?????????????????????? BCD, EBCDIC, ASCII

1
????? 3 ??????? ???????????????????

• ??????????????? (???? ??? 2 ??? 8 ??? ??? 16)
• ?????????????
• ????????????????????? 2 ??? 8 ?????? 16
• ?????????????????????????????????
• ?????????????????????? BCD, EBCDIC, ASCII
• ??????????????????????????? ????????? ?????????

2
?????????? (??? 2,8,10,16)

• Place Value ?????????????????????????????????
• ???????????? ??? ?????????????????
  ?????????????????????????? ??? ?????
• Least significant digit ????????????????????????
  ???
• Most significant digit ?????????????????????????
  ?
• ??????????????????????????????? ????????? 10

3
????????????????

• ??? 2 ????? 0,1
• ??? 8 ????? 0,1,2,3,4,5,6,7
• ??? 10 ????? 0,1,2,3,4,5,6,7,8,9
• ??? 16 ????? 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

4
?????????????

• ???????????????? ???? ??? 10
• ????????????? 10 ???? ??????
• ????????????? 2 ???? ??? 8 ??? 16
• ????????????? 8 ??? 16 ???? ??? 2

5
??????????????????????? 10

• ????????????????? ??????????????????
  ?????????????????????

• ?.?. 11012 ( )10
• ???????????? ???
• 23 22 21 20
• (18)(14)(02)(11) 13

6
????????????? 10 ??????????

• ???? ????????????
• ??????? MODULO ???
• ?????? 10 ??????????? ???????????????????????????
• ???????????????????
• ???????????????????????????????????
• ????????????????????????? ????????????????? Most
  significant

7
????????????????????? 10 ??????????

• ????????????

1310 ( )2
1310 ( ) 4
4 13 3 1
13
2
2 6 1
2 3 0
1 1
??? 11012
??? 314
8
????????????? 10 ??????????

• ???? ???????????? ??????????????? 2 ????
• ???????????????????????? MODULO
• ????????????????????
• ??????????????????????????? ?????????????????????
• ???????????????????????? ?????????????????????????
  ?????????

9
????????????????????? 10 ??????????

• ????????????

13.4 10 ( )2
.4 2 0 .8 .8 2 1 .6 .6 2 1
.2 .2 2 0 .4
13
2
2 6 1
2 3 0
1 1
Ans 1101.01102
10
????????????? 2 ???? ??? 8 ??? 16

• ????????????????????????
• ?????? 2 ???? ??? 8 ?????????? 3 ???
• ?????? 2 ???? ??? 16 ?????????? 4 ???
• ??????????????????????????????????
  ????????????????????????? 0

11
????????????????????? 2 ??????? 8

• ????????? 111112 ( 37 ) 8

0 1 1
1 1 1
(04)(12)(11)
(14)(12)(11)
3
7
12
????????????????????? 2 ??????? 16

• ???????????? 0001.112 (1.C ) 16

1 1 0 0
0 0
0 0 0 1
(18)(14)(02)(01)
(08)(04)(02)(11)
12 C
1
13
????????????? 8 ??? 16 ???? ??? 2

• ??????????????????????????????????? ???
• ?????? 8 ????????? ???????????????? 2 ??? 3 ???
• ?????? 16 ????????? ???????????????? 2 ??? 4 ???

14
????????????????????? 8 ??? 16 ???? ??? 2

• ???? ????????????

738 ( ) 2
A316 ( ) 2
7 3
10 3
0 0 1 1
1 1 1 0 1 1
1 0 1 0
Ans 1010000116
Ans 1110112
15
????????????????????? 8 ??? 16 ???? ??? 2

• ???? ????????????

7.38 ( ) 2
A3.B16 ( ) 2
7 . 3
10 3 . 11
1 1 1 0 1 1
1 0 1 0
0 0 1 1
1 0 1 1
Ans 10100001.101116
Ans 111 . 0112
16
??????????????

• ????????????
• ???????????
• ??????????? ??? Complement

17
????????????

• ??????

