The equation to calculate dB

[Xiao Z]

In p.145 of Elements, it writes “the ratio is 255, so the difference in dB is 20 * log255”. But I remember log(ratio) should time 10 instead 20.

Also I was wondering why 8bits and 16bits are used normally. I mean, will something go wrong if we choose 9-15bits?

[Simon King]

[please ask one question per post – see the topic bit depth for your second question]

dB is always 10 log(ratio) because the 10 is converting from Bels to decibels

the 20 comes from 10 log (ratio^2), where the raising to the power of 2 is converting magnitude to power

remember that log(x . x) = log(x) + log(x) = 2 log(x)

the key point to remember is that dB is a logarithmic scale, which is generally much more useful, when plotting a spectrum for example

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