Mind you, presumably, some civilizations in our universe will go on beyond that. Referencing this† chart, silicon-based life (e.g. maybe even us humans, if uploaded into computers) might be able to survive about half-way into "the Degenerate Era", before the material substrate we run on just radiates away through proton decay. Representing the last second life could exist would require a continuum of 4e32 seconds, or 108 bits.
† https://en.wikipedia.org/wiki/Graphical_timeline_from_Big_Ba...
And also keep in mind, computers (including any silicon-based life-forms) think much faster, and so are in want of much more fine-grained measurements than our unit of "seconds" to place events on their own timelines. We already use nanosecond timestamps for our computer-system-internal log events (which would add a 30-bit fractional part to our 108-bit timestamp, to create a combined 138-bit fixed-point representation.)
But let's be "safe." We don't know how fine-grained we'll need to get! We might want to record data about the first events of our universe, for example. I would think that a "really ultimate", future-proof, archival format for time record-keeping, would probably be denominated in Planck time units.
Interestingly, counting in Planck time units instead of nanoseconds, "only" requires 144 bits for the fractional part!
108 + 144 = 252. Or, rounding up, 256. We could represent any instant of time we could ever care about, in fixed-point encoding††, in a 256-bit word.
†† (It wouldn't really be fixed-point encoding. It'd just be an integer number of Planck time units since the Big Bang. But you can right-shift by 144 to get something close to a count of seconds, which is useful.)
Finally: you still want more? Any time between the creation and heat death of the universe, even though nothing will be around to experience it? Well, that'd be 333 bits worth of seconds. 333 + 144 = 477, which would fit a 512-bit machine word.
One could assume, then, that any Matrix-like universe simulation substrate will have a 512-bit Time Stamp Counter register.
...presuming, that is, that it was built to simulate a universe like our own, and not one that has finer-grained Planck units or which goes on for longer. :)
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Does all of this have any use? Maybe! If we could figure out precisely what time it is in some objective sense—how many Planck time units have passed here in our reference frame since the creation of the universe—that might be a useful "handshake format" to describe "when" something happened to aliens, when building things like Voyager's Golden Record. (After all, we can teach them about our calendar, but how do we describe+transmit when our calendar began in a way they can measure against in their reference frame, in order to know how to do the math to translate dates back and forth?)