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

1 Answer

  • 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:

    [tex]8=2^3\implies 8_{10}=1000_2[/tex]

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

    [tex]15=16-1=2^4-2^0\implies 15_{10}=16_{10}-1_{10}=10000_2-1_2=1111_2[/tex]

    [tex]17=16+1=2^4+2^0\implies 17_{10}=10000_2+1_2=10001_2[/tex]