Данные и информация

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« «Y?ae??:

1. ?®¬?iiaYp?§ ae?i ®!eYaac .

2. ?aYp?pYa ae?i ¤ ea.

3. ”®p¬ ?pY¤aa c«Y?i ¤ ea.

4. •p Y?Y, ?®¤?p®c ?Y ? ?pY®!p §®c ?Y ?ae®p¬ ae??.

5. ?«icYceY a«®c .

6. ?®ap®«ieY c®?p®ae ? ?pY¤«®¦Y?i.

1. ?®¬?iiaYp?§ ae?i ®!eYaac .

…¤?aac® § ?®®c ®!p !®a?? ?ae®p¬ ae?? c a?aaY¬ a p §«?c®© ?p?p®¤e
(ae?§?cYa??a, i?®®¬?cYa??a, !?®«®F?cYa??a ? a.?.) ic«iYaai aea¤ ¬Ya «i®©
®a®c®© aY®p?? ?ae®p¬ ae?®ea ?p®aeYaa®c, ®?pY¤Y«iieY© YY ®!eY§ c?¬®aai ?
a?Yae?ae?c®aai. ?!eY?a®¬ ?§acY?i ia®© aY®p?? ic«iYaai ?ae®p¬ ae?i –
?®ia?Y c® ¬®F®¬ !aap ?a®Y, aaeYaacaieYY “a ¬® ?® aY!Y” cY aci§? a
?®?pYa®© ®!« aaii § ?i, c ?®a®p®© ® ?a?®«i§aYaai.

a® ®!aa®iaY«iaac® ?« ¤ec Ya ®?pY¤Y«Ye© ®a?Yc a®? cai ?ae®p¬ a??a ? ?
a?a ®! ®pF ?§ ae?? ?®¬?iiaYpea ?ae®p¬ ae?®ea a?aaY¬, – a ??Y a?aaY¬e
¬®Faa ?a?®«i§®c aiai c a ¬ea p §ea ?pY¤¬Yaea ®!« aaia, ?p?c®ai c ?a
“ac®? ?p c?« ?Fpe”, ac®? § ?®®¬Yp®aa?, ®Fp ?cY?i ¬ c¬YaaY a aY¬ ®ceY
c®§¬®¦®aa? ®pF ?§ ae?? !?§Ya , ?®a®peY !e«? !e Y¬ea«?¬e !Y§ ?ae®p¬ a???
? aci§ ®F® a Y© ?®¬?iiaYp . ‚ ia®¬ ?« Y Yc®§¬®¦® ?YpY®aeY?ai a ??Y
ac®©aac ?ae®p¬ ae?? ? ? ¤®aaa?®aai, ac®YcpY¬Y®aai ?®«acY?i,
?®¬¬YpcYa? i aeY®aai, ¤Y¦®aai.

?ae®p¬ ae?®eY pYaapae c a®cpY¬Y®¬ ®!eYaacY ?Fp ia Y ¬Yieai, YpY¤?® ?
!®«ieai p®«i, cY¬ pYaapae ¬ aYp? «ieY. ‡ ?i, ?®¬a, ?®F¤ ? F¤Y ?p®¤ ai
a®c p, ¬®¦Ya aeY?aiai Y ¬YieY, cY¬ a®!aacY® a®c p,- ? c ia®¬ ?« Y
¤? ¬?? p §c?a?i ®!eYaac ac?¤YaY«iaacaYa ® a®¬, ca® “cYa a”
¬ aYp? «iea ? ?ae®p¬ ae?®ea pYaapa®c ?®a«Y¤?Y c? ia ?pYc «?p®c ai,
?p?cY¬ aY¬ a?«iYY, cY¬ !®«YY ®!eYaac® ®a?pea®, cY¬ !®«YY p §c?ae c Y¬
apY¤aac ?®¬¬a?? ae??, cY¬ !®«ieY© ?ae®p¬ ae?Y© ®® p a?®« F Ya.

‘ ?®§?ae?© pe? ?ae®p¬ ae?i ¤ c® a¦Y aa « a®c p®¬ ? ia® ®!aa®iaY«iaac®
apY!aYa ?aYa?c®F® p §c?a?i ?p ?a???, ?p®¬ee«Y®aa? ? aY®p??
?®¬?iiaYp?§ ae?? ®!eYaac . ?®¬?iiaYp ? ? ?ae®p¬ ae?® i apY¤ Y a®«i?®
?®§c®«?« a®cYpe?ai ? cYaacYe© a? cY? c ®pF ?§ ae?? ?p®¬ee«Y®aa?, a?? ?
pe? , ® ® ®?pY¤Y«?« ®ceY a ¬®aeYeY ®!« aa? ?p®?§c®¤aac : cec?a«?aY«i i
aYa?? , aY«Y?®¬¬a?? ae??, ?p®Fp ¬¬eY ?p®¤a?ae.

