We have basic words for the numbers zero to three, so why not use them to count?
- None (0)
- Single (1)
- pair (2)
- Multiple (3+ but we’ll use it as three)
So with those “digits” we can construct some numbers:
- Single
- pair
- Multiple
- Single nothing
- Single single
- Single pair
- Single multiple
- Pair of nothing
- Pair of singels
- Pair of pairs
And of course we can construct bigger numbers like:
42 = 4²×2+4¹×2+4⁰×2 = pair of pairs of pairs
128 = 4³×2 = pair of absolute complete nothinges
For this last one I just use some adjectives to repeat the “nothing” as it looks really weird with multiple nothing in a row.
The distance between Stockholm and Gothenburg is a single multiple of none multiple multiples
Could I have a single multiple of bananas please?
Sure, I was simplifying a bit. But on the hardware level, TLC SSDs (the vast majority of SSDs in 2024) will physically address flash memory outside of the SLC cache as base-8. Each cell that gets written is written with a base-8 digit. But yeah, what gets exposed to the computer is all base-2. I just wanted an example of modern computers using higher bases.
I guess another example would be busses that use PAM, such as Wifi, modern 100mbit+ ethernet over copper, 100gbit+ ethernet over fiber, PCIe 6.0+, and GDDR6X. These all send symbols that count in higher bases than the traditional base-2 NRZ/PE/BPSK signalling. Often these are base-4, but they can go up to insanely large numbering systems, like base-4096 with Wifi 7.
You’re absolutely right on that count. If you switch fast enough, everything has a capacitance. That’s why with CMOS designs once you go above a few kHz you start worrying about fan out.
It’s also why, once the ceiling is reached, everything starts using modulation tricks previously used in RF. Ethernet started with 1GbE, USB with 3.0, DSL did it from the start, with PCIe even gamers have probably seen eye diagrams in riser tests, and coax is the very definition of pushing RF over a wire.