How many addresses are enough?

The Internet Protocol version 4 assigns each connected computer a 4-byte address known as an IP address. Each message, or packet, includes this address so that routers know where to forward it. This is the Internet's version of mailing addresses. Each region of the world has been given a range of IP addresses to administer locally, with America taking the largest share. Asia, with a significantly larger population, received a disproportionately small range of numbers and is afraid of running out. Anticipating this problem, the Internet Engineering Task Force adopted IPv6, which uses addresses 16 bytes long. Although slow to be adopted, all Internet root servers now support IPv6, and Internet service providers are rolling it out as needed while maintaining backward compatibility for IPv4. The U.S. federal government had mandated the change to IPv6 for all federal agencies by 2008.

a. Express as a power of 2 the number of nodes that can exist using IPv4.
b. Express as a power of 2 the number of nodes that can exist using IPv6.