1) I'll write a / b = (x, y) to mean that a divided by b gives the integer ratio x and the remainder y. E.g., 12 / 3 = (3, 0) and 7 / 3 = (2, 1).

So...

1427 / 2 = (713, 1)

713 / 2 = (356, 1)

356 / 2 = (178, 0)

(Several lines skipped)

11 / 2 = (5, 1)

5 / 2 = (2, 1)

2 / 2 = (1, 0)

1 / 2 = (0, 1)

You stop when the integer ratio is 0. Now read the remainders up. The result is 1011...011.

2) This is pretty similar to addition to the base 10. You mark the column to the left of the current one as having a carry if the current column adds to 2 or more (including the carry for the current column). I got the row of carries to be 01101110.