Electrical engineer, here. This is going to be more of an ELi12 answer.
So, let’s count in binary!
0000 is 0.
0001 is 1
0010 is 2
0011 is 3
0100 is 4
0101 is 5
0110 is 6
0111 is 7
1000 is 8
And so on. That means that xxx0 is our ‘1’s, xx0x is our ‘2’s, x0xx is our ‘4’s, and 0xxx is our ‘8’s place. This is with 4 bits, where the highest we can count is 1111 which is 8+4+2+1 = 15. If we count from 0000,0000-1111,1111 we can count to 255.
So, when it comes to computers, picture a library where each page of a book receives a number. A 4 bit computer can count up to 16 pages (because 0000, or 0 is a number). An 8 bit computer can count up to 256 pages, and so on and so forth.
You still have to connect the physical hardware that can store them, but a 4 bit or 8 bit computer can only count up to 16 or 256 pages. Even if you attach more hardware. A 32 bit computer can count 4294967296 pages, which is a really big library. A 64 bit computer can count 18446744073709552000 pages.
That’s for the memory controller, which manages a library. The technical term is actually ‘memory pages’. But there are other instances where you’ll hear things measured in bit size.
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An 8-bit number is one that can be between 0 and 255 (or signed 8 bit integers, -128 to 127) to . So if you’re doing math on 8 bit integers, 120+10 = -125 because it ‘loops back’. https://www.cs.auckland.ac.nz/references/unix/digital/AQTLTBTE/DOCU_031.HTM this explains more about bit size and integers (whole numbers) floats (decimal numbers), and integral (numbers that we translate to letters) types.
So, 32 bit and 64 bit computers refer to the memory controller. 8 and 16 bit video game consoles refer to the types of numbers they are best at counting with (though an 8 bit processor can count higher than 256 by using tricks! https://forums.nesdev.org/viewtopic.php?t=22713 )
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You’ll also often hear about bit size with audio, I.E. 8 bit, 16 bit, 24 bit, and 32 bit digital audio. This refers to the distinct levels of volume that an audio signal can have.
Take a deep breath and at a constant volume go “EEEEEEEEEEE-AAAAAAAAA-OOOOOOOO”. Then stop. Then go “EEEEEEEEEEE-AAAAAAAAA-OOOOOOOO”. Then stop. This would (for purposes of explanation) be encoded as 1 bit audio, because it only has two possible volume levels even if it can have different pitches/frequencies to it.
Now repeat that exercise, but do your first EEEEEEEEEEE-AAAAAAAAA-OOOOOOOO at normal volume. Then your second quieter, then your third louder. This is 2 bit audio (00, 01, 10, 11) because you have four distinct volumes.
8 bit audio has 256 distinct levels of volume, 16 bit and 24 bit and 32 bit have more distinct levels. (This is separate from the maximum frequency they can capture, or the highest pitch sound that can be recorded or reproduced, which has to do with sample rate and Nyquist frequencies. The Nyquiest frequency is the highest frequency that can be reliably recorded. It is 1/2 the sample rate, so 44.1kHz sample rate can only record/reproduce up to 22.05kHz sounds, which is pretty high pitched!)
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You’ll hear about video signals encoded as 16 bit, 24 bit, 32 bit, and more. This is the same thing. 24 bit video is encoded as the red, green, and blue channels each having 8 bits, so red=0 to 255, green = 0 to 255, and blue = 0 to 255. (32 bit adds a transparency layer of 0 to 255). You can have 30 bit, where each channel gets 10 bits so red = 0 to 1024, blue = 0 to 1024, and green = 0 to 1024, and then 36 bit, where each channel gets 12 bits, and so on and so forth.
More video bits means more distinct colors. Very high bit depths help artists work.
And lastly, there is the use of bits with communication bandwidth. This gets highly specific to the thing being discussed. https://www.techpowerup.com/forums/threads/explain-to-me-how-memory-width-128-192-256-bit-etc-is-related-to-memory-amount.170588/ this thread explains it in context of graphics card memory. Edit: I can answer some specific questions about this if anyone’s curious, but it can get complicated! 🙂
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