‚? – ?pY¤aa c?aY«Y© a ¬ea p §ea ®!« aaY© § ?©, Y ic«iie?aai
a?Yae? «?aa ¬? ?® ?®¬?iiaYp ¬ c a§?®¬ a¬ea«Y, ® a¬Yie?a ?a?®«i§®c ai ?a
¤«i pYeY?i ac®?a a?Yae?ae?cYa??a § ¤ c.

‚? (?«? ?®Yce© ?®«i§®c aY«i) ¤®«¦Y § ai ®!e?Y ?p?ae??e ®pF ?§ ae??
?ae®p¬ ae?®ea ?p®aeYaa®c c ?®¬?iiaYp®© apY¤Y, a¬Yai ce!p ai a¦eY Y¬a
?ae®p¬ ae?®eY a?aaY¬e ? aYa?cYa??Y apY¤aac ? !eaap® ®ac®?ai ?a
?p?¬Y?aY«i® ? ac®Y© ?pY¤¬Ya®© ®!« aa?. “c?aec i ?aYa?c®Y p §c?a?Y
cec?a«?aY«i®© aYa??? ? c® ¬®F®¬ aeeY®aai pe? ?p®Fp ¬¬ea ?p®¤a?a®c, ¤c
?®a«Y¤?a ? cYaac ?p?®!pYa ia ®a®!®Y § cY?Y.

Y aaeYaacaYa aap®F® ®cYpcYea p ¬®?, ®?pY¤Y«iie?a ia® ?®ia?Y, – ? ¦¤e©
?®«i§®c aY«i ®?pY¤Y«iYa ?a ¤«i aY!i a ¬, ® c¬YaaY a aY¬ ®aaaaaac?Y a ?®©
Fp ¬®a®aa? ¤Y« Ya aYF®¤i Yc®§¬®¦e¬ ¤®aaa? ?® ¬®F?¬ a§?® a?Yae? «ie¬
?p®aeYaa?i¬, ?Ypce© c§F«i¤ cYai¬ ¤ «Y??¬ ®a ?®¬?iiaYp .

2. ?aYp?pYa ae?i ¤ ea

a ¬®¬ ¤Y«Y, ? ? ce ®aYaYaYai, ?p?¬Yp, ? a«Y¤aie?¬ ¤ e¬:

(1) – “ap?¤ae ai aY¬i a ?®«®c?®©”;

(2) – “2 + 2 = 4″;

Yap®c aa « ¤?pY?a®p®¬”.

Yap®c? ‚® caYa ?p?cY¤Yea ?p?¬Yp a ¤ eY Y?ae®p¬ a?ce (a®ai ?® p §e¬
?p?c? ¬), ? ¤«i a®F®, ca®!e ?p?¤ ai ?¬ ?ae®p¬ a?c®aai, a.Y. ?pYcp a?ai
?a c ?ae®p¬ ae?i, Y®!a®¤?¬® ®aaeYaac?ai ?aYp?pYa ae?i ¤ ea.

p®aeYaa ?aYp?pYa ae?? ¬®¦Ya ®aaeYaac«iaiai cY«®cY?®¬ ?«? Fpa??®© «?ae,
?p? ia®¬ ® ¬®¦Ya !eai ac®pcYa??¬ ( ?p?¬Yp, ¬a§?ae?p®c ?Y ?® ®a®© § ??a?)
?«? ae®p¬ «ie¬ (®?pY¤Y«Y?Y cpY¬Y? ?® c a ¬). ’ ?®© ?p®aeYaa ¬®¦Ya
®aaeYaac«iaiai !?®«®F?cYa??¬? ®!eY?a ¬? (aa«®ceY pYae«Y?ae a®! ?, ®!eY?Y
¤Y«iae?®c), ¬®F?¬? aaap®©aac ¬? aYa?cYa?®© ca®¬ a??? (®! pa¦Y?Y a?F «
®a aeY«? c p ¤?®«®? ae?? a ?®a«Y¤aie?¬? ¤Y©aac?i¬?) ?, ?®Yc®,
?®¬?iiaYp®¬.

?p?¬Yp, ae®p¬ «i® p §«?ceY a®®!eY?i “¤® § cap ” ? “see you tomorrow”
[1] Yaaa ®¤a ? aa ¦Y ?ae®p¬ ae?i. P §eY § ?? “x” ? “*” ¬®Faa
a®¤Yp¦ aY«i® ®!®§ c ai ®¤® ? a® ¦Y – ®?Yp ae?i a¬®¦Y?i, ae®p¬ «i®
p §«?ceY aap®?? “21” ? “XXI” ®?pY¤Y«iia ®¤® ? a® ¦Y c?a«® (c p §«?cea
a?aaY¬ a ac?a«Y?i).

