???? ????
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???? ????
[1]
(
???????????
:
Numeral system
)? ?? ????? ??? ??????? ????? ????? ???????? ???? ??????? ?? ?????? ?????? ?????
???????? ????????
?????. ??????? ????? ?? ?????? ???? ???????. ?????? ???????
16
(2A) ?
8
(52) ?????? ??? ??????
10
(42) ???? ?????? ??? ??????. ????? ??? ??????? ?????? ?????? ?? ??? ????? ??? ??????? ?? ?????? ???????? ?????? ?????? cheval (???? ??????) ??????? equus (???? ???????) ??????? horse (???? ????????) ??? ??? ?????? ≪????≫.
????? ?????? ?????? (??????) ?????? ??????? ?? ?????? ???? ?????? ?????? (???????) ???? ???????. ???? ???? ??? ??? ?????? ?? ?? ??? ???? ??? ???? ??????? ?????? ????? ????? ???????. ??? ????? ?? ??????? ?????? ????? (??? ???? ??????? ?? ?????? ?????? ???? 10 ????? ???? ??? ??????? ????? ???) ??? ???? ????? ??????? ?????? ???????.
???? ????? ???? ???? ?????? ??? ??????? ???????? ???????? ????? ???? ?????? ?????? ??? ??? ?????? ????????? ??? ????? ?? ??????? ??????? ?????? ???? ????? ?????? ≪????≫ ????? ?? ?????? ??? ??????
?????? ??????
??????? ?????? ????? ??? ?? ??? ???????? ???? ?????? ?????? ???????:
n = ± S
k-1
× b
k-1
+ S
k-2
× b
k-2
+...+ S
1
× b
1
+ S
0
× b
0
+ S
-1
× b
?1
+ S
-2
× b
?2
+ ... + S
-L
× b
-L
??? ?? ????? (n) ???? ??? ??. ?????? (±) ???? ????? ????? (n) (????? ?? ?????). ?????? (S) ???? ≪???≫ ???? ?????? ??????. ?????? (b) ???? ????? ?????? ?????? (???? ?? ????? ??...)? ????? ?????? (k) ???? ????? (S)? ? (L) ?? ????? (b) ??? ??????? ??????? ?????.
??? ??????? ??? ??????? ?? ????????? ??? ?????? ??????? ?????? ???? ???:
??? ??????? ?? ????? (1234.5678)
10
?? ??? ?? ?????? ?????? (??? ???? ??????? ??????? ?? ??????) ??? ??? ???? ????? ?????? ??????? ?????? ??? ???? ???:
1- ????? (b) ????? ????? ????? ?????? ??? ?????? ?????? ??? ?? ?? ???? ???? ???? (Base ?? radix) ??? ?? ???? ????? ????? ??? ?????? ????????? ?? ???? ????. ?? ?????? ?????? ???? (b) ?? "10" ??? ??? ?????? ????????? ?? ?????? ?????? ????? ???? ???? (0-1-2-3-4-5-6-7-8-9).
2- ?????? ???????? ????? (S) ?? (b) ??? ?? ???? ????? ?? ????? ??? ?? ?????? ??????? (k) ?? ????? ??? ?? ????? ????? ??? ??? ????? ??????? ??????? (L) ????? ??? ?? ????? ????? ??? ??? ????. ??? ??? ????? ?? ?????? ??????? ???? ???? ??????? (. ???) ?????? ?? ?????? ??????? ???? ???? ???????.
3- ?????? ????? ?????? ?? ????? ?????? ?? ?????? ??????? ???? ???? ?????? ?????? (. ???) ?????? ????? ????? ?????.
4- ?? ?????? ??????? ????? ?? ?????? ???????? ???? ??? ?? ?????? ?? ≪????? ??????≫ ?? ????? (?? ?????? ????? 4) ?? ???? ????? ?????? ???????? ???? ??? ?? ≪????? ??????≫ ?? ????? (?? ?????? ????? 1) ?? (k-1) ??? k ?? ??? ??????? ???? ??? ????? ????? ?????? ?? ????? (??? ??????? ????? ?????? ?? ?????? (4) ?????).
