Binary and Decimal Codes: BCD, Gray, and ASCII, Slides of Digital Logic Design and Programming

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Codes

Class 3 outline

• Alphanumeric Codes
  • ASCII
  • Parity
• Gray Codes
• Material from sections 1-5 and 1-6 of text

Binary Codes

• “An n -bit binary code is a group of n bits that

assume up to 2 n^ distinct combinations of 1s

and 0s, with each combination representing

one element of the set being coded”

• For the 10 digits need a 4 bit code. One code

is called Binary Coded Decimal (BCD)

Decimal and BCD

• The BCD is simply the 4

bit representation of the

decimal digit.

• For multiple digit base 10

numbers, each symbol is

represented by its BCD

digit

• What happened to 6

digits not used?

Another

• A second example
  • 3 0 0 1 1
  • +3 0 0 1 1
  • Getting 6 or 0 1 1 0
  • And in range and a BCD digit representation

And now

• Consider 5 + 5
• 5 0 1 0 1
• +5 0 1 0 1
• giving 1 0 1 0 which is binary 10 but not

a BCD digit!

• What to do?
• Try adding 6??

Another carry example

• Add 7 + 6
  • have 7 0 1 1 1
  • plus 6 0 1 1 0
  • Giving 1 1 0 1 and again out of range
  • Adding 6 0 1 1 0
  • Giving 1 0 0 1 1 so a 1 carries out to the next BCD digit
  • FINAL BCD answer 0001 0011 or 13 (^10)

Multibit BCD

• • Add the BCD for 417 to
• • Would expect to get
  • – – BCD setup - start with Least Significant Digit
  • –
  • –
  • – Adding
  • – Gives

Still Continuing multibit

• Had a carry to the 3rd BCD digit position
  • 1
  • 0 1 0 0 done done
  • 0 0 0 1 0 0 0 1 0 0 1 0
  • 0 1 1 0
  • And answer is 0110 0001 0010 or the BCD for the base 10 number 612

Alphanumeric Codes

• How do you handle alphanumeric data?
• Easy answer!
• Formulate a binary code to represent

characters! 

• For the 26 letter of the alphabet would need

5 bit for representation.

• But what about the upper case and lower

case, and the digits, and special characters

ASCII Code

• Represents the numbers
  • All start 011 xxxx and the xxxx is the BCD for the digit
• Represent the characters of the alphabet
  • Start with either 100, 101, 110, or 111
  • A few special characters are in this area
• Start with 010 – space and !”#$%&’()*+.-,/
• Start with 000 or 001 – control char like ESC

ASCII Example

• Encoding of 123
  • 011 0001 011 0010 011 0011
• Encoding of Joanne
  • 100 1010 110 1111 110 0001
  • 110 1110 110 1110 110 0101
• Note that these are 7 bit codes

Example of Parity

• Consider data 100 0001
  • Even Parity 0100 0001
  • Odd Parity 1100 0001
• Consider data 1010100
  • Even Parity 1101 0100
  • Odd Parity 0101 0100
• A parity code can be used for ASCII characters

and any binary data.

Other Character Codes

• Once upon a time, a long, long time ago, there

existed cards, called punch cards!

• And a code for those cards called Hollerith code. (patented in 1889)
• The code told you what character was being represented in a column when there was a punch out in various rows of that column.
• And another code for characters called EBCDIC

(Extended Binary Coded Decimal Interchange

Code) (1963, 1964 IBM) - similar to ASCII –

• Digits are coded F0 through F9 in EBCDIC