Awesome!

That is very high praise, thank you very much and rest assured I do intend to keep making more content ☺️

Thank you! I am really glad I could help :)

Appreciate it!

Thanks! I'm happy you're liking the channel :)

Derp *6502 lol oops

Math is so hard to teach, sometimes it's like a "right place / time / explanation" thing. I have so many "aha!" moments throughout the years that came from messing around with it outside the classroom or seeing a video done by a particularly adept teacher (like 3blue1brown)

Appreciate it. I thought this would be relatively easy but it was a lot harder to summarize the topic than I thought.

I’m glad I could help!

You're welcome!

It’s been over a year since I put that Easter egg in the video, and you’re the first to find it :D

Heckin' yeah. Computer science is founded, almost entirely, in mathematics. It's an indispensable tool for making games. I'm actually planning on doing more videos about game math and algorithms in the future. So something to look forward to :)

Heckin’ yeah, that’s my original one from college. I still reference it from time to time :)

I wrote and recorded the intro :)

@@NesHacker Awesome job. Sounds very pleasing. My compliments.

@@NesHacker kind of disappointed though. I was hoping this would give me a new artist to listen too. Maybe in the future. 👀

She's doing great, nicely done finding the Easter egg :D

Mathematically hex numbers can have any number of digits, but in a hex editor they're usually broken into two digit values because two hex digits maps to one byte. When writing programs it's not uncommon to use longer hex numbers, although the NES doesn't really encouter this because it's an 8bit system and thus works on single-byte values. Likewise, binary values can have any number of digits, but in computing representations they're often grouped into series of four bits, or sometimes eight, although in those cases there's usually a small gap in the middle to separate the eight bits into two groups of four. Incidentally, while eight bits is referred to as a byte, the four bit sequences are sometimes called a nybble. ASCII can be worked with using a chart, but most hex editors have a "character" field to the right hand side of each line of bytes, where the ASCII representation of the bytes is displayed and can be edited directly. HxD is a free hex editor that you can use to examine or edit files on your PC, if you want to become familiar with hex editors. Alternatively, the NES emulator Mesen has a full suite of hacking and debugging tools that includes hex editors for viewing the RAM and ROM contents while running a game.

Oh, I forgot to mention, but yes, four bits correspond to one hex digit. However, it's much easier to just learn to read four bit values in your head and memorize the decimal values of A thru F. Then you can easily do conversions on the fly rather than using a chart.

Hexadecimal is usually written as 2 digits because they're used as an expansion for what basically base-256, kind of like how digital clocks effectively display base-60 numbers using pairs of decimal digits for each base-16 digit. For ASCII letters, it's actually possible to convert directly from binary to a letter and back. If the binary starts with 010_____, then it's an uppercase letter, and if it starts with 011_____, then it's a lower case letter. The remaining 5 digits directly count from 1 to 26 mapping the range to the letters A through Z. You may not of something else that usually has 5 "digits", and while it can take good dexterity to represent the entire range as distinguishable values, it's possible to count from 0 to 31 (which contains the numbers between 1 and 26) on a single hand by treating each finger as a distinct bit, while sounding out the alphabet to tell which letter maps to which 5-bit number. If the number instead starts with 0011____, then it's likely a number, with the remaining 4 bits being the binary form of the digit in question, and can also be counted on one's fingers from 0 to 9 if you haven't memorized the 1 digit decimal-binary conversions. For symbols, there's not much you can do to avoid memorizing or looking up the chart. The best I can say there is that 000_____ are control codes that don't map to any symbols, and 0010_0000 (20₁₆ = 32₁₀) is space.

I totally forgot I added that little joke xD

@@NesHacker :D

I taught myself to program as a kid when I got ahold of a floppy containing a bunch of QBasic code and games. Kinda kept going from there and ended up getting a degree in computer science.

Haha, no I used the table. :)

Nice :D

I am confused... At 9:59 I explain what all the numbers and letters mean. Was it not clear or something?

Yeah sorry, that part was actually. I was commenting in order of watching it. But funnily enough, like… still it’s such a funny leap that people always make when explaining binary. There needs to be this one… totally different section that says. “Now… once we have that, different people come up with different codes in order to represent different symbols.” They just jump straight to letters, which you DID do. But then, thankfully, you happened to explain it later. Like… in the order of the video, you’d say this looks like jibberish. And I’m like… yeah of course it does. You just spent 10 minutes telling me this is all about numbers and now, with no explanation you just told me it now represents, letters? But yes, you got to it later. Thanks! I assume then… that there are other codes that use different lettering systems? I actually don’t know.

