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Hamming Algorithm

MAC7200 Microcontroller Family Reference Manual, Rev. 2

Freescale Semiconductor

395

19.2.4

Initialization/Application Information

It is essential that each memory address be written to a known value before it is read. This includes reads

generated from the read/modify/write operation which occurs when a write transfer of less than 32 bits or

unaligned write is requested (see Section 19.2.3.5.2, “Less than 32-bit Writes”). Without writing an

address to a known value first, a read from this address will most likely generate an ECC multiple error.

19.3

Hamming Algorithm

19.3.1

Basic Algorithm

The ECC algorithm is a modified form of the basic Hamming code. First is a description of how the basic

Hamming Code is calculated.

19.3.1.1

The Hamming Rule

The number of parity bits required to detect a single-bit error is given by the Hamming rule, and is a

function of the number of bits of information transmitted. The Hamming rule is expressed by the

following inequality:

Eqn. 19-3

Where d is the number of data bits, and p is the number of parity (ECC) bits. Therefore, to code 32 bits

of data and detect single errors, 6 ECC bits are needed. By adding an extra ECC bit to check the overall

parity of the entire code word, two-bit errors can be detected.

19.3.1.2

Creating A Hamming Codeword

The code word can be created as follows. (Assume the code word bit positions to be laid out as follows:

msb < position 1, 2, 3, .... d+p-1, d+p > lsb, this is contradictory notation from the actual rtl notation where

the msb is labelled with the highest number as in syndrome[6:0])

1. Mark all bit positions in the code word that are powers of two as ECC bits. (position 1, 2, 4, 8, 16,

etc.)

2. Place the data to be encoded in remaining bit positions skipping positions reserved for ECC bits.

(data_bit[x] goes into position 3, data_bit[x-1] is placed into position 5, data_bit[x-2] into

position 6, etc.)

3. Each ECC bit calculates the parity for some of the bits in the code word. The position of the ECC

bit determines the sequence of bits that it alternately checks and skips in its parity calculation

beginning with its own position.

4. These Hamming ECC bits are based on even parity, therefore if the total number of 1’s in the

positions it checks is odd, the parity bit is set to a 1 to make the entire parity check even. If the

total number of 1’s in the positions checked is even, the parity bit is set to 0.

Example

•

Data Byte = 10011010

dp1

≤

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