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Binary Codes

  • bit is just called as binary digit
  • To represent 2n elements, n bits are needed

Here are the following Binary Codes,

image

For example, the BCD code is otherwise called as 8421 code where the 8,4,2,1 are the weights assigned to the digits

for number 3 (0011), the weightage will be 0 * 8 + 0 * 4 + 1 * 2 + 1 *1

in 84-2-1 code, the weights are arranged like this,

for example, for number 2 (0110),  it is 0 * 8 + 1 * 4 + 1 * –2 + 0 * –1

similarly the same case for 2421 codes.

Excess – 3 is a code which is in excess of 3 in decimal numbers .

Error Detection Codes

  • Binary information is usually transmitted from one place to other through wired medium, due to the electromagnetic radiation or external noise, the information bits can be changed (ie 1 to 0 or 0 to 1), in this scenario, there is a provision to check whether the given word or byte is correct or not. Parity bits are used for that.
  • Odd parity or even parity is adopted based on the application, but mostly even parity is adopted.
  • Parity bit is an extra bit added along with the given byte to make the number of 1’s in the total word is even or odd (based on even or odd parity)
Message odd parity bit Message Even parity bit
0000 1 0000 0
0001 0 0001 1
0010 0 0010 1
0011 0 0011 0
0100 0 0100 1
0101 1 0101 0
0110 1 0110 0
0111 0 0111 1
1000 1 1000 1
1001 1 1001 0
1010 1 1010 0
1011 0 1011 1
1100 1 1100 0
1101 0 1101 1
1110 0 1110 1
1111 1 1111 0

Gray Code

Gray code is different from binary code in which only one bit change is there in the code group. Moving from one number to another number, there is just only one bit change. here is an example of Gray Code

Gray Code Decimal Equivalent
0000 0
0001 1
0011 2
0010 3
0110 4
0111 5
0101 6
0100 7
1100 8
1101 9
1111 10
1110 11
1010 12
1011 13
1001 14
1000 15

 

Other Alpha Numeric Codes

  • ASCII (American Standard Code for Information Interchange)
    • used in Keywords,
    • take 7 bit data
    • can able to address 128 characters

image

  • EBCIC  (Extended Binary Coded Decimal Interchange Code)
    • This code is from IBM
    • uses 8 bits, so addresses up to 256

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