei, eioi?ia iiaeii caeiaee?iaaoue).

Iniaia ianoi caieiaao aaee/eia 0. Iia oaeaea eiaee?oaony a oi?ia n
ieaaathuae caiyoie, i?e/ai eae aa ii?yaeie, oae e iaioenna(!)
iieaaathony ?aaiuie ioeth.

Iniaaiiinoe a?eoiaoe/aneeo iia?aoeee iaae /eneaie

I?e auiieiaiee a?eoiaoe/aneeo iia?aoeee ana /aou?a aeaenoaey a?eoiaoeee
ei??aeoiu. Neaaeoao iaeiaei eiaoue a aeaeo, /oi aeene?aoiue oa?aeoa?
i?aaenoaaeaiey /enae a oi?ia n ieaaathuae caiyoie e ?acaeaiea /eneiaie
ine ia iaeanoe, a ?yaea ec eioi?uo iaaiciiaeii i?aaenoaaeoue ie iaeiiai
/enea, i?eaiaeeo:

Ai-ia?auo, e oiio, /oi i?e auiieiaiee a?eoiaoe/aneie iia?aoeee
oai?aoe/anee aiciiaeii oi?ie?iaaiea ?acoeueoaoa, eioi?ue iiiaaeaao a
iaeanoe 2 eee 5, ii eioi?ue iaeuecy caeiaee?iaaoue a oi?ia n ieaaathuae
caiyoie oi/ii. A yoii neo/aa, ?acoeueoao caiaiyaony aeeaeaeoei ec
iiiaeanoaa aeiionoeiuo cia/aiee n o/aoii i?aaeea ie?oaeaiey (ioeaea
iaoiaea i?aaenoaaeaiey /enae, aucaaiiay ia?aie/aiiie ?ac?yaeiinoueth
iaioennu).

Ai-aoi?uo, e oiio, /oi i?e auiieiaiee a?eoiaoe/aneie iia?aoeee
oai?aoe/anee aiciiaeii oi?ie?iaaiea ?acoeueoaoa, eioi?ue iiiaaeaao a
iaeanoue 1 eee a iaeanoue 6. Yoio neo/ae yaeyaony e?eoe/aneei,
iineieueeo ?acoeueoao i?aaenoaaeoue iaeuecy i?eioeeieaeueii.
?anniao?eaaaiay neooaoeey iacuaaaony “Ia?aiieiaiea n ieaaathuae
caiyoie” (Overflow), a i?e aa aicieeiiaaiee i?ienoiaeeo aiia?aoiia
i?a?uaaiea ?aaiou YAI e auiieiaiea i?ia?aiiu aaa?eeii i?ae?auaaony.
I?e/eiie yoiai yaeyaony ia?aie/aiiay ?ac?yaeiinoue ii?yaeea.

A-o?aoueeo, e oiio, /oi i?e auiieiaiee a?eoiaoe/aneie iia?aoeee
oai?aoe/anee aiciiaeii oi?ie?iaaiea ?acoeueoaoa, eioi?ue iiiaaeaao a
iaeanoue 3 eee a iaeanoue 4. ?anniao?eaaaiay neooaoeey iacuaaaony
“Iioa?y cia/eiinoe”, a i?e aa aicieeiiaaiee ?acoeueoao caiaiyaony
aeeaeaeoei aeiionoeiui, eae i?aaeei ioeai. Auiieiaiea i?ia?aiiu iinea
yoiai i?iaeieaeaaony. A iaeioi?uo YAI i?e yoie neooaoeee au?aaaouaaaony
i?aaeoi?aaeeoaeueiia (eioi?iaoeeiiiia) niiauaiea. I?e/eiie yoie
neooaoeee oaeaea yaeyaony ia?aie/aiiay ?ac?yaeiinoue ii?yaeea.

A caeeth/aiee ioiaoei, /oi i?e auiieiaiee a?eoiaoe/aneeo iia?aoeee
iaioennu /enae e eo ii?yaeee ia?aaaouaathony ii ?aciui aeai?eoiai.
I?e yoii a iia?aoeeyo neiaeaiey e au/eoaiey /enae ii?yaeee
au?aaieaathony ca n/ao naeaeaa iaioennu iaiueoaai iia?aiaea ia /enei
?ac?yaeia, ?aaiia ?acieoea ii?yaeeia iia?aiaeia, a a iia?aoeeyo
oiiiaeaiey e aeaeaiey ii?yaeee /enae niioaaonoaaiii neeaaeuaatho eee
au/eoatho. Iineieueeo, eae iu oaea aeaeaee ?aiueoa, au/eoaiea
aeaaa?ae/aneeo /enae (o.a. n o/aoii eo ciaeia) a i?yiii eiaea
?aaeeciaaoue ia i?inoi, a ii?yaeee i?aaenoaaeythony eae /enea oeaeua ni
ciaeii a i?yiii eiaea, a ?yaea YAI i?e i?aaenoaaeaiee /enea n
ieaaathuae caiyoie ii?yaeie /enea caiaiyaony aai oa?aeoa?enoeeie.

