Question 37

Components of the 50-bit Globally Unique ID:

• Every host has a globally unique IPv4 address, which occupies $32$ bits.
• Remaining bits for host-local identification: $50 - 32 = 18$ bits.

Bit Allocation for Unique IDs per Second:

• Each host generates up to $1000$ unique identifiers per second.
• To represent $1000$ distinct counter values within a single second, the required number of bits is:
  $$\lceil \log_2 1000 \rceil = 10\text{ bits}\quad (2^{10} = 1024 \ge 1000).$$

Remaining Bits for the Seconds Timestamp:

• Bits remaining for the 1-second resolution clock counter:
  $$18 - 10 = 8\text{ bits}.$$

Wrap-around Period:

• An 8-bit timestamp counter can count $2^8 = 256$ distinct seconds before wrapping back to zero.
• Therefore, the identifiers generated by a host will wrap around after 256 seconds.