¤®a?Y ®!eic«Y?© ?® p §¬Ya ?c pa?p i ac?¤Y« ®!eic«Y?Y a® a«Y¤aie?¬?
¤ e¬?: “(2+2)=(3+1)”, ca® ®§ c «® “?Yii ¤cY ¤caa?®¬ aea apYa?®¬ aai ?
®¤®?®¬ aai”,- ¬®¦® «? !e«® !e ?pY¤?®«®¦?ai a ?ai ?aYp?pYa ae?i ia?a
¤ ea, ?p?¬Yp, c acY!??Y ?® p?ae¬Ya??Y?

p?cY¤YeY ?p?¬Ype «iaYp a?c®© ?aYp?pYa ae?? ®¤?a ? aYa ¦Y ¤ ea
?««iaap?paia ?®ia?Y ?®«?¬®pae?§¬ (¬®¦YaacY®© ?aYp?pYa ae??), ?®a®p®Y c
?®Yc®¬ acYaY ? ®?pY¤Y«iYa !aap ?ae© a p ?aYp ia®F® ?p®aeYaa .

®aYpi ?«? ?a? ¦Y?Y ?®a«Y¤Y© «YF?® c®aaa c«?c Yaai ?® ?®aY?aaa, ?®aYpi
§ ?ia®© ac®¤?a ?ae®p¬ a?c®aai a®®!eY?i c aeY«®¬ ? a«i. …eY ®¤? ?p?¬Yp.
„®?aaa?¬, ce p a?®« F YaY a«Y¤aie?¬ aep F¬Ya®¬ a !«?aee:

UAeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAAe
AeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAeAe?

? ’®c p ? ‘a ®? ? „pY«i ? ”pY§ ? „c?F aY«i ?

AAeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAAe
AeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAeAe?

? ‘a®?¬®aai ? 757,7 ? 123 ? 78,5 ? 356 ?

AAeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAAe
AeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAeAeU

P?a.1.1

®aYpi a«®c “‘a®?¬®aai” c® ca®p®© aap®?Y ¤Y« Ya Yc®§¬®¦®© ?p c?«iai
?aYp?pYa ae?i c?a«®c®F® ¬ aYp? « caY© a !«?aee, c a® cpY¬i ? ? ?®aYpi
a«®c “’®c p” «YF?® c®aaa c«?c Yaai ?® ?®aY?aaa.

’ ??¬ ®!p §®¬, ¤ eY – ia® !®p Y®¤®p®¤ea ?«icYcea a«®c (?®§?ae?©, § ?®c
? a.?.), Yaae?a ?ae®p¬ ae?i p §®© aaY?Y? aeY®aa?.

3. ”®p¬ ?pY¤aa c«Y?i ¤ ea.

?a®ceY c?¤e c®a?p?ia?i ¤ ea cY«®cY?®¬ aci§ e a ?a?®«i§®c ?Y¬ §p?aY«iea
®!p §®c, a.Y. ®!p §®c, c®a?p??¬ Y¬ea a ?®¬®eii §pY?i. ‚aY c®§p aa ieYY
§ cY?Y ?¬YYa ?a?®«i§®c ?Y §ca?®cea ? a ?a?«iea ®!p §®c (c®a?p??¬ Y¬ea
®ai§ ?Y¬). ?!®i?Y ? c?aa c ia®¬ pi¤a aa®ia ?®a«Y¤Y¬ ¬YaaY.

‡p?aY«ieY ®!p §e aaeYaacaia c ¤caa ®a®cea ae®p¬ a: a?¬c®«i®© ?
Fp ae?cYa?®©. P §a¬YYaai, ? ¦¤ i ?§ ?a ¬®¦Ya ?a?®«i§®c ai aecYa.

‘?¬c®«i i ae®p¬ ?pY¤aa c«Y?i ¤ ea ¬®¦Ya !eai ®?pY¤Y«Y ? ? Y?®a®pe©
?®Yce© !®p ?§®!p ¦ ie?a § ?®c. ’ ?®© !®p «YF?® ?pY¤aa c?ai aY!Y ? ?
a®c®?a?®aai ie??®c, ? ¦¤®¬ ?§ ?®a®pea ?§®!p ¦Y a®®acYaaacaie?© § ? ? c
?®a®p®¬ «Y¦?a ¬®¦Yaac® ae?eY? – ?®??© ia®F® § ? . ’Yp¬? “?®Yce© !®p”
®§ c Ya §¤Yai ?®Yc®Y c?a«® ie??®c,- !®p ae?eY? c ie??Y Y ®Fp ?cY.

