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When you want to note a base ten number in base two, think of it like a different language with different grammar.
Normally, in base ten, we tend to do things from left to right.
To convert a base ten number to base two, you gotta "tranlate" it. And since I learned this for computing crap, I'll just use that as my basis. There are 8 bits in a byte. Each bit being an on or off switch.
1 0 0 0 0 0 0 1 That is one byte, if you want to read the number of that, you read it from right to left. Like this.
1 0 0 0 0 0 0 1 128 64 32 16 8 4 2 1
Each of the top bits, represent the lower base ten numbers. A 1 means an on switch, so you use the number below it. A 0 is an off switch, you don't use the number below it. So if you wanted to write say, 33 in binary, you'd have to find the combination of the lower numbers that adds up to 33.
In binary, it'd look like this 00100001, or you can drop the first 2 0's off and write it like this 100001. If the number you're looking for is larger than the sum of all the numbers on the lower set, you need more bytes.
That's my very base, very limited understanding of binary. But I can count in binary, and do some very basic stuff with it. Of course, application of knowledge is harder than attaining it. I'd be hard pressed to actually use this for anything useful, but at least I'm not completely lost when it comes up.
If I've made an ass out of myself, you can all point and laugh, heh.
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