Base 10 to Base 2

Anaerobic Membrane Bioreactor for Continuous Lactic Acid Fermentation

Computers only know binary. Base 2 is binary. Let’s convert a couple of integers to their binary representation.

The number 10.

n = 10

n/2 = 5 with a remainder of 0, so the last number in our binary string is 0.

0

Now n=5

n/2 is 2 with a remainder of 1.

So our second to last number is 1.

10

Now n = 2

n/2 = 1 with a remainder of 0

So our third to last number is 0.

010

And that leaves us with 1, which is our first number

1010

Another representation of what we just did:

n | / | quotient | remainder
----------------------------
10  2      5           0
5   2      2           1
2   2      1           0
                       1
result = 1010

Let’s try 7!

n | / | quotient | remainder
----------------------------
7   2      3           1
3   2      1           1
                       1
result = 111

There are converters that will do this for us, but math is fun and it is important to know how and why things work.