t sstata st

1
????µ?t??? s?st?µata st?? ?/?

• ?e?ad???, d?ad???, ??tad??? ?a? de?ae?ad???
  s?st?µa a???µ?s??.
• http//pshfiakh-texnologia-epal-b.ggia.info

2
????µ?t??? s?st?µata

• ? a????? t?? a????p?? ??a µet??se?? ?d???se
• ?????? st?? ep????s? t?? a???µ??
• ?at?p?? st?? ep????s? s?µß???? ??a t??
• pa??stas? t???
• ????? st? d?µ??????a t?? a???µ?t????
• s?st?µ?t?? ?.?. de?ad???, d?ad???, t??ad???,
  tet?ad???, , ??tad???, .., de?ae?ad??? ..

3
?? de?ad??? s?st?µa a???µ?s??

• ?p????t?se st?? ?a??µe???? ??? µa?
• ???s?µ?p??e? ta a?aß??? ??f?a 0, 1, 2, ,9
• St? s?st?µa a?t? ?? µa??µat???? p???e?? ?????ta?
  µe µe???? e????e?a ap? t?? ?????p?
• ?pe?d? t? µa?a??e? ap? µ???? ?????a
• ???t?s? ?? ??aße? t? a???µ??? ???s?µ?p?????e

4
??????? ????µ?t???? ??f???
5
?? e???????? a???µ??
6
?????????? ????µ??
??t???? a???µ?? ???s?µ?p?????ta? st?? s?aß????
???e?. G?a pa??de??µa st?? ??s?a
???s?µ?p?????ta? µ???? t? 1700, µ???? p?? ?
?e????? ??t??? ? (ts????) t??? ???a?e ????et??ta?
t??? ???st??? µa? a?aß????? a???µ??? (0,1,2).
7
Roman numbers (?at??????)

• ????de?
• ?e??de?
• ??at??t?de?
• ?????de?

MCMXLV -gt 1945 MCMXCVII -gt 1997 ??t?????
a???µ??? ???p??µe se pa???? ?a???e? s??eµ?.
?d? t? MDCCCCX d????e? t? 1910 / MCMX (e??????
?at?????? a???µ??)
8
??d???p???s? a???µ?? µe d?af??et??? s?µß??a

• ?e t?? p??????µe?e? d?af??e?e? e?daµe µe????
  pa?ade??µata ??d???p???s?? t?? a???µ?? ap?
  d?af??et????? p???t?sµ???.
• ? ??d???p???s? t?? a???µ?? e?e??????e ??a t??
  a????e? t?? ???e p???t?sµ?? ??a ?a a?apa?asta????
  ?????????e?, µ???de? µ?t??s?? a?a???, ???µat????
  s??a??a??? ??p ??p.
• ?a??e?????e ? ???s? t?? ???st?? a?aß???? a???µ??
  ?a? t? de?ad??? s?st?µa a???µ?s?? µe 10 ??f?a 0,
  1, 2, 3, 4, 5, 6, 7, 8, 9

9
????µ?t??? s?st?µata

• ?? ???µa e??? s?st?µat?? a???µ?s?? p?????eta?
  ap? t?? a???µ? t?? ??f??? p?? ???s?µ?p??e? ??a
  t?? pa??stas? t?? a???µ??.
• ? a???µ?? a?t?? ???µ??eta? ß?s? t?? s?st?µat??
• ?? de?ad??? s?st?µa (ß?s? 10) ???s?µ?p??e? ta
  ??f?a
• 0,1, 2, 3, 4, 5, 6, 7, 8 ?a? 9
• ?? d?ad??? s?st?µa (ß?s? 2) ???s?µ?p??e? ta ??f?a
  0,1
• ?? ??tad??? s?st?µa (ß?s? 8) ???s?µ?p??e? ta
  ??f?a 0,1,3,4,5,6,7
• ?? de?ae?ad??? s?st?µa (ß?s? 16) ???s?µ?p??e? ta
• ??f?a 0, 1, 2, 3, 4, 5, 6, 7, 8 , 9, A, B, C, D,
  E ?a? F
• ??a ap? ta s?µß??a s?µa??e? t?? ???e???
  p?s?t?ta?, t? µ?d??, ?a? ta ???a s?µß??a
  d?af????? ap? t? p??????µe?? t??? (?p?? ta ????µe
  ?ata????e?) ?at? µ?a a???a?? µ???da.

10
????µ?t??? s?st?µata

• ? a???µ?? p?? pe?????fe? µ?a p?s?t?ta ??e? d??
  tµ?µata p?? ???????ta? µe ?p?d?ast??? (s??????
  µ?a te?e?a). ?? a??ste?? tµ?µa e??a? t? a???a??
  µ???? t?? p?s?t?ta? ?a? t? de??? tµ?µa e??a? t?
  ??asµat??? µ???? t?? p?s?t?ta?. ?ta? ?p???e?
  ??asµat??? µ???? ? a?a??af? t?? ?p?d?ast????
  e??a? ?p???e?t???.
• ?a??de??µa ? a???µ?? 2143,45 ??e? a???a??
  µ???? t? 2143 ?a? ??asµat??? µ???? t? ,45.

