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.
Base eight and base sixteen make great shorthand for binary. Useful for computer programming and granting permissions on UNIX machines. Also, the role-playing game Taveller could express a character or starship as a hexidecimal number for reasons I'll never really understand.
Okay, so, in binary, the number 111 means that there is one 4, one 2, and one 1, so it would equal 7?
Woo!
Base eight and base sixteen make great shorthand for binary.
Cause, man, those binary numbers get LONG.
So if 111 = 7, each column except the furthest right is a value of 2? Like, furthest right is 1s, and then moving left is 2s, 4s, 8s, and then....? Does the value of the rows double as you progress left? Would 16s be next, and then 32s?
Would 111111 = 63?
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.
Okay! See, THIS makes sense!
So if 111 = 7, each column except the furthest right is a value of 2? Like, furthest right is 1s, and then moving left is 2s, 4s, 8s, and then....? Does the value of the rows double as you progress left? Would 16s be next, and then 32s?
Exactly.
So, 111111 = 63?
