A genome contains the information underlying an organism's form and function. Yet, we lack formal framework to represent and study this information. Here, we introduce the Bitome, a matrix composed of binary digits (bits) representing the genomic positions of genomic features. We form a Bitome for the genome of Escherichia coli K-12 MG1655. We find that: (i) genomic features are encoded unevenly, both spatially and categorically; (ii) coding and intergenic features are recapitulated at high resolution; (iii) adaptive mutations are skewed towards genomic positions with fewer features; and (iv) the Bitome enhances prediction of adaptively mutated and essential genes. The Bitome is a formal representation of a genome and may be used to study its fundamental organizational properties.