What percentage of the address space of IP4 do the network classes of A, B, and C represent? ( Hint: Think of the classes in terms of power of 2.)
To determine the percentage of the address space represented by the network classes A, B, and C in IPv4, we need to consider the total number of available addresses in each class.
Class A addresses have a 1-byte network portion and a 3-byte host portion. This means that the first octet (8 bits) represents the network portion of the address, and the remaining three octets (24 bits) represent the host portion. Therefore, Class A addresses have a total of 2^7 (128) network IDs.
Class B addresses have a 2-byte network portion and a 2-byte host portion. This means that the first two octets (16 bits) represent the network portion, and the remaining two octets (16 bits) represent the host portion. Class B addresses have a total of 2^14 (16,384) network IDs.
Class C addresses have a 3-byte network portion and a 1-byte host portion. This means that the first three octets (24 bits) represent the network portion, and the last octet (8 bits) represents the host portion. Class C addresses have a total of 2^21 (2,097,152) network IDs.
To calculate the percentage, we need to sum up the total number of network IDs for the three classes (A, B, C) and divide each class's network IDs by this total.
Total network IDs = 2^7 + 2^14 + 2^21 = 128 + 16,384 + 2,097,152 = 2,113,664
Percentage of Class A = (2^7 / Total network IDs) * 100
Percentage of Class B = (2^14 / Total network IDs) * 100
Percentage of Class C = (2^21 / Total network IDs) * 100
Now we can calculate each percentage:
Percentage of Class A = (128 / 2,113,664) * 100 ≈ 0.00607%
Percentage of Class B = (16,384 / 2,113,664) * 100 ≈ 0.7749%
Percentage of Class C = (2,097,152 / 2,113,664) * 100 ≈ 99.218%
Therefore, Class A represents approximately 0.00607% of the address space, Class B represents approximately 0.7749%, and Class C represents approximately 99.218%.