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Mavzu: Shaxsiy kompyuterning axboriy-mantiqiy asoslari. Kompyuterda axborotlarni qayta ishlashning arifmetik asoslari RejaShu qonuniyatdan foydalanib, quyidagi birinchi 10 ta butun sonni hosil qilamiz
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səhifə | 4/10 | tarix | 23.12.2023 | ölçüsü | 0,9 Mb. | | #155649 |
| 2-MavzuShu qonuniyatdan foydalanib, quyidagi birinchi 10 ta butun sonni hosil qilamiz:
10 lik sanoq sistemasida
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
2 lik sanoq sistemasida
|
0
|
1
|
10
|
11
|
100
|
101
|
110
|
111
|
1000
|
1001
|
5 lik sanoq sistemasida
|
0
|
1
|
2
|
3
|
4
|
10
|
11
|
12
|
13
|
14
|
8 lik sanoq sistemasida
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
10
|
11
|
16 lik sanoq sistemasida
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
Jadvaldan ko’rinadiki, turli sanoq sistemalarida o’xshash sonlar bor ekan. Shu sababli bu sonlarni farqlash uchun informatikada 102, 105, 108 kabi belgilash qabul qilingan.
Pozitsiyali bo’lmagan sanoq sistemalari:
Sonlarni boshqacha usul va qoidalar asosida shakllantiriladigan sanoq sistemalar ham mavjud. Bunday sistemalar jumlasiga rim raqamlari sistemasi kiradi. Mazkur sistemada raqamlar va sonlarni ifodalovchi maxsus belgilar to’plami bo’lib, ixtiyoriy son ana shu belgilar yordamida tuziladi. Bunda ishlatilayotgan belgilar raqam va sonlar guruhiga bo’linmaydi hamda shu belgi sonni ifodalovchi raqamlar ketma-ketligining qaysi o’rnida turishidan qat’i nazar o’z miqdorini bildiraveradi.
Masalan, rim raqamlari2 sistemasida ma’lum belgilar mavjud bo’lib, ular quyidagilarni ifodalaydi:
1 raqami «I» belgi bilan;
5 raqami «V» belgi bilan;
10 soni «X» belgi bilan;
50 soni «L» belgi bilan;
100 soni «С» belgi bilan;
500 soni «D» belgi bilan;
1000 soni «М» belgi bilan ifodalanadi.
Ular orasidagi boshqa sonlar miqdor jihatdan katta bo’lganidan ma’lum sonni ayirish yoki miqdor jihatdan kichik bo’lganiga biror sonni qo’shish ko’rinishida belgilanadi.
Masalan:
Son o’qilishi
|
Belgisi
|
Rim raqamlari sistemasida
|
Mazmuni
|
To’rt
|
4
|
IV
|
5-1
|
Olti
|
6
|
VI
|
5+1
|
To’qqiz
|
9
|
IX
|
10-1
|
O’n to’rt
|
14
|
XIV
|
10+(5—1)
|
O’n to’qqiz
|
19
|
XIX
|
10+(10-1)
|
Qirq besh
|
45
|
XLV
|
10+10+10+10+5
|
Qirq to’qqiz
|
49
|
XLIX
|
50-1
|
Bir yuz oltmish sakkiz
|
168
|
CLXVIII
|
100+50+10+5+3
|
Bir ming to’qqiz yuz to’qson yeti
|
1997
|
MCMXCVII
|
