27 base 10 is equal to 11011 base 2
can someone explain why that is so?
I remember when I was in HS, we did thsi in a math class and I really struggled with it, then one day, POP, it clicked. I think it was when the teacher tried a different approach.
It's like this. The deal is, you have to have a fundamental understanding of what a number system "base" is. That's what this all comes down to... once you get that, you can do math in any system you want (decimal, hex, quad, octal...)
Think of it this way. The reason we use 10 is because, well, look at your hands. Once you've used all your fingers, what do you do? You need a way to account for more. We only have 10 mnumbers (inluding 0) to work with. So when you run out ,of them you just tack another one to teh front, and start over. It kind of "wraps around".
E.g., 10 = 1 whole set of numbers. now it you have a whole set and one more, that's 11. A whoel set plus 5, well that's 15.
5 whole sets, plus 7, that's 57. etc etc.
In Binary, you only have 2 numbers in your set, 0 and 1. Once you've used both of them, you have to tack on another one in front. So 11 = 1 complete set, + 1 more. (since 1 complete set = 2 digits, teh total is 3 (2+1).
1011 = 1 group of 1, 1 group of 2, 0 groups of 4, and 1 group of 8. 8+0+2+1 = 11.
Same logic with Hexidecimal. There are 16 numbers (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F). So 1 complete group + 1 more = 11 hex, which is 16 (1 more than 15) in decimal.
I know don't know if that helps. Just imagien having only 2 fingers to work with, try and think about how you would count things.