How do you convert between 11B (Base-16) to Base-8?

Though we could go via decimal, we can convert via binary to result in a far simpler method.
First, you convert each digit of the base-16 value into 4 bit binary:
11B = 0001 0001 1011
Then, split this string into sets of 3 bits
000 100 011 011
And convert each of those sets into Octal.
0433 (we can ignore the leading 0)
This works because 1 digit of hexadecimal is stored in 4 bits of binary, whilst 1 digit of octal is stored into 3 bits.