What characterizes binary system?

Answer 1

In normal counting (termed Arabic notation) each digit position is greated than the one to its right by a factor of ten.

So 2045 is

1x5 + 10x4 +100x0 + 1000x 2

Another way to show the same sum would be:

100x5 + 101x4 + 102x0 + 103x2

In binary we use 2 instead of 10. We only need the digits 1 and 0, just as with normal numbers we don't need any digit higher than 9.

So 1100100 would be:

20x0 + 21x0 + 22x1 + 23x0 + 24x0 + 25x1 + 26x1

We can work out all those powers and we get:

1x0 + 2x0 + 4x1 + 8x0 + 16x0 + 32x1 + 64x1

That simplifies to:

4 + 32 + 64 = 100