?®aapa?p®c ?Y §p?aY«i®F® ®!p § c a?¬c®«i®© ae®p¬Y ®aaeYaac«iYaai ?aaY¬
p §¬YeY?i ae?eY? c ®?pY¤Y«Y®© ?«®a?®© ?«Ya®c®© aapa?aapY, – aap®?Y,
aa®«!aeY, ?«Ya®c®¬ ?®«Y, ?p®aac®p¤Y, ?Fp®c®¬ ?®«Y ? a.?. ‚ ? ¦¤®© ?«Ya?Y
a ?®© aapa?aape ¬®¦Ya !eai p §¬YeY a®«i?® ®¤ ae?e? !®p .
P §®c?¤®aaii a ?®F® ?«Ya®c®F® ?®«i ic«iYaai ? i?p ?®¬?iiaYp ,
p !®a ieYF® c pY¦?¬Y cc®¤ a?¬c®«iea ¤ ea.

‘?¬c®«i i ae®p¬ ?¬YYa ¬®¦Yaac® p §®c?¤®aaY©, apY¤? ?a ?!®«YY
p a?p®aap Ye i§e?®c i ? a !«?c i (?aYc¤®Fp ae?cYa? i).

?§e?®c i ae®p¬ ®!ec® aci§ec Yaai a ?®ia?Y¬ «ae c?a ? ? a?®pi¤®cY®F®
!®p ?§®!p ¦ ie?a § ?®c, ®a®cY ?®a®p®F® ?®aapa?paiaai aep §e i§e?
?aaY¬ p §¬YeY?i ?§®!p ¦ ie?a ae?eY? c aapa?aapY aap®?? ?«? aa®«!ae . ‚
®¤?a i§e? a aap®? § ?®«iYaai a«Yc ?p c®, c ¤paF?a a?p c «Yc®
(?cp?a, ?p?¬Yp), c apYai?a acYpaa c?§ (?® aa®«!aea) ? a«Yc ?p c® ?
a.¤.

®ia®¬a c® ¬®F?a a«ac ia «ae c?a pcaa¬ ap?c ia ? ? a?®?¬ ?®ia?i ” !®p
?§®!p ¦ ie?a § ?®c”, ?pY¤ ¬YpY® ®?aa? i ®a®eY?i ?®pi¤? c a ?®¬ !®pY.

‚ ia®© aci§? ®a¬Ya?¬, ca® ?®F¤ i§e?®cai ae®p¬a §ec ia aY?aa®c®©, ?p?
ia®¬ ?®ia?Y “aY?aa” c e?p®?®¬ a¬ea«Y Y apY!aYa ?? ??a ®Fp ?cY?© Y a®«i?®
!®p ?§®!p ¦ ie?a § ?®c, ® ? ?p c?« ?aYp?pYa ae?? aY?aa . ‹i! i
?ae®p¬ ae?i, ?pY¤aa c«Y i c a?¬c®«i®© ae®p¬Y ¬®¦Ya p aa¬ ap?c aiai ? ?
aY?aa.

P §a¬YYaai, p §eY i§e?? ¬®Faa ?¬Yai a®cYpeY® p §eY «ae c?ae, ?p?cY¬
«ae c?a i§e? ¬®¦Ya p ae?piaiai ?aaY¬ ccY¤Y?i c YF® ®cea ?§®!p ¦ ie?a
§ ?®c, ?aYp?pYa?paY¬ea, ?p?¬Yp, ? ? § ?? ?pY?? ?i ?«? pY «?§aie?a ®ceY
ep?aeae.

p?¬Yp®c ie?®c ®cYi ¬®F®: ?p®¬Y YaaYaacYea i§e?®c (paaa??©, F«?©a??© ?
a.?.) ia® YeY ? i§e?? ?pY¤aa c«Y?i c?aY« ( p !a??a, p?¬a??a, ¤Yaia?cea,
¤c®?cea ? a.¤.), i§e?? ae®p¬a« ( «FY!p ?cYa??a, a?¬?cYa??a ? a.¤.), i§e?
®??a ?i e a¬ aea ? pa?©, i§e? aaY®Fp ae??, i§e?? ?p®Fp ¬¬?p®c ?i ? a.¤.

