2^0 = 1
2^1 = 2
2^2 = 2 x 2 = 4
2^3 = 2 x 2 x 2 = 8
2^4 = 2 x 2 x 2 x 2 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
Binary system number is based on power of two (2^n).
1 x 2 = 2 | half the size
2 x 2 = 4 | A
4 x 2 = 8 | |
8 x 2 = 16 | |
16 x 2 = 32 | |
32 x 2 = 64 | |
64 x 2 = 128 V |
128 x 2 = 256 double the size |
In terms of subnetting,
1 = /32 = 255.255.255.255 2 = /31 = 255.255.255.254 4 = /30 = 255.255.255.252 8 = /29 = 255.255.255.248 16 = /28 = 255.255.255.240 32 = /27 = 255.255.255.224 64 = /26 = 255.255.255.192 128 = /25 = 255.255.255.128 256 = /24 = 255.255.255.0
In terms of IP address quantity
/32: 2^0 = 1 = 1 IP address within the subnet /31: 2^1 = 2 of /32 = 2 x 1 = 2 = 2 IP addresses within the subnet /30: 2^2 = 2 of /31 = 2 x 2 = 4 = 4 IP addresses within the subnet /29: 2^3 = 2 of /30 = 2 x 4 = 8 = 8 IP addresses within the subnet /28: 2^4 = 2 of /29 = 2 x 8 = 16 = 16 IP addresses within the subnet /27: 2^5 = 2 of /28 = 2 x 16 = 32 = 32 IP addresses within the subnet /26: 2^6 = 2 of /27 = 2 x 32 = 64 = 64 IP addresses within the subnet /25: 2^7 = 2 of /26 = 2 x 64 = 128 = 128 IP addresses within the subnet /24: 2^8 = 2 of /25 = 2 x 128 = 256 = 256 IP addresses within the subnetSide Note:
Some people refer the xxx.xxx.xxx.xxx notation as octet (8-based number system). There are four octets in the notation. To separate the octets, there are dots between them. I call them 4-tuple octet.
For /24 to /32 subnets, the 1st three octets remain the same. The only octet that changes is the 4th octet (the last octet).
Subnet Mask
Subnetting always relates to something called Subnet Mask. Subnet Mask is the way an IP address represent which subnet it is under.
To show you how a subnet mask looks like, let's review the previous table.
1 = /32 = 255.255.255.255 2 = /31 = 255.255.255.254 4 = /30 = 255.255.255.252 8 = /29 = 255.255.255.248 16 = /28 = 255.255.255.240 32 = /27 = 255.255.255.224 64 = /26 = 255.255.255.192 128 = /25 = 255.255.255.128 256 = /24 = 255.255.255.0
As mentioned, there are octets separated by dots that I called 4-tuple octet. This 4-tuple octet is commonly known as Subnet Mask.
Another format of displaying subnet mask is by using CIDR (Classless Inter-Domain Routing) format. Where the 4-tuple octet format is shown on the above table rightmost column, the CIDR format is shown on the above table leftmost column. To clarify, check out following table.
IP Address Quantity CIDR format subnet mask 4-tuple octet format subnet mask
Within Subnet (Prefix)
1 /32 255.255.255.255
2 /31 255.255.255.254
4 /30 255.255.255.252
8 /29 255.255.255.248
16 /28 255.255.255.240
32 /27 255.255.255.224
64 /26 255.255.255.192
128 /25 255.255.255.128
256 /24 255.255.255.0
資料來源:可參考(http://www.dslreports.com/faq/8426)