11
????µ?t??? s?st?µata

• ? ??s? t?? s?µß???? µ?sa st?? a???µ? t??? d??e?
  ?a? t?? s??????? a???µ?t??? t??? a??a, ??at? ???e
  s?µß??? p???ap?as???eta? µe t?? ß?s? ???µ??? se
  ??p??a d??aµ?.
• ? e???t?? t?? ??s?? a???ß?? a??ste?? ap? t??
  ?p?d?ast??? e??a? µ?d??. ?? e???te? a??????ta?
  ?at? µ?a µ???da a? p??a????µe se a??ste??te??
  ??s? ?a? µe?????ta? ?at? µ?a µ???da a? p??a????µe
  se de???te?? ??s?. ??e? ?? ???s?µ?p????µe?e?
  ??se??, ap? t?? µe?a??te?? µ???? t?? µ????te??,
  p??pe? ?a pe??????? ??p??? s?µß???, ?st? ?? a?
  a?t? e??a? t? µ?d??.

12
?a?ade??µata de?ad???? (DEC)
13
?p???a G?at? ? ?/? de? ???s?µ?p??e? t? de?ad???
s?st?µa a???µ?s??

• ?? ???aµe ?a pa?ast?s??µe t??? a???µ??? st??
  ?p?????st? µe t? 10d??? s?st?µa, ?a ?p?epe ?a
  ?atas?e??s??µe ??a f?s??? µ?s? p?? ?a pa??st??e?
  10 d?af??et???? ?atast?se??
• ???a? p??? a???ß?te?? (??e?t?????? ?????µata).
• ???? p?? d?s???? (p.?. ?a ?????? a???µ?t????
  p???e?? se a?t?).

14
?? d?ad??? s?st?µa a???µ?s??

• ???a? t? p?? d?aded?µ??? s?st?µa st???
  ?p?????st??.
• ?a ??f?a p?? ???s?µ?p????µe e??a? t? 0 ?a?
  t?1.
• Se ??a ??e?t?????? ?????µa ? a?apa??stas? t??
  ??f??? 1 µp??e? ?a e??a? pe???e? ?e?µa e?? 0 de?
  pe???e? ?e?µa.

15
??t?st????a 2ad????-10d???? S?st?µat??
????d?? µe t?? ?p??a s??µat????µe t???
(a???a????) a???µ??? ??µa-? ?????µe t? 0
st?? ??s? µe e???t? µ?d??. ??µa-? ???s??t??µe
st?? a???µ? µ?a a???a?a µ???da, ?p?te
???s?µ?p????µe st?? ??s? µe e???t? µ?d?? t?
ep?µe?? s?µß???. ??µa-G ?? de? ?p???e? ep?µe??
s?µß???, ß????µe 0 st?? ??s? a?t? ?a? p??s??t??µe
1 st?? a??ste?? d?p?a?? ??s?.
16
S??µat?sµ?? 2ad???, 4ad???, 8ad???, 10d???,
16ad???
????d?? µe t?? ?p??a s??µat????µe t???
(a???a????) a???µ??? st? ???e s?st?µa
a???µ?s?? ??µa-? ?????µe t? 0 st?? ??s? µe
e???t? µ?d??. ??µa-? ???s??t??µe st?? a???µ?
µ?a a???a?a µ???da, ?p?te ???s?µ?p????µe st??
??s? µe e???t? µ?d?? t? ep?µe?? s?µß???. ??µa-G
?? de? ?p???e? ep?µe?? s?µß???, ß????µe 0 st??
??s? a?t? ?a? p??s??t??µe 1 st?? a??ste?? d?p?a??
??s?. ???s??te     St? d?ad??? 10 e??a? t?
d??.    St? tet?ad??? 10 e??a? t?
t?sse?a.    St? ??tad??? 10 e??a? t?
??t?.    St? de?ad??? 10 e??a? t? d??a.   
St? de?ae?ad??? 10 e??a? t? de?a???. ?? 10
d????e? t?? ß?s? t?? s?st?µat?? a???µ??!
17
S????asµ?? 1 ?? d????e? t? 10 se ???e s?st?µa
a???µ?s??

• Se ??a ta a???µ?t??? s?st?µata ? ß?s? ???feta?
  10, (1 ß?s?1 0 ß?s?0). (?t??µa??µaste
  ?a ??????µe t?? ß?s? µ???? µa? te?e??s??? ta
  ??f?a, ??a ß????µe 0 st?? ??s? t?? µ???d?? ?a? 1
  a???ß?? a??ste?? t??).    St? d?ad??? 10
  e??a? t? d??.    St? tet?ad??? 10 e??a? t?
  t?sse?a.    St? ??tad??? 10 e??a? t?
  ??t?.    St? de?ad??? 10 e??a? t? d??a.   
  St? de?ae?ad??? 10 e??a? t? de?a???.