1000+(1000-100)+(100-10)+5+2
|
Quyidagi jadvalda ba’zi birliklarni ko’rishlaring mumkin:
Arab raqamlari
|
Rim raqamlari
|
Arab raqamlari
|
Rim raqamlari
|
Arab raqamlari
|
Rim
raqamlari
|
Arab raqamlari
|
Rim
raqamlari
|
1
|
I
|
104
|
CIV
|
270
|
CCLXX
|
1966
|
MCMLXVI
|
2
|
II
|
105
|
CV
|
280
|
CCLXXX
|
1967
|
MCMLXVII
|
3
|
III
|
106
|
CVI
|
290
|
CCXC
|
1968
|
MCMLXVIII
|
4
|
IV
|
107
|
CVII
|
300
|
CCC
|
1969
|
MCMLXIX
|
5
|
V
|
108
|
CVIII
|
310
|
CCCX
|
1970
|
MCMLXX
|
6
|
VI
|
109
|
CIX
|
320
|
CCCXX
|
1971
|
MCMLXXI
|
7
|
VII
|
110
|
CX
|
330
|
CCCXXX
|
1972
|
MCMLXXII
|
8
|
VIII
|
111
|
CXI
|
340
|
CCCXL
|
1973
|
MCMLXXIII
|
9
|
IX
|
112
|
CXII
|
350
|
CCCL
|
1974
|
MCMLXXIV
|
10
|
X
|
113
|
CXIII
|
360
|
CCCLX
|
1975
|
MCMLXXV
|
11
|
XI
|
114
|
CXIV
|
370
|
CCCLXX
|
1976
|
MCMLXXVI
|
12
|
XII
|
115
|
CXV
|
380
|
CCCLXXX
|
1977
|
MCMLXXVII
|
13
|
XIII
|
116
|
CXVI
|
390
|
CCCXC
|
1978
|
MCMLXXVIII
|
14
|
XIV
|
117
|
CXVII
|
400
|
CD
|
1979
|
MCMLXXIX
|
15
|
XV
|
118
|
CXVIII
|
410
|
CDX
|
1980
|
MCMLXXX
|
16
|
XVI
|
119
|
CXIX
|
420
|
CDXX
|
1981
|
MCMLXXXI
|
17
|
XVII
|
120
|
CXX
|
430
|
CDXXX
|
1982
|
MCMLXXXII
|
18
|
XVIII
|
121
|
CXXI
|
440
|
CDXL
|
1983
|
MCMLXXXIII
|
19
|
XIX
|
122
|
CXXII
|
450
|
CDL
|
1984
|
MCMLXXXIV
|
20
|
XX
|
123
|
CXXIII
|
460
|
CDLX
|
1985
|
MCMLXXXV
|
21
|
XXI
|
124
|
CXXIV
|
470
|
CDLXX
|
1986
|
MCMLXXXVI
|
22
|
XXII
|
125
|
CXXV
|
480
|
CDLXXX
|
1987
|
MCMLXXXVII
|
23
|
XXIII
|
126
|
CXXVI
|
490
|
CDXC
|
1988
|
MCMLXXXVIII
|
24
|
XXIV
|
127
|
CXXVII
|
500
|
D
|
1989
|
MCMLXXXIX
|
25
|
XXV
|
128
|
CXXVIII
|
600
|
DC
|
1990
|
MCMXC
|
26
|
XXVI
|
129
|
CXXIX
|
700
|
DCC
|
1991
|
MCMXCI
|
27
|
XXVII
|
130
|
CXXX
|
800
|
DCCC
|
1992
|
MCMXCII
|
28
|
XXVIII
|
131
|
CXXXI
|
900
|
CM
|
1993
|
MCMXCIII
|
29
|
XXIX
|
132
|
CXXXII
|
1000
|
M
|
1994
|
MCMXCIV
|
30
|
XXX
|
133
|
CXXXIII
|
1100
|
MC
|
1995
|
MCMXCV
|
31
|
XXXI
|
134
|
CXXXIV
|
1200
|
MCC
|
1996
|
MCMXCVI
|
32
|
XXXII
|
135
|
CXXXV
|
1300
|
MCCC
|
1997
|
MCMXCVII
|
33
|
XXXIII
|
136
|
CXXXVI
|
1400
|
MCD
|
1998
|
MCMXCVIII
|
34
|
XXXIV
|
137
|
CXXXVII
|
1500
|
MD
|
1999
|
MCMXCIX
|
35
|
XXXV
|
138
|
CXXXVIII
|
1600
|
MDC
|
2000
|
MM
|
36
|
XXXVI
|
139
|
CXXXIX
|
1700
|
MDCC
|
2001
|
MMI
|
37
|
XXXVII
|
140
|
CXL
|
1800
|
MDCCC
|
2002
|
MMII
|
38
|
XXXVIII
|
141
|
CXLI
|
1900
|
MCM
|
2003
|
MMIII
|
39
|
XXXIX
|
142
|
CXLII
|
1901
|
MCMI
|
2004
|
MMIV
|
40
|
XL
|
143
|
CXLIII
|
1902
|
MCMII
