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This chapter is from the book

2–11 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 nonzero 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 here are some possibilities, illustrated for a 3-bit field. They all require three instructions, not counting possible loads of constants.

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