Ultimate units

The first bit is the most practical, then it gets difficult.

Use the Planck time as the basic unit of time, the Planck length as the unit of length, the velocity of light in vacuo as the unit of velocity, the mass of the electron as the unit of mass and the charge of the electron as the unit of electrical charge. Define other units from these terms. Rather than using the usual decimal multiple units, use the binary multiple system kibi-, mebi- and so forth. No subunits are needed, because nothing physical can be said to exist at a smaller scale than the basic units.

Two more, less practical, proposals. Base the calendar on these units. This is not in itself difficult, but finding a date to count from is unless an event in the early Universe can be pinpointed. Clearly the Big Bang is the most important such event, but it can't be precisely dated. Therefore, provisionally, choose the Julian date until a better one comes along. This would unfortunately mean there would be negative dates.

Clearly days would be a peculiar number of units in length, as would years, but these are parochial considerations based on an insignificant little blue-green planet orbiting an unregarded yellow sun rather than anything that really matters.

The other proposal, even less practical, is to get the whole population of the planet to abandon their current counting systems in favour of binary. Rather than using cumbersome long strings of ones and zeroes, however, they are to say the sounds /i/ for one and /o/ for zero separated by glottal stops, and there would be no ambiguity.

There you go, it's all sorted.