|
2005
|
MMV
|
41
|
XLI
|
144
|
CXLIV
|
1903
|
MCMIII
|
2006
|
MMVI
|
42
|
XLII
|
145
|
CXLV
|
1904
|
MCMIV
|
2007
|
MMVII
|
43
|
XLIII
|
146
|
CXLVI
|
1905
|
MCMV
|
2008
|
MMVIII
|
44
|
XLIV
|
147
|
CXLVII
|
1906
|
MCMVI
|
2009
|
MMIX
|
45
|
XLV
|
148
|
CXLVIII
|
1907
|
MCMVII
|
2010
|
MMX
|
46
|
XLVI
|
149
|
CXLIX
|
1908
|
MCMVIII
|
2011
|
MMXI
|
47
|
XLVII
|
150
|
CL
|
1909
|
MCMIX
|
2012
|
MMXII
|
48
|
XLVIII
|
151
|
CLI
|
1910
|
MCMX
|
2013
|
MMXIII
|
49
|
XLIX
|
152
|
CLII
|
1911
|
MCMXI
|
2014
|
MMXIV
|
50
|
L
|
153
|
CLIII
|
1912
|
MCMXII
|
2015
|
MMXV
|
51
|
LI
|
154
|
CLIV
|
1913
|
MCMXIII
|
2016
|
MMXVI
|
52
|
LII
|
155
|
CLV
|
1914
|
MCMXIV
|
2017
|
MMXVII
|
53
|
LIII
|
156
|
CLVI
|
1915
|
MCMXV
|
2018
|
MMXVIII
|
54
|
LIV
|
157
|
CLVII
|
1916
|
MCMXVI
|
2019
|
MMXIX
|
55
|
LV
|
158
|
CLVIII
|
1917
|
MCMXVII
|
2020
|
MMXX
|
56
|
LVI
|
159
|
CLIX
|
1918
|
MCMXVIII
|
2021
|
MMXXI
|
57
|
LVII
|
160
|
CLX
|
1919
|
MCMXIX
|
2022
|
MMXXII
|
58
|
LVIII
|
161
|
CLXI
|
1920
|
MCMXX
|
2023
|
MMXXIII
|
59
|
LIX
|
162
|
CLXII
|
1921
|
MCMXXI
|
2024
|
MMXXIV
|
60
|
LX
|
163
|
CLXIII
|
1922
|
MCMXXII
|
2025
|
MMXXV
|
61
|
LXI
|
164
|
CLXIV
|
1923
|
MCMXXIII
|
2026
|
MMXXVI
|
62
|
LXII
|
165
|
CLXV
|
1924
|
MCMXXIV
|
2027
|
MMXXVII
|
63
|
LXIII
|
166
|
CLXVI
|
1925
|
MCMXXV
|
2028
|
MMXXVIII
|
64
|
LXIV
|
167
|
CLXVII
|
1926
|
MCMXXVI
|
2029
|
MMXXIX
|
65
|
LXV
|
168
|
CLXVIII
|
1927
|
MCMXXVII
|
2030
|
MMXXX
|
66
|
LXVI
|
169
|
CLXIX
|
1928
|
MCMXXVIII
|
2031
|
MMXXXI
|
67
|
LXVII
|
170
|
CLXX
|
1929
|
MCMXXIX
|
2032
|
MMXXXII
|
68
|
LXVIII
|
171
|
CLXXI
|
1930
|
MCMXXX
|
2033
|
MMXXXIII
|
69
|
LXIX
|
172
|
CLXXII
|
1931
|
MCMXXXI
|
2034
|
MMXXXIV
|
70
|
LXX
|
173
|
CLXXIII
|
1932
|
MCMXXXII
|
2035
|
MMXXXV
|
71
|
LXXI
|
174
|
CLXXIV
|
1933
|
MCMXXXIII
|
2036
|
MMXXXVI
|
72
|
LXXII
|
175
|
CLXXV
|
1934
|
MCMXXXIV
|
2037
|
MMXXXVII
|
73
|
LXXIII
|
176
|
CLXXVI
|
1935
|
MCMXXXV
|
2038
|
MMXXXVIII
|
74
|
LXXIV
|
177
|
CLXXVII
|
1936
|
MCMXXXVI
|
2039
|
MMXXXIX
|
75
|
LXXV
|
178
|
CLXXVIII
|
1937
|
MCMXXXVII
|
2040
|
MMXL
|
76
|
LXXVI
|
179
|
CLXXIX
|
1938
|
MCMXXXVIII
|
2041
|
MMXLI
|
77
|
LXXVII
|
180
|
CLXXX
|
1939
|
MCMXXXIX
|
2042
|
MMXLII
|
78
|
LXXVIII
|
181
|
CLXXXI
|
1940
|
MCMXL
|
2043
|
MMXLIII
|
79
|
LXXIX
|
182
|
CLXXXII
|
1941
|
MCMXLI
|
2044
|
MMXLIV
|
80
|
LXXX
|
183
|
CLXXXIII
|
1942
|
MCMXLII
|
2045
|
MMXLV
|
81
|
LXXXI
|
184
|
CLXXXIV
|
1943
|
MCMXLIII
|
2046
|
MMXLVI
