Binary Odometer

Binary as an Odometer

One great way to understand binary numbers is to look at it from an odometer standpoint. There are several sites online that have great visualization about this binary odometer, so what I'm going to do is just type in binary odometer to take a look at one of these sites. The one I'm going to show you is this one from GitHub, although this other one here is a really nice one as well.

Counting in Base 10

I'm going to open this up in a new tab here. This is a site that goes through the explanation of binary numbers and talks about binary numbers. One of the things it starts out with is base 10, and how base 10 counts up, and this is what we're used to working with.

You can click this little increment value to see how the odometer counts up. We've got the ones column here, and we just click on it and that ones continues to count up: 3, 4, 5, 6, 7, 8, 9. And then when we get to nine, what happens is that this column resets and turns to zero, the ones column, and we now have a one in the 10 column. Then it counts up again until we hit 19, and same thing, we click it again and then this moves the 10 column to a two. So this will just keep going up and up as it goes along, just like an odometer would in your vehicle.

This is showing you just a slightly larger number here, 1 2 3 4, so we can count up and we can keep going until we get to something where there are 91, and then once we do that it then flips over our hundreds column. So there is 1,299; we click it one more time and then now it's 1,300, so we've got three in the hundreds column here.

Counting in Binary

So what does a binary number look like? What we can do is we can increment this value. As we go up, it's going to go to a one. There is no two, so when we click it again it's got to put a one in the twos column, so now it's 1 0. Then we click it again and it's 1 1. We click it again, now it's 1 0 0. Then we click it again, 1 1 1 1 0 1 1 1. And now we click this again and now we have a one in the eight column, and then 1 0 0. So then we can continue to go up. So this is a great way to visualize what's happening with these numbers.

The Other Visualization

The other one that I skipped over here - you can click on this, and this is just one that we can start. I'm going to turn this down, make it slow at first, so you can see that the first one here is the binary numbers and it's counting up, 1, 1 0, 1 1. At the same time it's showing you an octal and decimal and hexadecimal. So hexadecimal is another good one, where this is a great visualization for hexadecimal as well. But you can see it counting up, or I could start speeding this up.

By going and doing this and looking at these sites, you can kind of see the pattern that starts forming with this. So this is a great visualization to study and to get familiar with, to understand how these binary numbers count.