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CCooddeess
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Codes
Codes are groupings of symbols thatCodes are groupings of symbols thatare used for information exchange...are used for information exchange...
Examples ?
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Example: Morse code (1844)
Used in telegraphy today is a historical code4
Example: Braille code
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Example: Nautical flag code
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Example: Maya code-numbers
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Example: Maya code (?)
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Binary Codes
To represent a group of 2 distinctTo represent a group of 2 distinctelements in a binary code, it requireselements in a binary code, it requiresa minimum ofa minimum of nn--bitsbits..
n
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Example-1
It is known that a digital computer usesIt is known that a digital computer usestwo states that are represented with:two states that are represented with:thethe zerozero andand thethe oneone..
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Example-1 It is known that a digital computer uses two states thatIt is known that a digital computer uses two states that
are represented with:are represented with: thethe zerozero andand thethe oneone..
A group ofA group of fourfour different binary elementsdifferent binary elementscan be represented withcan be represented with 22 bits.bits.
0 0
0 1
1 0
1 1
4
2
0
1
2
3
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Example-2
A group of eight distinct elements can beA group of eight distinct elements can berepresented by 3 bits.represented by 3 bits.
00 00 00
00 00 11
00 11 00
00 11 11
11 00 00
11 00 11
11 11 00
11 11 11
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Special Codes
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Special Codes
88--44--22--11
BCDBCD
ExcessExcess--33
AikenAiken
22--outout--ofof--55
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Binary (8-4-2-1)
Weighted Code
84218421
00 00000000
11 00010001
22 00100010
33 00110011
44 01000100
55 01010101
66 01100110
77 01110111
88 10001000
99 10011001
1010 10101010
1111 10111011
1212 11001100
1313 11011101
1414 11101110
1515 11111111
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Binary Coded Decimal (BCD)
BCDBCD
00 00000000
11 00010001
22 00100010
33 00110011
44 01000100
55 01010101
66 01100110
77 01110111
88 1000100099 10011001
10101010
10111011
11001100
11011101
11101110
11111111
n
o
t
u
s
e
d
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Excess-3 (XS3)
XS3XS3
00000000
00010001
00100010
00 00110011
11 01000100
22 01010101
33 01100110
44 01110111
55 10001000
66 10011001
77 10101010
88 10111011
99 11001100
11011101
11101110
11111111
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Excess-3 (XS3)XS3XS3
00000000
00010001
00100010
00 00110011
11 01000100
22 01010101
33 01100110
44 01110111
55 10001000
66 10011001
77 10101010
88 10111011
99 11001100
11011101
11101110
11111111
Symmetric code
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Aiken codeAikenAiken
00 00000000
11 00010001
22 00100010
33 00110011
44 01000100
01010101
01100110
01110111
10001000
10011001
10101010
55 10111011
66 11001100
77 11011101
88 1110111099 11111111
2-4-2-1 Code
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Aiken code
AikenAiken
00 00000000
11 00010001
22 00100010
33 00110011
44 01000100
01010101
01100110
01110111
1000100010011001
10101010
55 10111011
66 11001100
77 11011101
88 11101110
99 11111111
Symmetric code
2-4-2-1 Code
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2-out-of-5
It is used as ErrorDetecting Code; natural even parity
VeryPracticalCode
22--outout--ofof--55
00 1100011000
11 0001100011
22 0010100101
33 0011000110
44 0100101001
55 0101001010
66 0110001100
77 1000110001
88 1001010010
99 1010010100
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2-out-of-5
22--outout--ofof--55
00 1100011000
11 0001100011
22 0010100101
33 0011000110
44 0100101001
55 0101001010
66 0110001100
77 1000110001
88 1001010010
99 1010010100Except for the zero (0)which is decimal 24. The
rest of the code followsthe weights: 74210 22
2-out-of-5
This code is used by theU.S. Postal Service---- Zip Code
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The first and last bars are the frame bars, used for aligningthe scanner which reads the bar-code. The last digits areused for error correction (checksum)..
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0 7 0 2 4 4 9 0 5
The first and last bars are the frame bars, used for aligningthe scanner which reads the bar-code. The last digits areused for error correction (checksum)..
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Bar Code based codes
11--D codesD codes
22--D codesD codes
PracticalCodes
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1-D codes
Code 39 = Code 3Code 39 = Code 3--ofof--9; alphanumeric (full ASCII)9; alphanumeric (full ASCII)bar code;bar code;applications in inventory, asset tracking, ID badgesapplications in inventory, asset tracking, ID badges
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1-D codes
Code 39 = Code 3Code 39 = Code 3--ofof--9; alphanumeric (full ASCII)9; alphanumeric (full ASCII)bar code;bar code;applications in inventory, asset tracking, ID badgesapplications in inventory, asset tracking, ID badges
Interleaved 2 of 5 ; NumericInterleaved 2 of 5 ; Numeric--only bar code,only bar code,industrial applications, carton labeling, laboratoryindustrial applications, carton labeling, laboratory
usesuses
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1-D codes
Code 39 = Code 3Code 39 = Code 3--ofof--9; alphanumeric (full ASCII)9; alphanumeric (full ASCII)bar code;bar code;applications in inventory, asset tracking, ID badgesapplications in inventory, asset tracking, ID badges
Interleaved 2 of 5 ; NumericInterleaved 2 of 5 ; Numeric--only bar code,only bar code,industrial applications, carton labeling, laboratoryindustrial applications, carton labeling, laboratory
usesuses UPC (Universal Product Code), Numeric Bar code;UPC (Universal Product Code), Numeric Bar code;
used in retail product labeling.used in retail product labeling.
