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WHAT'S YOUR ENGINEERING QUOTIENT?

Problem 6—For a given bit error rate, how do you calculate the probability of an error in an 8-bit byte?

If the probability of a bit error is p, then the probability of an error-free bit is 1–p. The probability of an error-free byte of 8 bits is (1–p)⁸. Therefore, the probability of a byte error is 1–(1–p)⁸.

For small values of p, this can be approximated as 8×p, but this breaks down at higher bit error rates, as shown in the following table:

p	1–(1–p)8	8×p
0.00001	0.0000799972	0.00008
0.0001	0.00079972	0.0008
0.001	0.0079721	0.008
0.01	0.07726	0.08
0.1	0.5695	0.8

Contributor: Dave Tweed

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