Every host in an IPv4 network has a 1-second resolution real-time clock with battery backup. Each host needs to generate up to 1000 unique identifiers per second. Assume that each host has a globally unique IPv4 address. Design a 50-bit globally unique ID for this purpose. After what period (in seconds) will the identifiers generated by a host wrap around?

A globally unique 50-bit ID consists of three components:

1. Host IPv4 address: A standard IPv4 address requires $32$ bits to uniquely identify the host globally [2].

2. Counter for unique IDs per second: To generate up to $1000$ unique identifiers per second, the number of bits required is $\lceil \log_2(1000) \rceil = 10$ bits (since $2^{10} = 1024 \ge 1000$).

3. Timestamp (in seconds): The remaining bits available for the real-time clock timestamp are:

With $8$ bits allocated for the timestamp at a $1$-second resolution, the counter wraps around after: