How to convert these numbers?

Question

I am trying to understand number systems binary and decimal number systems. How can I convert the following numbers using the least amount of digits?

1. $(47)\text{base}-10$ to signed binary.

2. $(-27)\text{base}-10$ to signed and binary magnitude

3. $(213)\text{base}-16$ to a 10 base number

Here are my attemps:

1. $00101111$

2. $10011011$ (or 2's complement: $11100101$)

3. $531$

Am I heading right?

Answer 1

These are all correct. For 2, the first is correct according to Wikipedia. Twos' complement is different, which you have also done correctly.