## The 1 bit = 6 dB Rule of Thumb, Revisited.

March 28, 2017

Almost ten years ago I wrote an entry about the “1 bit = 6 dB” rule of thumb. This rule states that for each bit you add to a signal, you add 6 dB of signal to noise ratio.

The first derivation I gave then was focused on the noise, where the noise maximal amplitude was proportional to the amplitude represented by the last bit of the (encoded) signal. Let’s now derive it from the most significant bit of the signal to its least significant.

## Deriving the 1 bit = 6 dB rule of thumb

December 9, 2008

This week, a more mathematical topic. Sometime ago, we—friends and I—were discussing the fidelity of various signals, and how many bits were needed for an optimal digitization of the signal, given known characteristics such as spectrum and signal-to-noise ratio.

Indeed, at some point, when adding bits, you only add more power to represent noise in the signal. There’s a rule of thumb that say that for every bit you add, you can represent a signal with $\approx 6 dB$ more of signal to noise ratio. Let me show you how you derive such a result.