18
S????asµ?? 2 ?? d????e? t? 100 se ???e s?st?µa
a???µ?s??

• F?s??? ??t? a?t?st???? ?s??e? ??a ??e? t??
  d???µe?? t?? ß?s??. ?? tet?????? t?? ß?s??, p??
  ???feta? p??t?te 100, ?s?d??aµe?
•     ??a t? d?ad??? s?st?µa µe 22 4,    ??a
  t? tet?ad??? s?st?µa µe 42 16,    ??a t?
  ??tad??? s?st?µa µe 82 64,    ??a t? de?ad???
  s?st?µa µe 102 100,    ??a t? de?ae?ad???
  s?st?µa µe 162 256.

19
?as???? p???e?? st? d?ad??? s?st?µa

• ???s?es?
• 000
• 011
• 101
• 1110
• ????ap?as?asµ??
• 0x00
• 0x10
• 1x00
• 1x11
• S?µe??s? ?? p???e?? st? 2ad??? s?st?µa a???µ?s??
  e??a? e?????te??? ap? ?t? st? ???st? µa? 10d???
  s?st?µa a???µ?s??.

20
??daµe t? pa??de??µa t?? de?ad???? (DEC)
21
?a?ade??µata d?ad???? (BIN)
22
?e?ad??? / ??ad??? / ??tad??? / ?e?ae?ad???
s?st?µa a???µ??.
23
?a?ade??µata o?tad???? (OCT)
24
?a?ade??µata de?ae?ad???? (HEX)
25
?????? () e??t?s?

• To 10 t? s?µß????e? st? 2ad???, 3ad???, 4t?ad???,
  5ad???, 6ad???, 7ad???, 8ad???, 9ad???, 10d???,
  11d???, 12d???, 13d???, 14d???, 15d???, 16d???
  s?st?µa a???µ?s??

??s? ?p?? e?daµe se p??????µe?? d?af??e?a t?
10 d????e? t?? ß?s? t?? s?st?µat?? a???µ?s??.
?ts? ? a???µ?? 10 s?µß????e? a?t?st???a t? 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.
26
???s?es? ?a? p???ap?as?asµ?? st? d?ad??? s?st?µa.
???s?es? 000 011 101 1110

• ????ap?as?asµ??
• 0x00
• 0x10
• 1x00
• 1x11

27
?????e??s? µe d?ad??? s?st?µa

• ???ß??µa () ?p??e? ?a fa??eta? se p??t? µat??
  t? d?ad??? s?st?µa a???µ?s?? d?s???? a??? a?t?
  ?fe??eta? ap?? st? ?t? de? e?µaste e?as??µ???? se
  a?t?.
• ??a?t??? ???? ?????ta? p????? as??se?? µe t?
  d?ad??? / ??tad??? / de?ae?ad??? s?st?µa
  a???µ?s?? µp????µe ?a t? ap?µ???p???s??µe..

28
? ???s?µ?t?ta t?? ???s?? t?? d?ad???? s?st?µat??.

• ? p????aµµat?sµ?? efa?µ???? ?ate??e?a? se ???ssa
  µ??a??? H/Y ???eta? se ???ssa µ??a??? (assembly)
  (p.?. ?d???? s?s?e??? drivers).
• ? ??d???p???s? t?? p????f???a? se ??a ??e?t??????
  ?p?????st? ???eta? p??ta se ??f?a 0 ?a? 1. ?.?.
  µ?a ??f?a?? f?t???af?a, ??a t?a???d? mp3 ??p..
  ??d???p??e?ta? se a???µ??? ?? ?p????
  a?apa??st???ta? µe 0 ?a? 1 ??p.
• ?? d?ad??? s?st?µa e??a? ???s?µ? a? ?????µe ?a
  µ????µe ?a p????aµµat????µe se ?p??ad?p?te ???ssa
  p????aµµat?sµ?? ?????? ep?p?d?? (p.?. Basic,
  Pascal, C/C, java ??p).

29
??ß?????af?a

• http//en.wikipedia.org/wiki/Arabic_numbers
• http//en.wikipedia.org/wiki/Greek_numerals
• http//www.geocities.com/rmlyra/Numbers.html
• http//www2.ignatius.edu/faculty/turner/arabic/anu
  mbers.htm
• http//utopia.duth.gr/ksiop/lessons/plhroforikh_i
  .html
• http//www.survey.ntua.gr/main/courses/general/csi
  ntro/lectures/IntroCS_2005_lecture_1.pdf
• http//www.cs.uoi.gr/kabousia/pdf/LogicDesign/Th1
  _BinarySystems.pdf
• http//www.cs.uoi.gr/lagaris/ITC/PowerPoint/Systi
  mataArithmisis.ppt
• http//en.wikipedia.org/wiki/Cyrillic_numerals
• http//en.wikipedia.org/wiki/Roman_numerals
• http//blogs.sch.gr/manolas/2008/09/25/CF83CF8
  5CF83CF84CEAECEBCCEB1CF84CEB1-CEB1
  CF81CEAFCEB8CEBCCEB7CF83CEB7CF82/