This paper explores the problem of knowledge in computational informational organisms, i.e. organisms that include a computing machinery at the artifact side. Although information can be understood in many ways, from the second half of the past century information is getting more and more digitised, von Neumann machines becoming dominant. Computational information is a challenge for the act of measuring, as neither purely quantitative nor totally qualitative approaches satisfy the need to explain the interplay among the agents producing and managing (...) computational information. In this paper, Floridi’s method of levels of abstraction is applied to the analysis of computational information, with a chief interest in the concepts of information measure, quantification and quality. (shrink)