’ !«?c i ae®p¬ ¬®¦Ya p aa¬ ap?c aiai ? ? a?Yae?ae?cYa? i p §®c?¤®aai
i§e?®c®©, ?®a®p i ?®§c®«iYa ?®aapa?p®c ai p §®F® p®¤ !« ??, a !«?aee,
®acYae ? a.?. ‚ Ya?®«i?® a?p®eY®¬ c?¤Y !®p ?§®!p ¦ ie?a § ?®c ¤«i
?®aapa?p®c ?i ia®© ae®p¬e c?«ic Ya c aY!i a«Y¤aie?Y § ??:

“?”, “Ae”, “A”, “A”, “?”, “A”, “U”, “U”, “?”, “A”, “A”.

p?a 1.1. ?p?cY¤Y ?p?¬Yp ?ae®p¬ ae?®®F® ®!p § c a !«?c®© ae®p¬Y,
?®aap®Ye© a ?a?®«i§®c ?Y¬ ia®F® !®p § ?®c, i§e? ?pY¤aa c«Y?i
¤Yaia?cea c?aY« ? paaa?®F® i§e? . ?®F¤ apY¤aac ?pY¤aa c«Y?i
?ae®p¬ ae?? c a !«?c®© ae®p¬Y §ec ia i§e? ¬? a?? “§ ?®«? !« ?”.

p? ia®¬ p §pYe ieai a?®a®!®aai ae®p¬e a«Y¤aYa ?®?¬ ai ? ? c®§¬®¦®aai
?pY¤aa c«Y?i p §«?cea ¤ ea c Y¤??aeY ?§®!p ¦ ieYF® ?®«i (i?p
?®¬?iiaYp ). …a«? ?p?iai § a ?ai Y¤??aea ®¤a ?«Ya?a (a¬.ceeY), a®
p §pYe ie i a?®a®!®aai !a¤Ya ®?pY¤Y«iaiai ?®«?cYaac®¬ c®§¬®¦ea
?§®!p ¦Y?© c ia®© ?«Ya?Y. „«i a?¬c®«i®© ae®p¬e – ia® c?a«® ?§®!p ¦ ie?a
a?¬c®«®c «ae c?a , ¤«i Fp ae?cYa?®© – ia® c?a«® F®p §¤® !®«ieY.

?p?¬Yp, ¤«i cYp®-!Y«®F® ?§®!p ¦Y?i ? p §¬Yp®c ?«Ya?? 8×8 (a®cY?) c?a«®
caYa c®§¬®¦ea ?§®!p ¦Y?© c Y© ®?pY¤Y«iYaai cY«?c?®© 264.

®ia®¬a a ??Y a?Yae?ae?cYa??Y c?¤e a?¬c®«i®F® ?pY¤aa c«Y?i ¤ ea §ec ia
?aYc¤®Fp ae??®©, a®ai a ¬®¬ ¤Y«Y ?cYF® ®!eYF® a Fp ae??®© ®? Y ?¬Yia.

® ?p?¬Y?aY«i® ? Fp ae?cYa?®© ae®p¬Y ?®¬?iiaYp a a a®p®e?¬? ¤?a?«Yi¬?
(a cea®?®© p §pYe ieY© a?®a®!®aaii) aecYa®aai ®!Ya?Yc?c Ya ? cYaacY®
®ceY c®§¬®¦®aa? ®!p !®a?? Fp ae?cYa?®© ?ae®p¬ ae??, – ?p?¬Yp, a®§¤ ?Y ?
¤Y¬®aap ae?i aecYaea c?¤Y®ae?«i¬®c ?®¬?iiaYpY.

?!aa¦¤ Y¬eY ae®p¬e ?pY¤aa c«Y?i ¤ ea ?pY¤ § cYe ¤«i a®§¤ ?i
?ae®p¬ ae?®ea §p?aY«iea ®!p §®c ?«®a?®aa? ? e?p®?® ?a?®«i§aiaai c
?®¬?iiaYpY, ?®a?®«i?a i?p ¤?a?«Yi ¬®¦Ya p aa¬ ap?c aiai ? ? ?«®a? i
?®cYpa®aai. ?!eY¬eY ?§®!p ¦Y?i ?pY¤aa c«iiaai ®!ec® c ?«®a?®©
Fp ae?cYa?®© ae®p¬Y ®a®cY ?Ypa?Y?a?ce, a ?®¬®eii p §«?cea aYcY?©,
?p®Y?ae?©, ¬Ya®¤®c ?p®Y?a?c®© FY®¬Yap?? ? a.?.

?p?¬Yp, a?¬c®«ie© pY¦?¬ aci§ a ap Y?Y¬ c ? ¬ia? ?®¬?iiaYp a?¬c®«®c,
Fp ae?cYa??© – ???aY«®c (?§®!p ¦ ie?a a®cY?), ca® c ®!eY¬ a«ac Y apY!aYa
§ c?aY«i® !®«ieYF® ®!eY¬ ? ¬ia?. (’Yp¬? “pixel” ?p®?§cY¤Y ®a F«?©a?®F®
“picture element” []).

