tuxgraphics.org binary numbers

binary numbers

2⁸	2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
256	128	64	32	16	8	4	2	1

It's easy to convert from binary to decimal:
101 = 1*2⁰+ 0*2¹+1*2²= 1 +0+4=5

011 = 1*2⁰+ 1*2¹+0*2²= 1 + 2 =3

101010 = 0*2⁰+ 1*2¹+0*2²+1*2³+ 0*2⁴+1*2⁵= 2+8+32=42

To convert decimal numbers into binaries is a bit more tricky:
Let's start with 12:

12 = 2 * 6 + 0
6 = 2 * 3 + 0
3 = 2 * 1 + 1
1 = 2 * 0 + 1

(to find the right numbers, divide 12 by 2, take the result, 6 in this case and again divide by 2 until you have reached 1)

Now you take the remainder starting at the bottom and you have the binary number.
12 = 1100.

Another example:

42 : 2 = 21 + 0
21 : 2 = 10 + 1
10 : 2 = 5 + 0
5 : 2 = 2 + 1
2 : 2 = 1 + 0
1 : 2 = 0 + 1

So as we have already seen above 42 = 101010.

And one more example:
123 : 2 = 61 + 1
61 : 2 = 30 + 1
30 : 2 = 15 + 0
15 : 2 = 7 + 1
7 : 2 = 3 + 1
3 : 2 = 1 + 1
1 : 2 = 0 + 1
That means 123 = 1111011.

references

https://www.rapidtables.com/convert/number/binary-to-decimal.html