Differential coding

Okay kiddo, let's learn about differential coding!

Imagine you have two numbers like 5 and 7, and you want to send them to your friend who lives far away. But you can't just tell him the numbers because they might get mixed up or lost on the way. So you need to send the numbers in a special way that will make sure they get there safely.

Differential coding is a way of sending numbers by telling your friend the difference between them, instead of telling them the actual numbers.

Let's use our example numbers of 5 and 7. The difference between them is 2 (because 7 - 5 = 2). So instead of telling your friend the numbers 5 and 7, you could just tell them the difference of 2.

But wait, what if your friend doesn't know the first number (5) to begin with? Then the difference (2) wouldn't make any sense. So to fix this, you can start by sending the actual first number (5), and then send the differences between the next numbers and the previous ones.

So, you would start by sending 5 to your friend, and then the difference between the second number (7) and the first number (5) which is 2. Your friend can then add that difference to the first number (5 + 2 = 7) to get the second number.

This way, your friend can figure out all the numbers you've sent by just knowing the first number, and all the differences between them.

It's like giving them a puzzle to solve, where they use the first piece (the actual number) to figure out the rest (the differences and the final numbers).

Pretty neat, huh? That's how differential coding works, and it's used a lot in things like sending digital signals, encoding video and audio, and even in some video games!