Answer 1

13 : 2 = 6 R 1
6 : 2 = 3 R 0
3 : 2 = 1 R 1
1 : 2 = 0 R 1

1101

Answer 2

Without array you can use stack frames to store partial results. I.e. think recursion. Symbolically

d2b(n) ≡ d2b(n>>1) + n&1

where d2b is a function converting decimal 2 binary.