Exercise 2 solution

    from datetime import datetime, timezone, timedelta

    EPOCH = datetime(1970, 1, 1, tzinfo=timezone.utc)

    def wrap32(n):
        n &= 0xFFFFFFFF
        return n - 2**32 if n >= 2**31 else n

    last = 2**31 - 1
    print("Last signed second:", last, EPOCH + timedelta(seconds=last))
    print("Wrapped next value:", wrap32(last + 1), EPOCH + timedelta(seconds=wrap32(last + 1)))
    now = datetime(2026, 11, 2, 12, 0, tzinfo=timezone.utc)
    left = (EPOCH + timedelta(seconds=last)) - now
    print("Time left:", left)
    print("Whole days:", left.days)
    print("Last unsigned second:", EPOCH + timedelta(seconds=2**32 - 1))
    for n in (last - 1, last, last + 1, last + 2, 2**32 - 1, 2**32):
        print(n, "->", wrap32(n))

Output (run, and exactly as shown):

    Last signed second: 2147483647 2038-01-19 03:14:07+00:00
    Wrapped next value: -2147483648 1901-12-13 20:45:52+00:00
    Time left: 4095 days, 15:14:07
    Whole days: 4095
    Last unsigned second: 2106-02-07 06:28:15+00:00
    2147483646 -> 2147483646
    2147483647 -> 2147483647
    2147483648 -> -2147483648
    2147483649 -> -2147483647
    4294967295 -> -1
    4294967296 -> 0

Explanation: 2**31 - 1 is the largest signed 32-bit value. One second later
the bit pattern reads as -2**31, which is a date in 1901, so software that
stores seconds in a signed 32-bit integer jumps backwards. The unsigned
limit, 2**32 - 1, is 68 years further on. Python integers never overflow, so
wrap32 simulates what a fixed-width integer would do. The fix is to store
64-bit values (or microseconds in 64 bits), not to change the epoch.