= Digit block frequency
{title2=$F_N(w)$}
For a finite prefix of $N\geq r$ digits in <positional notation>, the digit block frequency $F_N(w)$ of a length-$r$ <word> $w$ is its number of overlapping occurrences divided by $N-r+1$, the number of available starting positions. All such <digit block frequencies> sum to one. The infinite <limit> used for a <normal number> can instead divide counts by $N$: the factor $(N-r+1)/N$ tends to one for fixed $r$.
For the six <binary digits> $010101$, the single-digit counts are three zeros and three ones. Its five adjacent pairs are $01,10,01,10,01$, giving
$$
F_6(00)=F_6(11)=0,\qquad F_6(01)=\frac35,\qquad F_6(10)=\frac25.
$$
This example explains both the overlapping convention and the end correction in a finite sample. The corresponding infinite <binary expansion> has pair frequencies $0,1/2,1/2,0$, rather than the four values $1/4$ required of a <normal number> in base two.
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