Converting Binary to Octal
Group the digits by three, starting from the right, and convert the sections to octal.
Converting Octal to Binary
Simply expand each number into its binary equivalent and squish the results together.
Converting Binary to Hex
First, recall counting to 15 in hex (the base 16 number system) is as follows: 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
So $47_{10} = (16^1 \times 2) + (16^0 \times 15) = 2F_{16}$
Now, to convert binary to Hex, group the digits by four, starting from the right, and convert the decimal equivalent of the grouping to hex.
Converting Hex to Binary
Similarly to octal to binary, simply take each number into its binary equivalent and squish the results together.