$*16\mathrm{.}22$ A logic$-$circuit type intended for use in a digital$-$signal$-$processing application in a newly developed hearing aid can operate down to single$-$cell supply voltages of $0\mathrm{.}9$ V$.$ If for its inverter, the output signals swing between $0$ and VDD$,$ the $$gain$-$of$-$one$$ points are separated by less than $|$ VDD$,$ and the noise margins are within $30\%$ of one another, what ranges of values of VIL, VIH, Vol, V$()$H$,$ NML$,$ and NMU can you expect for the lowest possible battery supply?