TL; DR. Because binary. 8bits is a byte, 16 is 2 bytes, and 64 is 4 bytes, all of which are natural holding spots for CPUs processing ability until the next leap in CPU design
Everything in computer science up to quantum computers runs on binary, 1s and 0s. It’s hard to think on binary for humans, but really easy for computers. So, we came up with a way to make it easier for us: hexadecimal. Now, all of a sudden, we could convert a single concept in our language to an 8-biy concept in computer speak. And we did, and this is where bytes come from. A byte, ICYDK, is a collection of 8 bits or 8 sets of either 1 or 0 (e.g 00011011). Bytes had the advantage of mapping to characters really well (e.g. “a” might be 01000001), so we could *almost* type in natural language, and, with the use of a compiler. Translate to machine code really, really quick. There was also the idea that a CPU could, through clever design, actually process multiples of 2 simultaneously. 8-bits (or 1 byte) go in and 8 bits come out the other end. There was stuff before this, of course, (the Atari was, IIRC, a 4-bit system, but thanks to the video game crash in ’83, nobody really cares). But 8-bit really allowed for great game design for the first time. As things went on, adding extra bytes made sense, and CPUs could handle them thanks to improvements in chip design. 8 and 16 are pretty famous, but there were attempts at 24-bit systems, and 32s aren’t unheard of, but it was a relatively short amount of time between 16 and 64-bit systems, so it just made sense to invest in the 64-bit systems instead of holding back and developing 32-bit systems, although this did happen.
But, basically, its all about how much data you can pass to the CPU at once, known as the bus rate. And the bus rate is currently only limited by the pathways to the CPU, not the CPU itself (8×8 is 256, which should be the next jump in processing capability, but 8×1, 8×2 and 8×4 are what we have now, representing the number of bytes that a given CPU can process simultaneously)
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