Subnetting counting on fingers with 2’s the easy way.

How many bits in the mask 255.255.255.240?

Answer: How many full 8 bits in each octet? The first 3 octets are 255. That’s all 8 bits. 3 x 8 = 24 bits so far in the network mask. The last octet is not 8 bits. A 2 is a bit. How many bits or 2’s do we subtract to see how many bits left masking the network number revealing the host number? 256 is 2^8 power. 256 – 240 = 16. How many bits/2’s in 16? 2 x 2 = 4 x 2 = 8 x 2 = 16. That was 4 2’s or 4 bits. There is 8 possible bits in the octet minus 4 bits = 4 bits. So the 3 previous octets totaling 24 bits plus the bits in the last octet of 4 equal 28. 28 network bits in the mask 255.255.255.240.

How many bits in the mask 255.255.192.0?

Answer: How many full 8 bits in each octet? The first 2 octets are 255. That’s all 8 bits. 2 x 8 = 16 bits so far in the network mask. The next octet is not 8 bits. A 2 is a bit. How many bits or 2’s do we subtract to see how many bits left masking the network number? 256 is 2^8 power. 256 – 192 = 64. How many bits/2’s in 64? 2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32 x 2 = 64. That was 6 2’s or 6 bits. There is 8 possible bits in the octet minus 6 bits = 2 bits. So the 2 previous octets totaling 16 bits plus the bits in the 3rd octet of 2 equal 18. The last octet is 0 bits so, 18 plus 0 = 18. 18 network bits in the mask 255.255.255.192.

Let’s go the other way?

What is the network mask for a /21 bit subnet mask?

Answer: How many whole 8’s in 21? 8 + 8 = 24 + 8 = 24. Twenty-four takes you over 21. It is time to stop. There are 2 full 8 bit octets in the first part of the mask. You have 255.255 so far. Now to figure out the 3^rd octet. How many bits left to go in the 3^rd octet? The first 2 octets are 8 + 8 = 16 bits. 21 – 16 = 5 bits in the 3^rd octet. What is the number 5 2’s squared out makes? 2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32. 32 bits subtracted from the decimal 256 (2^8 power) is 256 – 32 = 224. So now you have 255.255.224 so far. Since there are no more bits left, the last octet of course is 0. So the mask for a /21 bit network mask is 255.255.224.0.