F31C16 235016 1266C16
1101.112 0111.012 10101.00 2

5345 1235
??????????? ????????????? 5 ????? 5
18
???????????

• ????????

1011.0112 - 0111.1012 0011.1102
4325 - 1435 2345
19
???????????????? (Complement)

• Complement ????????? (??? R ??????) ?? 2 ??????
  ??? Complement R ??? Complement R-1
• ??? R-1 Comp. R
  Comp

2 1 Comp 2 Comp. 8
7 Comp 8 Comp 10
9 Comp 10 Comp
20
???????????????????

• ???????????????? ??? R-1 ?????????
• ???????????????????????????????????
• ??????????? ??????????????????????????
• ??? 2910 ??????????? ??? 99
• 9 Comp 99 -29 70
• ??? 101.112 ?????????????? 111.11
• 1 Comp 111.11 - 101.11 010.00

21
???????????????????

• ???????????????? ??? R ?????????
• ??????????????????????????????????????????????
  ??????????? ???????????? ?????????????
  ???????????????????????
• ??? 2910 ?? ??????????? ????
• 10 Comp (99 1) - 29 71
• ??? 101.112 ????????????????
• 2 Comp (111.11 .01) - 101.11 0010.01

22
??????????????????????????????

• ????? R-1 Complement ??? ?????????????????????????
  ?????????
• 1 Complement ???????? 2 ??? ????????????????????
  ?????????????????
• ??? R-1 Complement ????????????? R Complement
  ???? 1 ???? ? ?????????????
• 2Comp 1 Comp 1 ????????????????

23
??????????????????????

• ?????????????????????????
• ????????????????????? ??? ?????????????
• ?????????????????????????????
• ???? R Comp. ??????????
• ???? R-1 Comp. ??????????????????? ?????????????
• ????????????????

24
??????????????????????????????

• R-1 Comp.

1011.011 2- 111.1012 ? 1) 111.111 -
111.101 000.010 2) 1011.011
1000.010 1
0011.101 1
0011.110
4325 - 1435 ?
1) 444 - 143 301 2) 432 301
1 233 1 234
1
0
1
25
??????????????????????????????

• ??????????? ??? R

1011.011 2- 111.1012 ? 1) 10000.000 -
0111.1011000.011 2) 1011.011
1000.011 1 0011.110

4325 - 1435 ?
1) 1000 - 143 302 2) 432 302
1 234
???????
26
?????????????????????????????? ???????????????
?????????????????

• ????????????????????????????????? ???????????????
• ????????????????????????????????????
• ??????????????????????????????????????????????????
  ??????????????????????????????
• ????????????????????????????????
  ?????????????????????????????????????????????

27
?????????????????????????????? ???????????????
?????????????????
???????? 10112-11002 ?
????????????? R-1 complement
28
?????????????????????????????? ???????????????
?????????????????

• ????????????????????????????????? ???????????????
• ????????????????????????????????????
• ??????????????????????????????????????????????????
  ??????????????????????????????
• ????????????????????????????????
  ?????????????????????????????????????????????

29
?????????????????????????????? ???????????????
?????????????????
???????? 10112-11002 ?
????? ?????????????????? R-1 ???? R complement
?
30
?????????????????????????????Data Representation

• ????????????????????????????? (Alphanumeric Data
  Representation)
• ??????????????????????????????? (Numeric Data
  Representation)
• ???????????? (Integer Representation)
• ????????????????? (Floating Point Representation)

31
?????????????????????????

• ???? BCD Binary Coded Decimal Code
• ???? EBCDIC Extended Binary Coded Decimal
  Interchange Code
• ???? ASCII American Standard Code for
  Information Interchange

32
???? BCD

• ??? 6 ???????????? 1 ???
• ??????????????????? 64 ??? ( 26 ??????)

C B A 8 4 2 1
Digit bit
Zone bit
Check bit/ Parity bit
33
???? BCD

• ?????????? BCD
• ??????????????? (0 - 9) Zone Bit ?????? 00
• ????????????????? ???? ?????????????? Zone bit
  ???? 11

34
???? EBCDIC

• ??? 8 ???????????? 1 ???
• ??????????????????? 256 ??? ( 28 ??????)

