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Hamming Code

Hello,

I'm having an issue starting a hamming code. I understand fundamentally how they work, in for example, an 8 bit system. 4 redundant bits will be added which are used as parity bits. I know their positions (powers of 2), but how exactly does one do this in code?
If I have 1111 and do

MOV r0, #0xF
LSR r0, r0, #2


I will get 0011 1100. This gives me my first two parity bits. But how do I get the next one? I don't know how to shift everything after bit 2 to the left without moving my data bit at bit 2. I think I need to use multiple registers for each insertion of redundant bit and possibly using something like an EOR operation to join them together.

Thank you very much