How is the binary number system different from ours?

Answer 1

In short, binary is a base-two system, while ours is base-ten. If that's not enough information for you, read on.

In our number system, the natural number sequence goes like this:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.

In binary, the same sequence goes like this:

1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, etc.

Therefore, 1 in binary is 1, 2 is 10, 3 is 11, 4 is 100, and so on. (Note that these should not be pronounced as "ten", "eleven", or "one hundred", but instead as "one zero", "one one", and "one zero zero".)

Binary works in powers of two. Take a look at the following number, which is 19 in binary:

10011

Each digit, starting from the right, represents 1, 2, 4, 8, and 16. These are equal to 20, 21, 22, 23, and 24. This might make a little more sense (maybe?):

1 0 0 1 1

↑ ↑ ↑ ↑ ↑

16 8 4 2 1

Now you can see that what each digit represents more clearly. The 1 on the left represents 16, the second 1 represents 2, and the 1 on the right represents 1. We don't need to worry about the 0's; they are just placeholders. If you add up what each 1 represents (16, 2, and 1), you get 19. This is why 10011 is 19 in binary. The same rules apply to reading and writing other binary numbers.

"There are 10 types of people in the world: those who understand binary and those who don't."