„«i a®§¤ ?i ? ?§¬YY?i a?¬c®«iea ®!p §®c (pY¤ ?a?p®c ?i) ?a?®«i§aiaai
?p®Fp ¬¬e, ?®a®peY §ec a a?¬c®«ie¬? pY¤ ?a®p ¬? (aY?aa®ce¬?
pY¤ ?a®p ¬?), Fp ae?cYa??a ®!p §®c – Fp ae?cYa??¬? pY¤ ?a®p ¬?.

p ©«i – ¤«i ?pY¤aa c«Y?i a ?a?«iea ®!p §®c, c®a?p??¬ Y¬ea ®ai§ ?Y¬.

p ©«i – ia® pY«iYae®-a®cYce© ep?aea ¤«i caY?i a«Y?ea. ‚ ®a®cY a ?®F®
ep?aea «Y¦?a ?®¬!? ae?i ?§ 6 a®cY?, ¤ ie i c®§¬®¦®aai ®!®§ c ai !a?ce,
ae?aepe, § ?? ?pY?? ?i, ¬ aY¬ a?cYa??Y, a?¬?cYa??Y ? ®aeY § ??.

4. •p Y?Y, ?®¤?p®c ?Y ? ?pY®!p §®c ?Y ¤ ea.

‚? (i«Y?ap®e¬? aaY¬ ¬?), a®aa c«iie?¬? aaY¬®aYa??a ?®¬?iiaYp , c ®a®cY
?®a®p®© «Y¦?a ?a?®«i§®c ?Y ¤c®?c®F® i«Y¬Ya ap Y?i ¤ ea. ’ ?®© i«Y¬Ya
(ap?FFYp) ?¬YYa ¤c aaa®©c?cea a®aa®i?i, aa«®c® ®!®§ c Y¬ea ? ? 1
(Y¤??ae ) ? 0 (®«i), ? a?®a®!Y ap ?ai ¬??¬ «iai ?®pae?i ?ae®p¬ ae??,
§ec Y¬ai !?a (ia®a aYp¬? ?p®?§cY¤Y ®a F«?©a?®F® “binary digit” –
¤c®?c i ae?aep ).

Ya, ‚e ®aa YaYai ?p? ac®?a § ?ia, ‚ e c®?p®a c ia®© a?aa ae?? «?!®
«?eY cai?®F® a¬ea« , «?!® ®a®a?aai ? p?a®p?cYa??¬.

®«ac i ®acYa, ‚e aaap iYaY iaa Y®?pY¤Y«Y®aai ?, a«Y¤®c aY«i®, ?®«ac YaY
?ae®p¬ ae?i. ’ ??¬ ®!p §®¬, ¤c®?ce© !®p c®§¬®¦ea ®acYa®c, Yaae?a
?ae®p¬ ae?i, ic«iYaai ¬??¬ «ie¬. ‘«Y¤®c aY«i®, ® ®?pY¤Y«iYa ¬??¬ «i®
c®§¬®¦ai ?®pae?i ?®«ac Y¬®© ?ae®p¬ ae??.

„c !?a Yaaa ?ae®p¬ ae?i, ¤®aa a®cai ¤«i aaap Y?i Y®?pY¤Y«Y®aa?,
§ ?«ic ieY©ai c ¤caa c®?p®a a ?p? ¤c®?c®© a?aaY¬Y ®acYa®c ? a.¤.

‚? c c?¤Y ?®¤®c®© ?®¬!? ae?? ?§ 8-¬? !?a, a®c®?a?®aai ?®a®pea ®!p §aYa
! ©a – ®a®c®© i«Y¬Ya ap Y?i ¤ ea c ?®¬?iiaYpY.

!®p ?p c?« ?®¤?p®c ?i ? ¤Y?®¤?p®c ?i ®?pY¤Y«iYa ?®¤®cai ae®p¬a
?pY¤aa c«Y?i ¤ ea ?«? ?p®aa® ?®¤. (P §a¬YYaai, ?p®aeYaae ?®¤?p®c ?i ?
¤Y?®¤?p®c ?i c ?®¬?iiaYpY ®aaeYaac«iiaai ca®¬ a?cYa?? !Y§ ac aa?i
?®Yc®F® ?®«i§®c aY«i).

?¤? ? aY ¦Y ¤ eY ¬®Faa !eai ?pY¤aa c«Ye c ?®¬?iiaYpY c p §«?cea ?®¤ a ?
a®®acYaaacY® ?® p §®¬a ?aYp?pYa?p®c e ?a?®«?aY«i®© a?aaY¬®© ?®¬?iiaYp .

p? ia®¬ «i!®Y ?§ a ??a ?®¤®cea ?pY¤aa c«Y?© aci§ ®

Y a®«i?® a a®!aacYe¬ c?¤®¬ ?aYp?pYa ae??, ® ? a p §«?ce¬? ?®¤®ce¬?
?®¬!? ae?i¬?, ?®¤?paie?¬? Y¤??aea.

