Question

express the numbers eight, fifteen and seventeen in base 2. I have forgotten how to do the base 2 question.

Answer 1

The quickest way for converting small numbers like this to binary would probably be to find the closest power of 2, then add/subtract intermediate powers of 2 as needed.

Converting 8 is immediate, since it's already a power of 2:

$8=2^3\implies 8_{10}=1000_2$

Converting 15 and 17 is also pretty easy if you're familiar with the rules of arithmetic in binary.

$15=16-1=2^4-2^0\implies 15_{10}=16_{10}-1_{10}=10000_2-1_2=1111_2$

$17=16+1=2^4+2^0\implies 17_{10}=10000_2+1_2=10001_2$