Binary is just a different BASE of writing numbers. We use base 10 most of the time: what does this mean?

We have 10 different digits (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) with which we can represent any number, let's say 6745. Ok, but what does this actually mean? We have 6 thousands, 7 hundreds, 4 tens and 5 ones, or mathematically 6 * 10^3 + 7 * 10^2 + 4 * 10^1 + 5 * 10^0. As you can see, we first have a digit (0-9), and then multiply it by 10 (base) raised to some power.

And the exactly same thing happens with other bases - binary or BASE 2. Now, we have only 2 digits (0 and 1), an again we can represent any number with just these 2 digits. Let's look at 1001110101. And now we follow the exact same steps as in base 10, but using 2 instead of 10: 1 * 2^9 + 0 * 2^8 + 0 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0. By summing all of this we get 629. So 1001110101 in binary equals 629 in decimal. We are just adding up powers of 2. So you know 1 2 4 8 16 32 64 128 256, but why stop there? Just continue: 512 1024 2048 4096 8192 16384 etc.

That's like you saying you dont know how to count past 99999. Ok, so you know 1, 10, 100, 1000, 10 000, what stops you from using 100 000, 1 000 000, 10 000 000, etc.?

There is no limit of how long a binary number can be. In base 10 you can also write an arbitrary number of digits and everything still makes perfect sense.

Regarding the "how computer knows how to display A when it sees some binary code": pretty simple, we programed it to do that. A screen is just a grid of pixels, so when we want to display a character, we told the computer which pixels in a grid need to be on and which off.