?®¤?p®c ?Y ? ap Y?Y ¤ ea c ?®¬?iiaYpY ¤®«¦® ®!Ya?Yc?c ai Y a®«i?® ¤Y¦®Y
¤Y?®¤?p®c ?Y, ® ? § e?aa ?ae®p¬ ae?? ®a p §®F® p®¤ a!®Yc, ?®¬Ya,
c?paa®c, Ya ?ae?®?p®c ®F® ¤®aaa? ? a.?.

®¬Ya®aaa®©c?c®Y ?®¤?p®c ?Y aci§ ® ®!ec® a ccY¤Y?Y¬ c ?®¤®ceY ?®¬!? ae??
¤c®?cea a?¬c®«®c ?§!ea®c®© ?ae®p¬ ae??, Y®!a®¤?¬®© ¤«i ®! pa¦Y?i a!®Yc.

‚? – Y ?a?®«i§®c ai a®¬?aY«ieY ¤?a?Yae. …a«? ?®¬?iiaYp a¦Y “§ p ¦Y”,
a«Y¤aYa ®!p a?aiai ? “¤®?a®pa” – a?Yae? «i®© ?p®Fp ¬¬Y ®! pa¦Y?i ?
aaap Y?i c?paa®c (Y ? ¦¤e© ?§ c?paa®c aaap ?¬!). ?a®!ai ®? a®aai c?paae
?pY¤aa c«iia c ?®¬?iiaYpea aYaia,- §¤Yai !®pi! a ?¬? ?YpYp aa Ya c
®a¤Y«iai ?p®!«Y¬a.

?Ya®¤e ?pY¤®acp eY?i Ya ?ae?®?p®c ®F® ¤®aaa? ? ?®¬?iiaYp®© ?ae®p¬ ae??
?¬Yia ?pi¬®Y ®a®eY?Y ? ?p??a®Fp ae?? – a?Y ®! ®pF ?§ ae?? e?aep®c.

?Ya®¤e ?pY®!p §®c ?i ?ae®p¬ ae?? ?§ ®¤®© ae®p¬e c ¤paFai ¤Y«iaai ¤cY
!®«ie?Y ? aYF®p??: ®!p a?¬eY ? Y®!p a?¬eY.

pY®!p §®c ?i a ?®¬Ya ¬? caYF¤ aci§ e a ?ae®p¬ ae?®e¬? ?®aYpi¬?.

®-c?¤?¬®¬a, ??a ©ae .

p?¬Yp®¬ Y®!p a?¬ea ?pY®!p §®c ?© ¬®¦Ya a«a¦?ai aa a?aa?cYa??© «?§ ?, c
c aa®aa?, ?®aap®Y?Y F?aa®Fp ¬¬.

a®a «?§ ?p?c®¤?a ? ?®aap®Y?i F?aa®Fp ¬¬e, ?®a®p i ¬®¦Ya ?¬Yai
a«Y¤aie?© c?¤:

UAeAeAeAeAeAeAeAeAeAeAeAeAe?

? P®¦¤ Y¬®aai AAeAeAeAeAeAeAeAeAeAeAeAeAe?

?°°°°°°°°°°°°°? ‘¬Ypa®aai ?

?°°°°°°°°°°°°°???????????????

AAeAeAeAeAeAeAeAeAeAeAeAeAeAAeAeAeAeAeAeAeAeAeAeAeAeAeU

P §a¬YYaai c®aaa ®c?ai ?® a ?®© F?aa®Fp ¬¬Y ?ae®p¬ ae?i ¦ap « ‡??‘
Yc®§¬®¦®.

Y®!p a?¬eY ?pY®!p §®c ?i ¤ ea ®!ec® ?p®c®¤iaai ?aaY¬ ?a ®!®!eY?i ?
?aYFp?p®c ?i a aeY«ii ceic?ai, ?®¤cYp?aai ? pY«iYae® ®!®§ c?ai Y?®a®peY
®!e?Y Yic® cep ¦YeY ?«? a?peaeY § ?®®¬Yp®aa?. ‚ c aa®aa? ®a®cY
F?aa®Fp ¬¬, «®F?cea ?p?cY¤Y®© ceeY, ¬®¦® a¤Y« ai ®!e?Y
¤Y¬®Fp ae?cYa??Y cec®¤e.

5. ?«icYceY a«®c

1. ?ae®p¬ a?? .

2. ?®¬?iiaYp i Fp ¬®a®aai.

3. „®aaa?®aai, ac®YcpY¬Y®aai ?®«acY?i, aeY®aai, ¤Y¦®aai.

4. „ eY.

5. ?aYp?pYa ae?i.

