Bit flipping help...

What is the best way to take an incoming byte value of 0x01 and change it to 0xFFFFFF81?

taking 0xFFFFFF80 ^(xor) 0x01 works.

regular OR would work also:
incomingByte = incomingByte | 0xFFFFFF80

or add to it:
incomingByte = incomingByte + 0xFFFFFF80

What is it you're trying to do?

What is the best way to take an incoming byte value of 0x01 and change it to 0xFFFFFF81?

a (incoming) byte value cannot be changed to 0xFFFFFF81. You need a (unsigned) long to hold such a large number.

If you have an incoming long you should use

switch(incoming)
{
case 0x01 : incoming = 0xFFFFFF81; break;
// add aditional values to process.
}

The examples mentioned before will work if the incoming value is restricted to 0 and 1 but have side effects when the incoming value is larger than 0x01, e.g. 0x37

Mavromatis:
What is the best way to take an incoming byte value of 0x01 and change it to 0xFFFFFF81?

Yeah, it would be helpful to have more context. Right now, I would say the answer to this question is...

if ( value == 1 )
  value = 0xffffff81;