New and simple numerical criteria based on a codon adaptation index are applied to the complete genomic sequences of 80 Eubacteria and 16 Archaea, to infer weak and strong genome tendencies toward content bias, translational bias, and strand bias. These criteria can be applied to all microbial genomes, even those for which little biological information is known, and a codon bias signature, that is the collection of strong biases displayed by a genome, can be automatically derived. A codon bias space, where genomes are identified by their preferred codons, is proposed as a novel formal framework to interpret genomic relationships. Principal component analysis confirms that although GC content has a dominant effect on codon bias space, thermophilic and mesophilic species can be identified and separated by codon preferences. Two more examples concerning lifestyle are studied with linear discriminant analysis: suitable separating functions characterized by sets of preferred codons are provided to discriminate: translationally biased (hyper)thermophiles from mesophiles, and organisms with different respiratory characteristics, aerobic, anaerobic, facultative aerobic and facultative anaerobic. These results suggest that codon bias space might reflect the geometry of a prokaryotic "physiology space." Evolutionary perspectives are noted, numerical criteria and distances among organisms are validated on known cases, and various results and predictions are discussed both on methodological and biological grounds.