Exercise 2 solution

    import struct


    def pack_date(year, month, day):
        if not (1980 <= year <= 2107 and 1 <= month <= 12 and 1 <= day <= 31):
            raise ValueError("date out of range")
        return ((year - 1980) << 9) | (month << 5) | day


    def pack_time(hour, minute, second):
        if not (0 <= hour <= 23 and 0 <= minute <= 59 and 0 <= second <= 59):
            raise ValueError("time out of range")
        return (hour << 11) | (minute << 5) | (second // 2)


    def unpack_date(value):
        return (value >> 9) + 1980, (value >> 5) & 0x0F, value & 0x1F


    def unpack_time(value):
        return value >> 11, (value >> 5) & 0x3F, (value & 0x1F) * 2


    d = pack_date(2026, 11, 2)
    t = pack_time(14, 30, 45)
    print(hex(d), hex(t))
    print(unpack_date(d), unpack_time(t))
    print(struct.pack("<HH", t, d).hex(" "))
    print(unpack_time(pack_time(14, 30, 45)), unpack_time(pack_time(14, 30, 44)))

    for label, call in [
        ("year", lambda: pack_date(1979, 1, 1)),
        ("month", lambda: pack_date(2026, 13, 1)),
        ("second", lambda: pack_time(0, 0, 60)),
    ]:
        try:
            call()
        except ValueError as e:
            print(label, "->", e)

    print(all(unpack_date(pack_date(y, m, dd)) == (y, m, dd)
              for y in (1980, 2026, 2107) for m in range(1, 13) for dd in (1, 15, 31)))

    # 0x5d62 0x73d6
    # (2026, 11, 2) (14, 30, 44)
    # d6 73 62 5d
    # (14, 30, 44) (14, 30, 44)
    # year -> date out of range
    # month -> date out of range
    # second -> time out of range
    # True

(Run as written; the output matched the comments.)

Explanation: Packing shifts each field to its place and ORs them together; unpacking
shifts each field back down and masks it to its width. The time stores seconds
divided by 2 in five bits, so 45 and 44 both come back as 44: the odd second is lost
on the way in, and nothing can restore it. The two 16-bit values are written
little-endian, so 0x73d6 appears in the file as d6 73. The day check of 31 is only a
range check; it does not know which months are shorter.