MAC7200 datasheet(474/976 Pages) FREESCALE

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Hamming Algorithm

MAC7200 Microcontroller Family Reference Manual, Rev. 2

396

Freescale Semiconductor

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p = 4 bits of ECC

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Code Word = __1_001_1010

NOTE

Remember code word positions 1, 2, 4, and 8 are reserved, so the msb of the

data byte is placed in position 3, the next in position 5, etc.

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Position 1 checks every other bit position 1, 3, 5, 7, 9, 11: (? represents the bit position being set)

? _ 1 _ 0 0 1 _ 1 0 1 0

: Even parity so position 1 set to a 0.

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Position 2 checks two bits, skips two bits 2, 3, 6, 7, 10, 11 (Notice it checks 2, skips 2, etc)

0 ? 1 _ 0 0 1 _ 1 0 1 0

: Odd parity so position 2 set to a 1.

•

Position 4 checks 4 bits starting with position 4, then skips 4, etc. Each parity bit continues in the

same way checking and skipping the same number as its position.

0 1 1 ? 0 0 1 _ 1 0 1 0

: Odd parity so position 4 set to a 1.

0 1 1 1 0 0 1 ? 1 0 1 0

: Even parity so position 8 set to a 0.

The resulting 12-bit code word is 011100101010. To create the syndrome, the code word is decoded.

Each of the 4 parity combinations are checked again using the same method as above, but now on the

completed 12bit code word. If the code word does not change, the syndrome will equal all zeros. If, for

example, if the bit in position 3 of the code word is inverted, the generated syndrome will be {position

8,4,2,1} = 4’b0011 ~ 3. Bit 1 of the syndrome is decoded as the parity of positions 1, 3, 5, 7, 9, 11. If bit

position 3 has flipped, then the number of 1’s has changed from 4 to 3. Therefore this syndrome bit is

assigned a 1 because the parity of the positions it calculates is odd. The same occurs for syndrome bit 2.

The entire syndrome decodes to 3. This number gives the exact bit position in the code word to be

corrected.

Adding one more ECC bit to check the parity of the entire code word allows for double bit detection. In

the PRAM_CTL this bit is based on odd parity. Therefore, for the example above, an odd parity based

ECC bit would be assigned the value 1’b1 and added to the end of the code word to make the entire code

word odd (there are 6 1’s otherwise in the code word). When code word bit 3 flips, the parity of the entire

codeword becomes even, signalling a single-bit error when the syndrome is non-zero. If the syndrome is

non-zero, and the parity check of the entire code word is a one (odd), then at least two bits must have

changed.

19.3.1.3

Hamming Parity Code Table

This simple Hamming code is nearly the same algorithm used in the PRAM_CTL, but on a larger scale of

32 bits at a time. Table 19-9 shows the would be relationship between each data bit and the ECC bits for

the basic Hamming Code. For each column, an ’X’ represents the inclusion of the corresponding data bit

in the XOR equation for the corresponding ECC bit. For instance, data bit 31 goes into the equations for

calculating ECC bits 0 and 1. Therefore, if the resulting syndrome is 6’b000011 ~ 3, then data bit 31 would

be corrected.

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