Oa?aeoa?enoeea /enea iieo/aaony ec aai ii?yaeea, anee inouanoaeoue
i?aia?aciaaiea eii?aeeiao: Cia/aiea 0 ia ine, ecia?aaeathuae
oa?aeoa?enoeeo, niaiaaeaao n cia/aieai -IaenIi?yaeie:

Ii?yaeie:

IaenIi?yaeie 0
+IaenIi?yaeie

Oa?aeoa?enoeea:

0
IaenOa?aeo.

I?e yoii oa?aeoa?enoeea /enea ?anniao?eaaaony oieueei eae
iieiaeeoaeueiia /enei, a neaaeiaaoaeueii, a iai ia iaaei e eiaee?iaaoue
ciae. I?eciaeii aea oiai, eaeie ciae eiaao ii?yaeie iaeioi?iai
/enea, yaeyaony niaea?aeeiia noa?oaai ?ac?yaea oa?aeoa?enoeee: Anee ii
?aaai 0 – ii?yaeie io?eoeaoaeueiue, a i?ioeaiii neo/aa – ii?yaeie
iieiaeeoaeueiue. A neo/aa caiene oa?aeoa?enoeee oeaii/eie oeeo?
1000..0 i?eieiaaony, /oi ii?yaeie ?aaai ioeth.

?anniio?ei aua iaeio neooaoeeth, oeie/ioth aeey iia?aoeee iaae
/eneaie a oi?ia n ieaaathuae caiyoie.

Ionoue iaiaoiaeeii au/eneeoue ?acieoeo /enae

X=13,45 e Y=13,45*10**(-5) ,

i?e oneiaee, /oi iie i?aaenoaaeaiu a oi?ia n ieaaathuae caiyoie i?e
?ac?yaeiinoe iaioennu, ?aaiie 4, e ii?yaeea, ?aaiie 2. Aeey i?inoiou
iia?aoeeth i?ieeethno?e?oai ia i?eia?a aeanyoe/iie nenoaiu n/eneaiey.

Caieoai /enea O e Y a oi?ia n ieaaathuae caiyoie:

X: 1 3 4 5 + 0 2

Y: 1 3 4 5 – 0 3

Eae aeaeii ec yoie caiene, iaa /enea i?aaenoaaeaiu a oi?ia n ieaaathuae
caiyoie aac eneaaeaiey. Ia aini?iecaiaey eiaeeo au/eoaiey, i?eiyooth a
YAI, auiieiei au/eoaiea a noieaee. Aeey yoiai i?aaenoaaei iaa iia?aiaea
a anoanoaaiiie oi?ia e oae, /oiau niioaaonoaothuea ?ac?yaeu iia?aiaeia
iaoiaeeeenue ae?oa iiae ae?oaii :

X: 1 3 , 4 5

Y: 0 , 0 0 1 3 4 5

=============

X-Y: 1 3 , 4 4 8 6 5 5

Ie?oaeei ?acoeueoao, o/eouaay, /oi a iaoai ?anii?yaeaiee aeey caiene
oeeo? /enea eiaaony anaai 4 ?ac?yaea, e caieoai aai aiiaue a oi?ia n
ieaaathuae caiyoie, a caaeaiiie ?ac?yaeiie naoea:

X-Y: 1 3 4 5 + 0 0

N?aaiea ?acoeueoao n enoiaeiuie iia?aiaeaie oaeaeei, /oi oioy iaa
iia?aiaea auee ioee/iu io ioey, ?acoeueoao e oiaiueoaaiia iieiinoueth
niaiaaeatho!

Auaiae. I?e au/eoaiee aeaoo /enae aieueoia cia/aiea eiatho niioiioaiea
eo aaee/ei e ?ac?yaeiinoue iaioenn, eniieuecoaiay aeey eo eiaee?iaaiey.
Oae /oi i?ia?aiienou iiaoo noieeiooueny n iaaeaeaoaeueiuie
iineaaenoaeyie auiieiaiey oeacaiiuo aeaenoaee a iaeioi?uo e?eoe/aneeo
ianoao aeai?eoia. Iai?eia?, anee iiaeiaiia au/eoaiea auiieiyaony a
oneiaee i?ae?auaiey oeeeea, eiathuai aeae “(X-Y)>0.01”, oi
aeaiiia oneiaea iiaeao ieeiaaea ia auiieieoueny, o.a. i?iecieaeao oae
iacuaaaiia caoeeeeeaaiea.

Aeiiieieoaeueiay eeoa?aoo?a ii iaoa?eaeo ?acaeaea.

1. Naaaeueaa A.ss. I?eeeaaeiay oai?ey oeeo?iauo aaoiiaoia. O/aaiee
aeey aoocia. I.: 1989.

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