  We devise a hierarchy of computational algorithms to enumerate the
microstates of a system comprising N independent, distinguishable particles. An
important challenge is to cope with integers that increase exponentially with
system size, and which very quickly become too large to be addressed by the
computer. A related problem is that the computational time for the most obvious
brute-force method scales exponentially with the system size which makes it
difficult to study the system in the large N limit. Our methods address these
issues in a systematic and hierarchical manner. Our methods are very general
and applicable to a wide class of problems such as harmonic oscillators, free
particles, spin J particles, etc. and a range of other models for which there
are no analytical solutions, for example, a system with single particle energy
spectrum given by {\epsilon}(p,q) = {\epsilon}0 (p^2 + q^4), where p and q are
non-negative integers and so on. Working within the microcanonical ensemble,
our methods enable one to directly monitor the approach to the thermodynamic
limit (N \rightarrow \infty), and in so doing, the equivalence with the
canonical ensemble is made more manifest. Various thermodynamic quantities as a
function of N may be computed using our methods; in this paper, we focus on the
entropy, the chemical potential and the temperature.