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1-D codes
Code 39 = Code 3Code 39 = Code 3--ofof--9; alphanumeric (full ASCII)9; alphanumeric (full ASCII)bar code;bar code;applications in inventory, asset tracking, ID badgesapplications in inventory, asset tracking, ID badges
Interleaved 2 of 5 ; NumericInterleaved 2 of 5 ; Numeric--only bar code,only bar code,industrial applications, carton labeling, laboratoryindustrial applications, carton labeling, laboratoryusesuses
UPC (Universal Product Code), Numeric Bar code;UPC (Universal Product Code), Numeric Bar code;used in retail product labeling.used in retail product labeling.
Code 128Code 128 Alphanumeric (full ASCII);Alphanumeric (full ASCII);
applications in Shipping, Warehouse management.applications in Shipping, Warehouse management.30
2-D code
--PDF417;PDF417;applications web postage stamp..applications web postage stamp..
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PDF417
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PDF417
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Alphanumeric codes
Used to print, teletype or view informationUsed to print, teletype or view informationor other means of human alphaor other means of human alpha--numericnumericcommunication.communication.
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Alphanumeric codes
Used to print, teletype or view informationUsed to print, teletype or view informationor other means of human alphaor other means of human alpha--numericnumericcommunication.communication.
EBCIDIC
ASCII
UniCode
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EBCIDIC
EBCIDICEBCIDIC ((EExtendedxtended BCD IBCD Interchangenterchange CCode):ode):
8 bits = 256 characters.8 bits = 256 characters.
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ASCII
EBCIDIC (Extended BCD Interchange Code):EBCIDIC (Extended BCD Interchange Code):8 bits = 256 characters.8 bits = 256 characters.
ASCII (AASCII (Americanmerican SStandardtandard CCodeode forforIInformationnformation IInterchangenterchange):):
7 bits = 128 characters (now Super7 bits = 128 characters (now SuperASCII use all 8ASCII use all 8--bits ).bits ).
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ASCII
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Unicode
EBCIDIC (Extended BCD Interchange Code):EBCIDIC (Extended BCD Interchange Code):8 bits = 256 characters.8 bits = 256 characters.
ASCII (American Standard Code forASCII (American Standard Code forInformation Interchange):Information Interchange):7 bits = 128 characters.7 bits = 128 characters.
Unicode (New standard for 16Unicode (New standard for 16 bitbitalphanumeric codes)alphanumeric codes)
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A useful code is the Gray
Gray code is of cyclic nature having theGray code is of cyclic nature having thefollowing property:following property:
From one number to the next, the Gray codeFrom one number to the next, the Gray codechanges only one bitchanges only one bit
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Bit changes
Gray code is of cyclic nature having the following property:Gray code is of cyclic nature having the following property:
From one number to the next, the Gray codeFrom one number to the next, the Gray code changes onlychanges onlyone bitone bit
Binary
00
01 1
10 2
11 1
Gray
00
01 1
11 1
10 1
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Gray Code
The Gray code is used for labeling KarnaughThe Gray code is used for labeling Karnaughmaps for logic circuit simplification, formaps for logic circuit simplification, forrouting in parallel computer systems,routing in parallel computer systems,etc..etc..
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Gray Codes
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Gray Codes
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Gray Codes
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Binary and BCD numbers
Bits obtained from conversion, ofBits obtained from conversion, ofbinary numbers, are binary digitsbinary numbers, are binary digits
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Binary and BCD numbers
Bits obtained from conversion, ofBits obtained from conversion, ofbinary numbers, are binary digitsbinary numbers, are binary digits
Bits obtained from coding (BCD) areBits obtained from coding (BCD) arecombinations of 1s and 0s arrangedcombinations of 1s and 0s arrangedaccording to the rules of the codeaccording to the rules of the code(BCD).(BCD).
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Example-1
(13)(13)1010 = (1101)= (1101)22,,
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Example-1
(13)(13)1010 = (1101)= (1101)22,,
butbut,,
(13)(13)1010 = (0001 0011)= (0001 0011)BCDBCD
(1 3)(1 3)1010
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Example-2
(7)(7)1010 = (111)= (111)22,,
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Example-2
(7)(7)1010 = (111)= (111)22,,
but,but,
(0111)(0111)BCDBCD
771010
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Another Example
(15)(15)1010 = (1111)= (1111)22,,
but,but,
(15)(15)1010 = (0001 0101)= (0001 0101)BCDBCD
(1 5)(1 5)1010
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Binary & BCD
((1515))1010
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Binary & BCD
((1515))1010
((11111111))22 ()()BCDBCD
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Binary & BCD
((1515))1010
((11111111))22 ((00010001 01010101))BCDBCD
END
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New codes
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Code-A
AA
00 00000000
11 00010001
22 00100010
00110011
01000100
33 01010101
44 01100110
01110111
1000100055 10011001
66 10101010
10111011
11001100
77 11011101
88 11101110
99 11111111
Symmetric code
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Code-BBB
00 00000000
11 00010001
22 00100010
00110011
01000100
01010101
33 01100110
44 01110111
55 10001000
66 10011001
10101010
10111011
11001100
77 11011101
88 1110111099 11111111
Symmetric code
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Code-CCC
00 00000000
11 00010001
22 00100010
33 00110011
01000100
01010101
01100110
44 01110111
55 10001000
10011001
10101010
10111011
66 11001100
77 11011101
88 1110111099 11111111
Symmetric code