What Does it Mean to Change the Base of a Number? | An Introduction to Binary and Hexadecimal
ฝัง
- เผยแพร่เมื่อ 28 ส.ค. 2024
- In this video, I'll cover how numbers can be represented in different ways using different base systems, and what makes those systems so useful.
Music used is from: • Outer Wilds Soundtrack...
Outer Wilds Soundtrack Piano Cover
A legend is born.
*[**8:26**]:*
Centovigesimal (base-120) is really cool for fractions, for example.
Truly Inspiring
Instant sub!!!
"We often write a little subscript denoting the base of the number so that it isn't ambiguous." So naturally the subscript is always written in decimal, because otherwise denoting the base of positional notation with positional notation is _maximally_ ambiguous. Without that arbitrary convention, you can write 10_10_10_10_10 and have the number represent _literally any value_ other than 1 or 0, though the nature of "10" means that every one of those is the same value; they all depend on the bottom-most "10".
Something that was seen earlier on in computing, though less commonly now, was binary-coded-decimal. This is representing digits 0-9 using 4 bits. This allows for easier conversion to and from decimals on less powerful hardware, and can pack two digits into a single byte. This idea of representing values in one base using the digits of another is something is effectively done every time you read the time. Time in most places that I'm aware of are actually Sexagesimal (base 60, or "base 6*5*2" if you want to be unambiguous), but written in decimal. Rather than increasing to 60 when adding 1 to 59, it instead rolls over to 1:00, much like how adding 1 to a BCD value of 0000_1001 rolls over to 0001_0000 rather than 0000_1010.
One that's fun to play with is base64, since you can use different dictionaries to do the translation. The standard dictionary for internet communications just seems wrong to me, so for my own personal use, as in it doesn't need to be decoded by anyone else, I'll use [0-9a-zA-Z\-+] which are even safer for URL encoding due to the lack of a /. Note that I don't use a \ literally, it's escaping the -. Now I'm going to play with some math and see if I can finally understand how sine and cosine were derived generically.
The animations look very cool. What SW do you use?
Believe it or not, this video was actually made using PowerPoint. My newest video was made with manim though.
Just a note: is now well established that binary was created by Leibniz in the 17th century, which is amazing if you think about it.
Very interesting! I didn’t know that
Love this