Hi, this is Wayne again with a topic “Binary Numbers and Base Systems as Fast as Possible”.
Modern-Day computers use electricity to work and inside of a microchip electricity is turned either on or off, which is represented by the symbols 1 and 0. This is called binary, you’ve, probably heard of binary already and that that’s how computers work, but do you know how binary works well, you’re about to find out, but first we need to understand exactly how our numerical based system known as decimal or base 10 works. The way it does so, there are 10 counting 10 symbols that we use for all of our numbers, starting from 0. We can count all the way up to 9 before we run out of symbols to use. Now we could just keep adding symbols at this point, but that would get out of hand very quickly. I mean, can you imagine having to memorize a specific symbol for every single number? That’S ridiculous and that’s why we reuse the same symbols over and over again in a very clever system called positional notation, so in the base 10 system. As soon as we get to 10 or an exponent of 10, we need to add another digit to the left of our current digit, because there are 10 symbols.
Each new digit has to have a value 10 times greater than the digit to it’s right. So that’s using 10 symbols, but what if you had only 2 symbols to work with? Well, then everything that I said still applies with just two symbols: each new digit needs to have a value 2 times greater than the digit to it’s right. So a sequence like this would equal 1 times, 128 plus 1 times 16 plus 1 times 8 plus 1 times 2 plus 1, which is 155, and that’s how you count in binary.
It’S actually really simple: it’s just multiplication and addition. Now it gets a lot more complicated from here with bits and bytes and boolean logic and ASCII, and the list just goes on and on so let’s return to base systems. There are a lot of ways to write numbers other than decimal and binary.
You’Ve got base to base 3 base for base 5. I could go on. They all work with the same principles of positional notation, so you might be wondering with all these numbering systems to choose from.
Why do we use base 10? That’S a good question. This goes all the way back to Roman numeral, an Egyptian hieroglyphs. It’S likely that we use base 10 simply because we have 10 fingers, also known as digits. Other based systems like base 8 and base 12 are actually superior for simple everyday math since 8 and 12 are much more easily divisible than 10, but it’s definitely too late to change our minds about using base 10, we’ll probably be stuck with it forever. Switching away from it now would be even harder than trying to convince America to drop the Imperial system and finally switch to metric.
You know like the rest of the civilized world like yeah. The metric system is superior, but who’s gon na tell America what to do now, if you’re going to be using base 12 or any other base system with more than 10 digits its standard to use letters to represent numerals higher than 9. So 10 is a 11 SB, 12 is C, and so on this is called alphanumeric. You know those URL shorteners that you see on Twitter and elsewhere.
Have you ever wondered how they work all those jumbled characters really just represent a very large number. By using numerals and every letter of the alphabet, you can get all the way up to base 36 using lowercase and uppercase. Letters gives you base 62 and with that you can get all the way up to 14 million, with only four digits with just 10 digits. You can get up to 839 quadrillion possible values.
That’S a lot of shortened URLs! So you just learned about positional, notation, binary numbers, numeral based systems, alphanumeric characters and URL shorteners. I hope you enjoyed it and, if you’re, in the mood for more learning, maybe you’ll like today’s video sponsor, which is the excellent lynda.com for the past six years. I have been using and recommending lynda.com to people as an excellent means of learning new things, especially software. You see over six years ago.
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