DIGITAL CODES

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DIGITAL CODES PARITY
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Binary Codes
A binary code is a group of n bits that assume up
to 2n distinct combinations of 1s and 0s with
each combination representing one element of the
set that is being coded.
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Codes and Parity

• Concept of a code, weighted and non-weighted
  codes, examples of 8421, BCD, excess-3 and Gray
  code
• Alphanumeric codes ASCII and EBCDIC
• Concept of parity, single and double parity and
  error detection

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Binary Digital Codes

• Gray Code Gray Code
• BCD 2421 BCD 2421 code
• BCD XS 3 BCD Excess 3 code
• BCD 8421 BCD 8421 code
• EBCDIC Extended BCD Interchange Code

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BCD Binary Coded Decimal

• BCD is a convention for mapping binary numbers to
  decimal numbers.
• When the decimal numbers are represented in BCD,
  each decimal digit is represented by the
  equivalent BCD code.
• Example BCD Representation of Decimal 6349

6 3 4 9 0110 0011 0100 1001
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BCD Binary Coded Decimal
Decimal BCD Number Number 0 0000
1 0001 2 0010 3 0011
4 0100 5 0101 6 0110
7 0111 8 1000 9 1001
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BCD Binary Coded Decimal
Decimal BCD Number Number 10 0001
0000 121 0001 0010 0001 234 0010 0011
0100 1003 0001 0000 0000 0011
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EXCESS 3 CODE

• The excess-3 code is obtained by adding 3 (0011)
  to the corresponding BCD equivalent binary
  number.
• Excess-3 have a self-complementing property

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EXCESS 3 CODE
Decimal BCD Excess-3 Number Number
Number 0 0000 0011 1
0001 0100 2 0010 0101 3
0011 0110 4 0100 0111 5
0101 1000 6 0110 1001 7
0111 1010 8 1000 1011 9
1001 1100
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BCD-to-Excess-3 Table
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BCD 2421 CODE

• 2421 and excess-3 have a self-complementing
  property
• 9s complement is obtained by 1s to 0s and 0s
  to 1s.
• Useful property when doing arithmetic operations
  with signed complement representation.
• 2421 is a weighted code
• Decimal equivalent if obtained by multiplying
  bits by the weights
• Ex 1101 gt 2 x 1 4 x 1 2 x 0 1 x 1 7

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ASCII

• ASCII (American Standard for Information
  Interchange)
• Uses 7 bits to code 128 characters upper and
  lowercase letters, decimal digits, and special
  characters, e.g.

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ASCII
Number ASCII Letter ASCII
0 0110000 1 0110001 2 0110010 3 0110011 4 0110100
5 0110101 6 0110110 7 0110111 8 0111000 9 0111001
A 1000001 B 1000010 C 1000011 D 1000100 E 1000101
F 1000110 G 1000111 H 1001000 I 1001001
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ASCII
Letter ASCII Letter ASCII
J 1001010 K 1001011 L 1001100 M 1001101 N 1001110
O 1001111 P 1010000 Q 1010001 R 1010010
S 1010011 T 1010100 U 1010101 V 1010110 W 1010111
X 1011000 Y 1011001 Z 1011010
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ASCII TABLE
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ASCII TABLE
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EBCDIC ALPHANUMERIC CODE
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GRAY CODE

• Unweighted and is not an arithmetic code
• Only one bit changes from one code to the next in
  the sequence
• Gray code can be any amounts of bits.
• The gray code originated when digital logic
  circuits were built from vacuum tubes and
  electromechanical relays
• Counters generated tremendous power demands and
  noise spikes when many bits changed at once
• Using gray code counters, any increment or
  decrement changed only one bit

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GRAY CODE
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VARIOUS DECIMAL CODES
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PARITY

• Parity bit used for bit error detection
• Even parity total number of 1s even
• Odd parity total number of 1s odd
• Example (even parity)
• Code transmitted 00101
• ?1s total even parity bit 0
• Code received 00001
• ?1s total odd parity bit 0 ? error

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PARITY
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Try this. Fill in the appropriate parity bit.
PARITY
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End of Digital Codes Parity