Also technically we don't have that many fingers. We have one more finger. We don't have a number digit for ten right? They go zero to nine. But out fingers go zero to ten.
If our numeric base matched our fingers, we should've used base eleven. Not many people think this through :)
I think the real breakthrough is having "order of magnitude" in numbers. So indeed the Roman Numerals suck and probably wouldn't last regardless.
I do 6502 ASM with bit tricks and all and i can tell you straight up that hex is never as intuitive as decimal IMO.
Base eleven sounds like the stuff of nightmares =)
For example we think of 10, 100, 50 as nice round convenient quantities.
CPUs see 16, 256, 2048 as convenient quantities--in hex that's visible: 0x10, 0x100, 0x800.
Say i were to name a random hex value like #$9C right now it would take me a few seconds to convert that to decimal in my head though... 156 took me a few seconds to sort out. I don't have to think about what 156 means in decimal because i just know what it is.
> It was $62 degrees Fahrenheit yesterday. I can't just go displaying that in a program. Nor is it meaningful to me without a decimal conversion.
It's just as meaningless to me even if you do the conversion to base10 for display... I don't do deg F intuitively and would have to convert to Celsius in my head. It's all about what we are familiar with.
No, you hadn't. I’m pretty sure there is no such thing.
Totally agree. I'm a programmer, so I do need to know those, and as an embedded developer, even more. The average person not so much. I thought that's what this particular thread was all about.
I have no trouble remembering those, and that the ratio of degree sizes is 5/9ths, so I can figure a formula out whenever I need to.
For instance, you say 0x9C... that's just over half (0x80) of 0x100, close to 2/3rds (0xAA). Given in embedded we're often using a byte to represent a quantity, that gives enough feel.
I should practice multiplying hex by hand, I reckon that would assist in getting there.
While I agree with that viewpoint I think it's missing the point. As humans with 10 fingers it's easy for us to group things into increments of 10, so base 10 comes naturally. Think about how you count a quantity over 10: once you run out of fingers you mark down (or remember) that you've already counted one quantity of 10, now you're counting the next quantity of 10, etc...
It's more like a shifted base 10 where we represent digits 1-10 instead of 0-9.
But every base starts with 0, there's no such thing as "shifted base" because then you literally can't represent 0.
Also "zero fingers" is still a thing that exists in this shifted base 10. So it remains base 11.
This is like the classic "0-based indexing" vs. "1-based indexing" dilemma. The "first" thing is represented by 1, we think.
But the "first" year of our life, we're zero years old. The "first" hour after midnight is 0 o'clock. Building your "first" million as a business is the period before you have 1 million. And so on.
As for bijective base 10, it's interesting, but it's still not the base 10 we're using, so we can't quite blame this on our fingers.