Audio Signal dB levels Matlab
It is not correct to have 0dB represent "off". dB is a relative scale and 0 dB, effectively, means "the same as some reference value", and your reference value can't be silence.

A more common implementation of such a control would be to have 0dB represent maximum volume and negative values represent lower output. This is what you see on all professional audio equipment analog and digital. You would then use -Infinity for no output. Many applications approximate this by making the slider go from 0 at the top to -96 [1] dB or so at the bottom. When the user slides the slider down all the way, the application will turn off the output.

[1] 96 is chosen because that's the approximate dynamic range of 16-bit audio. In the presence of dither, this value has no real special meaning, though, so some applications use an even larger value.