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Computer Organization and Architecture/Introduction to Computer Organization and Architecture

Notes 7. Error Correcting Codes: These codes not only detect errors in data, but also correct them
significantly. Error correction codes are a method by which a set of symbols can be represented
such that even if any 1 bit of the representation gets accidentally flipped, we can still clearly
identify the earlier symbol. Error correcting codes depend mainly on the notations and results
of linear algebra. Error correction can be done using many methods like parity checking,
Hamming codes, Single-bit Error Correction Double-bit Error Correction (SECDED), and so
on.

Notes Error correcting codes are used in memories, networking, CDROM, and so on.

Example: Error correction using parity checking is as follows:
In parity check, an extra bit is added to the binary number to make all the digits
in the binary number to sum up to an even or odd value. When the number adds
up to an even number, we call it even parity and when the number sums up to an
odd number, we call it odd parity. Consider the following two binary numbers:
1011010
1101011
Now, if we want to use even parity, we can add a parity bit to these numbers to
obtain an even number as shown below:

01011010 4
11101011 6
If we want to use odd parity, we can add a parity bit to the number as follows:
11011010 5
01101011 5
Most of the modern applications use even parity. Let us consider even parity in
our example.
The two binary numbers that need to be transmitted are:
01011010……………….The even parity

11101011……………….The even parity
Suppose during transmission the bits get changed as follows:
01111010 5
10101011 5

We can observe that the digits in the number sum up to odd numbers. Since we
are using even parity, the computer knows that there is an error in the
transmission.

8. Alphanumeric Codes: These are codes that consist of both numbers and alphabets. The most
commonly used alphanumeric codes are ASCII and EBCDIC.

(a) EBCDIC Code: EBCDIC (Extended Binary Coded Decimal Interchange) is mainly used
with large computer systems like mainframe computers. It is an 8-bit code which
accommodates up to 256 characters.

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