Essentially, IPv4 addresses[2] are just numbers from 1 to 2147483647, for example 3405804031. However, since address routing is often based on common binary prefix, more intuitive methods like 203.0.113.255 are used. This notation is just a length-4 list of integers from 0 to 255. To convert from an integer to a common IP address, you divide-with-remainder with a constant divisor of 256. For example, 3405804031 /% 256 = (13303921,256), 13303921 /% 256 = (51968,113), 51968 /% 256 = (203,0), and 203 /% 256 = (0,203).[1] Collecting all the remainders in reverse order, then joining them with periods, produces 203.0.113.255. (This notation is just for people to read; aside from parsing code, none of IPv4 uses this notation.) When you enter an IPv4 address, the opposite happens — an expression like ((203 * 256 + 0) * 256 + 113) * 256 + 255, which evaluates to 3405804031, is performed. These octets are just numbers — using 203.000.113.255 or 203.00.113.255 in place of 203.0.113.255 is merely a choice of how to write the address, as 203 * 256 + 0 = 203 * 256 + 000. mraow
[1]: this operation can be omitted; I include it for symmetry.
[2]: though all of this holds true for IPv6, I really didn’t feel like going through 128 bits of address
Essentially, IPv4 addresses[2] are just numbers from 1 to 2147483647, for example 3405804031. However, since address routing is often based on common binary prefix, more intuitive methods like 203.0.113.255 are used. This notation is just a length-4 list of integers from 0 to 255. To convert from an integer to a common IP address, you divide-with-remainder with a constant divisor of 256. For example, 3405804031 /% 256 = (13303921,256), 13303921 /% 256 = (51968,113), 51968 /% 256 = (203,0), and 203 /% 256 = (0,203).[1] Collecting all the remainders in reverse order, then joining them with periods, produces 203.0.113.255. (This notation is just for people to read; aside from parsing code, none of IPv4 uses this notation.) When you enter an IPv4 address, the opposite happens — an expression like ((203 * 256 + 0) * 256 + 113) * 256 + 255, which evaluates to 3405804031, is performed. These octets are just numbers — using 203.000.113.255 or 203.00.113.255 in place of 203.0.113.255 is merely a choice of how to write the address, as 203 * 256 + 0 = 203 * 256 + 000. mraow
[1]: this operation can be omitted; I include it for symmetry. [2]: though all of this holds true for IPv6, I really didn’t feel like going through 128 bits of address