|
82
|
LXXXII
|
185
|
CLXXXV
|
1944
|
MCMXLIV
|
2047
|
MMXLVII
|
83
|
LXXXIII
|
186
|
CLXXXVI
|
1945
|
MCMXLV
|
2048
|
MMXLVIII
|
84
|
LXXXIV
|
187
|
CLXXXVII
|
1946
|
MCMXLVI
|
2049
|
MMXLIX
|
85
|
LXXXV
|
188
|
CLXXXVIII
|
1947
|
MCMXLVII
|
2050
|
MML
|
86
|
LXXXVI
|
189
|
CLXXXIX
|
1948
|
MCMXLVIII
|
2100
|
MMC
|
87
|
LXXXVII
|
190
|
CXC
|
1949
|
MCMXLIX
|
2200
|
MMCC
|
88
|
LXXXVIII
|
191
|
CXCI
|
1950
|
MCML
|
2300
|
MMCCC
|
89
|
LXXXIX
|
192
|
CXCII
|
1951
|
MCMLI
|
2400
|
MMCD
|
90
|
XC
|
193
|
CXCIII
|
1952
|
MCMLII
|
2500
|
MMD
|
91
|
XCI
|
194
|
CXCIV
|
1953
|
MCMLIII
|
2600
|
MMDC
|
92
|
XCII
|
195
|
CXCV
|
1954
|
MCMLIV
|
2700
|
MMDCC
|
93
|
XCIII
|
196
|
CXCVI
|
1955
|
MCMLV
|
2800
|
MMDCCC
|
94
|
XCIV
|
197
|
CXCVII
|
1956
|
MCMLVI
|
2900
|
MMCM
|
95
|
XCV
|
198
|
CXCVIII
|
1957
|
MCMLVII
|
3000
|
MMM
|
96
|
XCVI
|
199
|
CXCIX
|
1958
|
MCMLVIII
|
5000
|
V
|
97
|
XCVII
|
200
|
CC
|
1959
|
MCMLIX
|
10,000
|
X
|
98
|
XCVIII
|
210
|
CCX
|
1960
|
MCMLX
|
50,000
|
L
|
99
|
XCIX
|
220
|
CCXX
|
1961
|
MCMLXI
|
100,000
|
C
|
100
|
C
|
230
|
CCXXX
|
1962
|
MCMLXII
|
500,000
|
D
|
101
|
CI
|
240
|
CCXL
|
1963
|
MCMLXIII
|
1,000,000
|
M
|
102
|
CII
|
250
|
CCL
|
1964
|
MCMLXIV
|
|
|
103
|
CIII
|
260
|
CCLX
|
1965
|
MCMLXV
|
|
|
Bir nechta o’nlik raqamlarni o’z ichiga olgan raqam quyidagi misollarda bo’lgani kabi, har biri uchun eng yuqori darajadan pastgacha rim raqamli ekvivalenti qo’shilishi bilan tuziladi:3
39 = XXX + IX = XXXIX.
246 = CC + XL + VI = CCXLVI.
789 = DCC + LXXX + IX = DCCLXXXIX.
2421 = MM + CD + XX + I = MMCDXXI.
160 = C + LX = CLX
207 = CC + VII = CCVII
1009 = M + IX = MIX
1066 = M + LX + VI = MLXVI
1776 = M + DCC + LXX + VI = MDCCLXXVI
1918 = M + CM + X + VIII = MCMXVIII
1954 = M + CM + L + IV = MCMLIV
2014 = MM + X + IV = MMXIV
3999 = MMM + CM + XC + IX
LIV = L + IV = 50 + 5 – 1 = 54
MIX = M + IX = 1000 + 10 – 1 = 1009
MMXXIV = MM + XX + IV = 1000 + 1000 + 10 + 10 + 5 – 1 = 2024
Ushbu yozuvda namoyish etilishi mumkin bo’lgan eng katta raqam – 3,999,999 (MMM CMXCIXCMXCIX), g’arbda arab raqamlari paydo bo’lishidan oldin, tizimning qadimgi va o’rta asr foydalanuvchilari kattaroq raqamlarni yozish uchun turli xil vositalardan foydalanganlar.
Shuning uchun ham bunday sanoq sistema raqamlari sondagi o’rniga bog’liq bo ‘lmagan, ya’ni pozitsiyaga bog’liq bo’lmagan sanoq sistema deyiladi.
Dostları ilə paylaş: |
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