Member Rara Avis
Binary math is easy. About ten times easier than decimal math, in fact.
When you add the digits 9 and 1, you know the answer can't be a digit greater than 9. So what do you do? You write down a zero and carry the one, and end up with 10.
What does this 10 mean? Since we're in base ten, it means no units and one ten.
When you add the digits 1 and 1 in a base two system, you know the answer can't be a digit greater than 1. So what do you do? You write down a zero and carry the one, and end up with 10.
What does this 10 mean? Since we're in base two, it means no units and one two.
When you see the number 1111 in the decimal system, you don't have to think real hard about what each digit really means, but that's only because it's been drilled into your head for so long. We know, without giving it much thought, that from right to left we have 1 unit of ones, 1 unit of tens, 1 unit of hundreds, and 1 unit of thousands. Each of those represents our base (ten) raised to a specific power.
1 * 10^0 = 1
1 * 10^1 = 10
1 * 10^2 = 100
1 * 10^3 = 1000
Add those all up an you get 1,111, or one thousand one hundred eleven. Simple stuff.
If you see that same 1111 in binary, you do EXACTLY the same thing.
1 * 2^0 = 1
1 * 2^1 = 2
1 * 2^2 = 4
1 * 2^3 = 8
Add those up and you'll know that binary 1111 is equivalent to decimal 15. It's *still* simple stuff.