5- ?? ?????? ??????? ????? ?? ?????? ???????? ???? ??? ?? ?????? ?? ≪????? ??????≫ ?? ????? (?? ?????? ????? 5) ?? (-1)? ????? ?????? ???????? ????? ??? ?? ≪????? ??????≫ ?? ????? (?? ?????? ????? 8) ?? (L-) ??? L ?? ??? ??????? ???? ??? ????? ????? ?????? ?? ????? (??? ??????? ????? ?????? ?? ?????? (4) ?????).
?????? ??????
[
???
]
?????? ????? ?? ???? ????????? ??????? ?????? ??????. ??? ???? ???? ?????? ??
??????? ???
????? ????. ??????? ???? ??????? ?? 0 ??? 9 ?? ??????.
????? ????? ???????? ??? ?????? (????
?????? ??? ????? ????????
)? ?? ??? ≪?????≫ ?????? ????? ??? ???.
?????? ???????
[
???
]
???? ?????
???????
?????? ????????. ????? ??? ????? ??????? ?? ?????? ??????? ??? ?? ??????? ?????? ??????? ???? ???? ?? ?????? ?? ??????? ??? ????? ?????. ??? ???? ???????? ??? ???? (1) ????? ?? ???? ???? ??????? ?? ??? (0) ????? ?? ??? ???? ???? ???????
???? ??????? ??????? ??????
[
???
]
?? ???? ??? ??? ????? ????? ?????? ???????? ?????? ??????? ??????
???????
?? ??????? ????. ???? ??? ????? ?? ???? ????? ?????? ????? ?????? ?????? ??? ????? ????? ????.??.??.
???? ????? ????? ??????? ??????? ????? ??????? ??????? ?? 0 ??? 15 ???? ??? ?? ?????? ??????? ?????? ????? ?? 0 ??? 9 ??? ????? ??? ???????? ??? ??????? ??? ???? ????? ?? ???? ????.??.??.
?????? ?????? ???????? ? ?????? ?????? ??????? ??? ??????? ?????? ??????? ?? ?????????? ??? ??? ??? ????? ?????? ????? ????? 6 ???? ???? ???? ????? ???? ?? ?????? ???????? ??? ?? ?????? ????? ?? ????? ?????? ????? ?? ?????? ??????? ??????? ?? ???? ??????? ??????? ?? ??? ??? ?????? ?? ??????.
???????? ??????? Numerical Codes
???? ??????? ??????? ?????? Binary Coded Decimal
????? ?????? ???? ???? ??????? ??????? ?? ????? ??????? ???? ?????? ????? ?????? ??? ??????
?? ????? ???? ???? ???????
1- ????? ?? ????? ??? ??? (0-1)
2- ??????? ???????? ?? ??? ????? ??????? ?????? ?????? ?????? ??????? ????? ??????
??? ?? ??????
1- ????? ????? ?????? ?????? ??????? ???? ?? ???? ?? ???? ?? ??? ????? ????? ???? ????? ?????? ????? ?? ?????? ???
2- ????? ??????? ??? ??????? ??????? ????????? ?? ???? ????????
??????? ??? ??? ?????? ???? ?? ???? ?? ??????? ???????? ???? ??????? ??????? ?????? ??? ??????? ??????? ???? ???????.
??????? ?? 0 ??? 20 ?????? ?? ??????
[
???
]
?????? ??????
|
?????? ???????
|
????.??.??
|
?????? ???????
|
?????? ??????? ????
