As far as I understand, scopes with an 8 bit A/D have 7 bits of resolution above the line and 7 bits below. If you’re looking at a waveform with alternating polarity, that’s fine. What about when you are looking at a waveform that is only positive going, for example. You only have 7 bit resolution. Do any scopes have the option of using the full 8 bits in this situation, with the expectation that there can be no display below the line? Maybe unsigned is the wrong word. Single polarity only, maybe.
That's what the vertical position adjustment is meant for. Actually, the 8 bits (of which anyway < 7 bits are valid -- check the typical ADC datasheets...) are (typically) what you see on the screen (there may be a slight extension beyond the screen borders of maybe 10 or 20%). The offset is generated by injecting a DC voltage into the scope's analog front end, so if you offset the trace right to the bottom line of the graticule, all the available resolution is in the positive input range and vice versa.