::braces for inevitable crosspost::

Captain! The shields are buckling! She can't take any more crossposting!

No let's a box to the egg scenario. Pe R. Son uses a box that holds 10 crates. Comp U. Ter uses a box that only holds two egg crates. So when presented with six eggs Pe R. Son still can't fill a crate so he says he has 6 eggs. Now Comp U. Ter fills up three 2-egg egg crates. Two of those egg-crates go into his 2-crate box, leaving one 1 unboxed crate. Therefore, the Comp U. Ter says he has 1 box, 1 crate, and 0 single eggs.

So for Pe R. Son - 6 single eggs or "6" for short.

For Comp U. Ter - 1 Box, 1 Crate, and no single eggs or "110" for short.

I"m not going to try and explain it because I think the mathy people here have it down. I'll just say that for me, it was understanding base 12 that got me to understand binary and all bases below 10. My math prof used t and e for the new numbers that came after 9 and then it clicked.

(Not sure if that post made sense)

For me, the only part of binary and base eight that every stuck was the basic definition. I always hated those parts of math classes where they'd make us do calculations in base eight.

What is the purpose of base eight?

instead of having a units place, tens place, hundreds, etc. you have a units place, twos place, fours, etc.

Okay, so, in binary, the number 111 means that there is one 4, one 2, and one 1, so it would equal 7?

Somehow it does seem easier to grasp bases larger than ten than those smaller than ten, I think because we keep wanting to say, okay, so what does 18 stand for? Base 16 helped me, what with the 1-9,A-F.

So far the egg explanation is the only one I vaguely understand.

Brains are weird. Because I swear I don't understand that one, and I have programmed in binary myself.

Here's a simple page on binary, but it may be in me-speak and not Steph-speak, and therefore not so helpful.

Say you have 143. 143 in regular #s = 1*10^2 + 4*10^1 + 3*10^0

Now say you have 110 in binary. That = 1*2^2 + 1*2^1 + 0*1^0

Well, I thought I had a rudementary english major's grasp on binary until I saw this post!

Tep, is this the kind of explanation you are needing? Cuz there's more where it came from at [link]

Computers don't use the ten digits of the decimal system for counting and arithmetic. Their CPU and memory are made up of millions of tiny switches that can be either ON or OFF. Two digits, 0 and 1, can be used to stand for the two states of ON and OFF. So we can see that computers could work with a number system based on two digits.

I believe it explains both the whys and hows of binary, um, stuff.

the number 111 means that there is one 4, one 2, and one 1, so it would equal 7?

You've got it!