MAC7200 datasheet(475/976 Pages) FREESCALE

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Hamming Algorithm

MAC7200 Microcontroller Family Reference Manual, Rev. 2

Freescale Semiconductor

397

19.3.1.4

PRAM_CTL Implementation

Although correct, the above table is not the most efficient way to map the 64 possible codes to the 32 data

bits for harware purposes. In Table 19-9, the first codeword used is 6’b000011. Each consecutive

codeword increments by 1, skipping each codeword which is a factor of 2. Notice above that each data bit

must factor into at least 2 parity bit equations. Another way to say all of this is at least 2 parity bits must

be used to cover a data bit.

Also notice that not all of the codewords are used. The final code word used, 6’b100110, is on data bit 0.

This leaves all of the codewords from 100111 to 111111 unused. By intelligently changing out codewords

with a large number of Xs for unused codewords with fewer 1’s in them, we can reduce the loading on the

data bits as well as more evenly distribute the number of data bits needed to calculate each parity bit. In

Table 19-10, you can see the number of data bits (or Xs in each row on the table) that are used to calculate

each parity bit. There is an average of 15 with a critical path of 18 data bits to XOR.

By creatively substituting some of the unused codewords we can balance the delay for each parity bit and

decrease the loading on the data bits. Table 19-11 shows a modified Hamming code where data bits 6, 7,

8, 10, 14, 21 and 22 have had their codewords changed for unused codewords. With this implementation

the average number of data bits to be XOR’ed for each parity bit reduces to 13.5 and the critical path

reduces to 14 data bits.

Table 19-9. Parity Codes: ECC Bits vs. Data Bits

XXX

XXXXXXXX

XXX

Table 19-10. Hamming Parity Delay

ParityBit

# Data Bits

415

315

218

118

018

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