I'm seeking some clarification on a description of the RAM model in CLRS on page 23, section 2.2 (Analyzing Algorithms).
Firstly, it is mentioned that we assume integers are represented with $c\cdot\log_2 n$ bits for some constant $c\geq 1$. Now take the integer value $2$, would it not be the case that we would need more than $\log_2 2=1$ bit to represent the integer value $2$? Since we must express two as $(10)_2$? Perhaps the constant $c$ is supposed to account for this discrepancy.
Secondly I'm a bit confused by this statement: "We require $c \geq 1$ so that each word can hold the value of $n$, enabling us to index the individual elements...". I understand that if $c$ were $0$ or negative then that would not make any sense, however, are we also to assume then that $c$ must be an integer?
Any intuitive descriptions of these basic properties would be great or relevant examples someone can come up with.