2-10 Decoding a "Zero Means 2**n" Field

Sometimes a 0 or negative value does not make much sense for a quantity, so it is encoded in an n-bit field with a 0 value being understood to mean 2ⁿ, and a non-zero value having its normal binary interpretation. An example is the length field of PowerPC's load string word immediate (lswi) instruction, which occupies five bits. It is not useful to have an instruction that loads zero bytes, when the length is an immediate quantity, but it is definitely useful to be able to load 32 bytes. The length field could be encoded with values from 0 to 31 denoting lengths from 1 to 32, but the "zero means 32" convention results in simpler logic when the processor must also support a corresponding instruction with a variable (in-register) length that employs straight binary encoding (e.g., PowerPC's lswx instruction).

It is trivial to encode an integer in the range 1 to 2ⁿ into the "zero means 2ⁿ" encoding—simply mask the integer with 2ⁿ - 1. To do the decoding without a test-and-branch is not quite as simple, but below are some possibilities (no doubt overdone), illustrated for a 3-bit field. They all require three instructions, not counting possible loads of constants.