®«?¬®pae?§¬.

7. ‘?¬c®«i i ae®p¬ ?pY¤aa c«Y?i ¤ ea.

8. ?«ae c?a.

9. ’ !«?c i ae®p¬ .

10. ?§e?®c i ae®p¬ .

11. ?p ae?cYa? i ae®p¬ ?pY¤aa c«Y?i ?ae®p¬ ae??.

12. P §pYe ie i a?®a®!®aai ae®p¬e.

13. ?ae®p¬ ae?® i Y¬?®aai ®!p § .

aYc¤®Fp ae?? .

??aY«.

16. PY¤ ?a?p®c ?Y.

17. ’Y?aa®ce© pY¤ ?a®p.

18. ?p ae?cYa??© pY¤ ?a®p.

‚?.

20. ‘aY¬®aYa?? ?®¬?iiaYp .

21. ’p?FFYp.

?a.

23. ?®¤?p®c ?Y.

24. „Y?®¤?p®c ?Y.

25. ?®¤.

26. ‚?paae.

®¬Ya®aaa®©c?c®Y ?®¤?p®c ?Y.

28. „®?a®p.

29. ?!p a?¬e¬eY ?pY®!p §®c ?i ¤ ea.

30. ?ae®p¬ ae?®eY ?®aYp?.

Y®!p a?¬eY ?pY®!p §®c ?i.

©a.

6. ?®ap®«ieY c®?p®ae ? ?pY¤«®¦Y?i.

®cY¬a?

p?cY¤?aY ?p?¬Ype pY¤ ?a?p®c ?i a?¬c®«iea ®!p §®c.

6. ? ? ¬®¦® §c ai ? cY pY¤ ?a?p®c ?Y Fp ae?cYa?®F® ®!p § ?

p?cY¤?aY ? ®!®aa©aY ?p?¬Ype Y®!p a?¬ea ?pY®!p §®c ?© ?ae®p¬ ae??. ? ?®ce
aeY«? ?a?®«i§®c ?i a ??a ?pY®!p §®c ?© c c e?a ?p?¬Yp a?

p?cY¤?aY ?p?¬Ype c§ ?¬®-®¤®§ c®F® a®®acYaaac?i ¬Y¦¤a Fp ae?cYa?®© ?
a?¬c®«i®© ae®p¬®© ?pY¤aa c«Y?i ¤ ea. ‘aeYaacaia «? «F®p?a¬e
?pY®!p §®c ?i ¤ ea ?§ ®¤®© ae®p¬e c ¤paFai ¤«i c e?a ?p?¬Yp®c?

“?p ¦Y?Y

2. _______ ‘?Yae? «i i ?p®Fp ¬¬ ®! pa¦Y?i ? aaap Y?i c?paa®c.

!®p ?p c?« ?®¤?p®c ?i ? ¤Y?®¤?p®c ?i ¤ ea

pY®!p §®c ?i, a p ?aYp?§aY¬eY Yc®§¬®¦®aaii ®!p a®F® ?pY®!p §®c ?i ?
c®aaa ®c«Y?i ?aa®¤ea ¤ ea

pY®!p §®c ?i, a®ap iie?Y c®§¬®¦®aai a®cYpe?ai ®!p a®Y ?pY®!p §®c ?Y a
F p a?Y© ?®«acY?i ?®«®F® a®c? ¤Y?i a ?aa®¤e¬? ¤ e¬?.

9. _______ ???¬ «i i ?®pae?i ?ae®p¬ ae??.

11. _______ ‘«Y¤aac?Y c«?i?i ?®¬Ya c ?p®aeYaa a ?pY®!p §®c ?i ? ?YpY¤ c?
¤ ea.

‚? ®a®cY ?a?®«i§®c ?i i«Y?ap®ea aaY¬.

a? ®! ®pF ?§ ae?? ?®¬?iiaYpea ?ae®p¬ ae?®ea ?p®aeYaa®c ? pY «?§aie?a
?a a?aaY¬.

p®Fp ¬¬ a®§¤ ?i ? ?§¬YY?i Fp ae?cYa?®F® ®!p § .

18. _______ ?§®!p ¦ ie i a®c? .

21. _______ ‘®§¤ ?Y ? ?§¬YY?Y ?ae®p¬ ae?®ea ®!p §®c.

23. _______ ?®¦YaacY i ?aYp?pYa ae?i.

p®aeYaa ?pYcp eY?i ¤ ea c ?ae®p¬ ae?i.

p®Fp ¬¬ a®§¤ ?i ? ?§¬YY?i a?¬c®«i®F® ®!p § .

31. _______ ‘?®?¬ ?®ia?i “p §pYe ie i a?®a®!®aai ae®p¬e”.

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