Binary Math 101
Binary maths - what you need to know in order to
subnet
Here is a Secret
Technically you can get away with not knowing
binary mathematics if you want to just be able to subnet your
network. So long as you understand that all IP addresses are
in binary and that each octet can only go from 0 to 255 then you
should be fine. If you have any IT exams coming up, especially
Cisco or Microsoft then you may well be asked to work out binary
numbers and convert them to decimal or even hex!
How Binary Works
We use the decimal counting system as humans
because we have ten digits on our hands so that is how mankind
learned to count. Computers only have electrical currents so
they can only see a current or no current. No current is 0 and
current is 1. The only numbering system that can cater for
this is binary.
Binary numbering starts with a 1 and then doubles
in columns. You can count from 0 to infinity and beyond with
this numbering system. Just keep adding columns (from right to
left). A 0 means don't use that number and a 1 means do use
that number.
Here you have a1 or 'on' number in the 2 column
and a 0 or 'off' in the 1 column so your number is 0.
| Numbers |
4 |
2 |
1 |
| Binary |
1 |
0 |
1 |
This time we have a 1 in the 1 and the 4 columns
so we simply add that together to get 5 as the answer.
| Numbers |
8 |
4 |
2 |
1 |
| Binary |
1 |
1 |
0 |
1 |
And this time we have a 1 in the 8,4 and 1 columns
so adding them together we have 13.
We could keep going here but we should stop at 8
columns because current IP addresses use eight binary places or an
octet. In fact an IP version 4 address uses 4 octets.
| Numbers |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
| Binary |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
In the above example we add 128+16+8+4+1 to get
157.
An IP address in binary would look like this to a
computer or router:
11010010.11101101.11000010.11110110 which is four
octets.
Convert Binary to Decimal
This is a very simple process. Just write
out the binary number putting it into the above chart. Add the
numbers together and you have your answer.
Convert Decimal to Binary
A little more tricky. Write out the above
chart again and put a 1 in the numbers which add up to your required
binary number. So if you wanted to work out 203 in binary you
would tick the 128 and 64 columns (192), ticking the 32 column would
give it too much, tick the 8 column (200) and then the 2 and 1
columns. If you prefer you can start from the other end adding
1 to 2 to 4 and so on but it does work better from the left to
right.
Your answer would look like this:
| Numbers |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
| Binary |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
There are loads more examples in
Subnetting
Secrets along with binary to decimal and hex to decimal test
questions.
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