Converting Base 10 to Base 2
Ok, here is a short tutorial on converting decimal numbers to binary form. Now this can be extremely important and it can also never affect you.
But having good skilz in number systems can aid you with IT stuff. you can solve problems faster without the aid of a calculator when one is not around.
Now the decimal system is based on powers of 10, duh. For example 10^0 is 1, 10^1 is 10, 10^2 is 100 etc.
| exponent 10^5 10^4 10^3 10^ 2 10^1 10^0 |
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| expanded 100000 10000 1000 100 10 1
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| number 3 5 2 4 8 1 |
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| 3 * 10000 5 * 10000 2 * 1000 4 * 100 8 * 10 1 * 1 |
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i take pride in my tables ;)
anyway the binary system is base 2, meaning based on 0, and 1.
so to convert binary you do something like this
an example
decimal number = 255
ok. for smaller numbers you use 128, 64, 32, 16, 8, 4, 2, 1
so. 128 64 32 16 8 4 2 1
will 128 go into 255? yes. you put a one down
then you subtract 128 from 255.
will 64 go into 127? yes. you put a 1 down.
then you subtract 64 from 128.
will 32 go into 64? yes you put a one down.
subtract 32 from 64.
will 16 go into 32? yes you put a 1 down.
will 8 go into 16? yes you put a 1 down.
will 4 go into 8? yes you put a one down.
will 2 goin into 4?
yes you put a one down
will one go into 2? yes you put a one down.
255 to binary = 11111111
now for something with zeroes.
128 64 32 16 8 4 2 1
for example the decimal number 165
will 128 go into 165? yes you put a 1 down.
take 165 - 128. which equals 37.
will 64 go into 37? no. so you put a zero down.
then you go onto the next number with 37.
will 32 go into 37? yes you put a one down.
subtract 32 from 37 which equals 5.
will 16 go into 5? hell no. so you put a zero down and go onto the next number.
will 8 go into 5? no, so you put another 0 down. and go on.
will 4 go into 5? yes so u put a one down.
will 2 go into 1? no so you put another zero down.
will 1 go into 1? yes. so you put a one down.
thus the conversion from 165 to binary is 10100101.
now if you want large numbers than those, you simply go up more, and start with 256, or 512, or 1024 etc. the same rules apply.
now you can convert decimal to binary. extremely easy eh?