C B A 8 4 2 1
Digit bit
Zone bit
Check bit/ Parity bit
35
???? EBCDIC

• ????????????????????? EBCDIC ?? 2 ???
• ???????????? Zone Decimal
• ???????????? Packed Decimal
• ?????????????????? Zone bit ?????????
• 1111 ?????????????????????????????????? ( 15
  ,F) 1100 ???????????????????????????? ???
  (,12 ,C) 1101 ???????????????????????????
  (-,13 ,D)

36
??????????????? Packed Decimal

• ??????????????????????????????? EBCDIC
  ????????????????
• ???????????????????????????????????????
• ???????????????????????????????

37
??????? PACK

• -123
• ???????? Zone bit ??? Digit bit ?????????????
• ??? Zone bit ??????? ????????
• ????????????????? Digit Bit ??????
• ????????????????? 16 (123D)16
• ???? Unpack ???????????? ?????? Pack

1101 0001 1101 0010 1101 0011
38
???? ASCII

• ?? 2 ???? ??? 7 ??? ??? 8 ??? ????????????????????
  ????????????????????????????????????????
• ??????????? EBCDIC ?? Zone bit ????
• ???????????? 0101 ??? 011
• ?????????????? 1010 ??? 100

39
Parity bit ???? Check bit

• ?????????????????????????????? ?? 2 ????
• Even Parity ???????????? ????????????????????????
  ?? 1 ????????????????????????
• Odd Parity ???????????? ??????????????????????????
  1 ????????????????????????

1 1 1 0 0 0 1
0 1 1 0 1 0 1
0 1 1 0 0 0 1

1 1 1 0 1 0 1
40
?????????????????????????????

• ?????????????????? ???????????????????????????????
  ??????? (Fixed length word) ??????????????? 1
  ?????
• half-word ??????????? 2 ????
• Full-word ??????????? 4 ????
• Double-word ??????????? 8 ????

41
??????????????????

• Sign Magnitude / Pure binary code
• 2 Complement
• 1 Complement

42
Sign Magnitude

• ??????????????????????????????????????? Sign bit
  ?????????????????????????? ???????? Magnitude

MSB
LSB
Sign bit
Magnitude
1 ??? ?? 0 ??? ???
1 Word 4 Byte 32 Bit
43
?????????????

• ??? Sign Magnitude

1 Word 4 Byte 32 bit
31 32
2 1 0
25110012
0 1 1 0 0 1
.........................
0 0 0
-25
1 0 0 ......................... 0 1
1 0 0 1
44
?????????????

• ??? 2 Complement
• ??????????????????
• ????????????????????????
• ?????? ????????????? Sign Magnitude
• ????? ?????????? 2 Complement ???????????????

45
???????? ????????? 2 Complement

• ???? 28 111002

MSB
LSB
0
000000.............0000000000 1 1 1 0 0
1 111111.............1111111111 0 0 0 1 1

1
1 111111.............1111111111 0 0 1 0 0
46
Floating Point Representation

• R - M B- E

31 30 24
0
Sign Exponent
Mantissa
S Sign ?????????????? ??? ?? ??????????? E
Exponent ?????????????? M Mantissa
?????????????????
47
???????????? Floating point

• ??????????????????? 16
• Normalization ?????? 16 (???????????? ???
  ???????)
• ??????? Sign, Exponent, Mantissa ?????????? 2
• Sign 1 ???????? 0 ?????????
• Mantissa ?????????????? 2 ????????????? ??
  ?????????????????????

48
???????????? Floating point

• Exponent ????????????????? ???? ?? ??????????????
  Excess 64
• exponent 16 4016 true exponent16
• exponent16 ----gt exponent 2

49
???????? ?? Floating point

• 28 ----gt 1C16
• 1C16 (.1C 102)16
• Sign ----gt 0
• Mantissa ----gt 0001 11002
• Exponent ----gt 4016 216 42 16 -----gt 100 00102

0 100 0010 0001 11000000.......................
...