Lab $4.$O $$ Hamming Code

DESCRIPTION

The Hamming code is a special technique for encoding and decoding information to enable error

detection and correction. Richard Hamming published his work in $1951.$ The high cost of

hardware in the past made this technique costly and, therefore, not practical. A CRAY computer

design was released to the marketplace which uses single error correcting techniques as

described in the Hamming paper.

ENCODING

A significant feature of the Hamming code is that all components of the algorithm are

mathematically sound and practical. The encoding procedure is to compute $$even parity$$ bits

based on the information to be transmitted and send those parity bits along with the transmitted

information. If the information contains $4$ bits $($abcd$),$ then three parity bits $($rst$)$ are needed.

These parity bits are called check bits. The encoded message is then structured as:

position $7654321$

bit a b c r d s t

where:

r is set to create even parity for bits $7,6,5$ and $4$;

s is set to create even parity for bits $7,6,3$ and $2$;

t is set to create even parity for bits $7,5,3$ and $1.$

You are to encode the contents of a byte in memory where the information bits a$,$ b$,$ c and d are

located as shown in the following:

xxxxabcd

For example, suppose that you have the following memory configuration, your task would be to

compose the encoded bytes as shown:

Memory Encoded Message

$2274$ xxxx$101101010101$

$2275$ xxxx$100101001100$

$2276$ xxxx$001100111110$