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
0001
|
1
|
1
|
2
|
10
|
0010
|
2
|
2
|
3
|
11
|
0011
|
3
|
3
|
4
|
100
|
0100
|
4
|
4
|
5
|
101
|
0101
|
5
|
5
|
6
|
110
|
0110
|
6
|
6
|
7
|
111
|
0111
|
7
|
7
|
8
|
1000
|
1000
|
10
|
8
|
9
|
1001
|
1001
|
11
|
9
|
10
|
1010
|
0001 0000
|
12
|
A
|
11
|
1011
|
0001 0001
|
13
|
B
|
12
|
1100
|
0001 0010
|
14
|
C
|
13
|
1101
|
0001 0011
|
15
|
D
|
14
|
1110
|
0001 0100
|
16
|
E
|
15
|
1111
|
0001 0101
|
17
|
F
|
16
|
10000
|
0001 0110
|
20
|
10
|
17
|
10001
|
0001 0111
|
21
|
11
|
18
|
10010
|
0001 1000
|
22
|
12
|
19
|
10011
|
0001 1001
|
23
|
13
|
20
|
10100
|
0010 0000
|
24
|
14
|
????? ?? ?????
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???? ??????? ???? ??????
???????? ???????
??? ?????? ??????. ???? ??? ?????? ???? | ??????? ||||| ??????? ||||||||| ??????? ?????
? ?????? ?????
?????? ?????
? ??? ??? ??? ????? ??? ?? ??????
...?????.
????: ????? ??? 25: |||||
??????? ??? ???????
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??? ??? ??????? ???? ??? ????? ??? ??? ????? ?? ???????? ???? ?? ??????? ?? ??? ?? ???? ???? ??????? ??????? ?? ?????? ????
??????? ?????????
. ???? ?????? ??????? ??????? ??? ????? ??????? ???? ???????? ?? ??????? ???? ?????? ?????? ??? ???? ??? ??? ??? ????? ?? ?????? ??????? ?????? ????? ??????? ??? ?????.
??? ??????
[
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]
??????? ?? ??? ??? 19
?????? ??????
? ?????? ???? ?????? ??????? ???????
??????? ???? ?????? ??
?????? ????????
???? ?? ?????? ????????? ?????? 20 ????????? ?????? ?????? ??????? ??????? ????? ?????? ??????? ?? ??????? ??????? ??????? ??????? ??????? ?????????? ???????? ???????? ????.
[2]
?? ?????
[
???
]
???? ?????? ?? ?????? ????? ?? ????? ??????? ?????? ?????? ???? ????? ?????? ????? 408 ?? 48 ?????? ?????? ???? ?????? ??????? ???????? ???????? ?????? ?? ???? ??????? ???? ??? ?????? ?? ????? ?????? ??? ??? ????? ?? ????.
??? ?????
[
???
]
???? ?? ????? ?? ?? ????? ≪?????≫ ???? ??????? ?????? ?? ?? ?????? ????? ?? ???????? ???? ???????? ????? ????? ??? ???? ??????. ?????
?????????
?? ??????? ??? ????? ?? ?????? ????? ?????? ??? 75-35 = 40 ????: ≪?? ?????? ?????? ??? ?? ??? ???? ????? ??? ????? ??? ???? ?????? ?????? ??? ?? ???? ??? ??? ???? ?????? ????? ???????≫. ????? ≪?? ????? ??? ?? ???? ?? ???? ?????? ??? ????? ??? ???? ??????? ????? 02 ?? ???? ?? ?????? ??? ???? ???? ?????≫ ?????? ?? ?????? ???? ???? ?????? ?????? ?????? ?? ?????? ?????? ?? ????? ??? ?????? ?????? ?? ????? ?????? ?? ?? ?????? ??? ?????? ?????? ??? ???? ??????? ???????? ?????.
??? ??????? ???? ??????? ???? ????? ????? ??? ????? ??????? ??? ????? ?? ???? ????? ?? 12? ??? ??????? ??????? ???? ??????? ???? ?????? ??????? ???????? ????????.
????? ?? ????????? ???????? ?????? ??????? ?? ????? ??????? ???? ???? ??? ??????? V ?> ??????? ?? ?????? ???????? ??????? ?? ??????? ???? ??????? ?? ??? ?? ?????? ??? ???? ?????? ???? ??????? ????? ???????? ???????? ?? ?????? ?????? ??? ?? ?????? ?????? ???? ????? ??? ??????? ??????????.
??????? ????????
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