In order to understand IP addressing and network subnetting, the binary and hexadecimal numeral systems must first be understood. A numeral system is a system of expressing numbers using a set of unique digits or symbols with consistency.
The binary(base2) numeral system uses only the symbols "1" and "0", decimal(base10) uses the familiar symbols "0123456789", and hexadecimal(base16) extends the decimal symbol space to "0123456789ABCDEF". With a numeral system of base n, where n is equal to the length of a symbol space of unique characters, the maximum value expressed by a string of symbols of length x is equal to nx - 1. For example, the maximum value expressed with 3 symbols in base2 is 23 - 1 or 7(base10)!
| Decimal | Binary | Hexadecimal |
|---|---|---|
| 100 + 0 = 0 | 20 + 0 = 0 | 160 + 0 = 0 |
| 100 + 1 = 1 | 20 + 1 = 1 | 160 + 1 = 1 |
| 100 + 2 = 2 | 21 + 0 = 10 | 160 + 2 = 2 |
| 100 + 3 = 3 | 21 + 1 = 11 | 160 + 3 = 3 |
| 100 + 4 = 4 | 22 + 0 = 100 | 160 + 4 = 4 |
| 100 + 5 = 5 | 22 + 1 = 101 | 160 + 5 = 5 |
| 100 + 6 = 6 | 22 + 21 = 110 | 160 + 6 = 6 |
| 100 + 7 = 7 | 22 + 21 + 1 = 111 | 160 + 7 = 7 |
| 100 + 8 = 8 | 23 + 0 = 1000 | 160 + 8 = 8 |
| 100 + 9 = 9 | 23 + 1 = 1001 | 160 + 9 = 9 |
| 101 + 0 = 10 | 23 + 21 = 1010 | 160 + A = A |
| 101 + 1 = 11 | 23 + 21 + 1 = 1011 | 160 + B = B |
| 102 + 2 = 12 | 23 + 22 = 1100 | 160 + C = C |
| 101 + 3 = 13 | 23 + 22 + 1 = 1101 | 160 + D = D |
| 101 + 4 = 14 | 23 + 22 + 21 = 1110 | 160 + E = E |
| 101 + 5 = 15 | 23 + 22 + 21 + 1 = 1111 | 160 + F = F |
| 101 + 6 = 16 | 24 + 0 = 10000 | 161 + 0 = 10 |
An IPv4 address is made up of 4 "octets", or 4 binary strings of length 8(32 in total). Each positional value, or bit, can hold the value of either "1" or "0". With a length of 8(bits), 28, or 256 unique values(0 - 255 in base10) can be expressed. With an entire 32-bit IPv4 address, 232, or 4,294,967,296 unique values can be expressed!
| base10 | 192.168.255.1 |
| base2 | 11000000.10101000.11111111.00000001 |
For a better understanding of numeral systems, clone this repository.
Converting between binary and decimal by hand can be difficult and time consuming. Below is a simple method of converting between base10 and base2.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 |
Subnetting is the process of splitting a broad network segment into multiple smaller portions. In doing so, a minimal amount of IPv4 address space is wasted. A network which only requires 250 hosts, sould not receive 16,777,214 hosts(/8), rather 254 hosts(/24).
Each network has two portions: a host portion, and network portion. The length(in bits) of the network portion is specified with a subnet mask(ex. /8, /12, /24). The host portion can then be used to assign addresses to individual host interfaces.
| network | host | |
|---|---|
| base10 | 10.0.0.0 /8 |
| base2 | 00001010.0000000.00000000.0000000 /8 |
| network | host | |
|---|---|
| base10 | 172.16.0.0 /12 |
| base2 | 10101100.00010000.00000000.0000000 /12 |
| network | host | |
|---|---|
| base10 | 192.168.1.0 /24 |
| base2 | 11000000.10101000.00000001.0000000 /24 |
After numeral systems and binary are understood, subnetting becomes simple!
Subnetting a broad network into multiple smaller networks involves simply dividing networks in half repeatedly until the desired subnet count/ size is reached. However, each network division consumes an additional 2 hosts within the network (network and broadcast addresses).
| 1-8 | 9-16 | 17-24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| octet1 | octet2 | octet3 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | |
| 192 | 168 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Subnet 1 | 192 | 168 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | /25 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subnet 2 | 192 | 168 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | /25 |
For a better understanding of subnetting watch this video.
More on IPv4 addressing.