But you know what? It still is weird… because you start by saying my name represent in binary. But that’s weird and misleading, like… your name doesn’t start by being representing in binary. But you make it seem that way. It STARTS as letters, that THEN (I suppose through ASCII) it gets coded into a number. So like A is 65? B is 66? C is 67? Etc… But… that’s completely arbitrary, no? Like … to me THAt is the part that needs the most explaining. That someone, somewhere was like ok… A is now the same as the decimal number 65 cause I said so. But! We’re going to write 65 in Hecidecimal (first) as 4E. THEN … we will code the 4E into binary as 1001 I dunno, just skipping that or assuming that that’s somehow normal or logical, when everything else totally is, is weird to me.

@@NesHacker No no it was. I shouldn't even be taking issue really. I just have noticed that people when explaining binary do a nice deep dive on the number part. then usually immediately jump right to letters. As if there is any actual connection between the two. You actually DID explain where the letters can eventually come from. But as I was watching it, in order. It was funny because the same leap RIGHT to letters was made and it made me scratch my head again and go, "why do they always jump right to.... and here is my name in binary." I guess what I usually feel is lacking is the fact that there is absolutely nothing inherent at all about letters in binary. But rather we have to simply decide at one point that some binary number is just going to literally equal a letter. And that's that. The number 36 or whatever, expressed in binary, under a certain context will simply just mean the letter 'M' or something. And I often feel like that concept, that leap, is under explained. You did the best job I've seen so far to be honest. I say this as a smart, yet confused person when it comes to coding etc. and I just get weirdly frustrated when people don't just level with the newly inducted to just say... yeah... we just made this part up. Someone made up a code one time that says the number 396 is now "Q" or whatever.

Mappings of characters to numbers are ultimately arbitrary, but ASCII does have some structure that you can use. If you know it's a letter, then the last 5 digits will be a binary number between 1 and 26, and the whole byte will be the letter with that place in the alphabet with 1 being A and 26₁₀ = 11010₂ being Z. If it's greater than 26 or if it's 0, then it's a symbol of some kind because encoding space was at a premium. Aside from those cases, you can tell if a binary number is a letter by checking if the first 2 bits are 01______, with the first bit immediately after being 0 if the letter is uppercase and 1 if the letter is lowercase. There are other codes like EBCDIC and Unicode, though nobody uses EBCDIC anymore (and one place that did actually got sued for doing so because it couldn't properly spell a client's name), and Unicode is backwards compatible with ASCII, with the first 128 Unicode codepoints exactly matching ASCII. UTF-8 is a mapping between Unicode characters and bytes that is _also_ backwards compatible with ASCII as those first 128 codepoints have the exact same binary representation as they would in ASCII. While ASCII has the aforementioned structure, Unicode gave up and the binary representation of each codepoint has no significance beyond what 16-character block it's in. "Someone made up a code one time" And that someone was the American Standard's Association (now American National Standards Institute) for ASCII, and the Unicode Consortium for Unicode. "I assume then… that there are other codes that use different lettering systems?" Absolutely! ASCII was pretty ubiquitous, so even people with other systems had letters in the same places as ASCII, and nowadays the world has pretty much standardized on Unicode, but those other systems had different mappings for other numbers. Often this meant assigning new letters or symbols to the remaining 128 possible byte values. Which new letters or symbols was never standardized and trying to read text written with one mapping as though it had a different mapping gave a result that has its own word to describe it: "mojibake". Yes, the word is Japanese and the "moji" part is the same as in the word "emoji" and just means "character". There are _many_ symbols used in Japanese text and _many_ different systems that people came up with for encoding them, most of which were incompatible with each other and could be completely unreadable if your devices were from different companies. Thankfully Unicode (and UTF-8) have _mostly_ ended mojibake worldwide, but even _they_ don't have every possible character that someone might want to type and some places can be slow to switch from a prior system.

Hue hue hue... I make terrible puns throughout my videos. It is a curse. I cannot escape it.

Correct: d0 * 10^0 + d1 * 10^1 + ... It's mathematical formalism to show the pattern, at the end of the day it just represents the "ones" place.