= Binary fraction
{title2=$\sum_j b_j2^j,\quad b_j\in\{0,1\}$}
A base-two positional <fraction> with a binary point separating nonnegative and negative powers of two. For example, $10.101_2=2+1/2+1/8=21/8$. A finite expansion is a <dyadic rational>: with $F$ fractional places, its value is an <integer> divided by $2^F$. Conversely, any nonnegative <reduced fraction> whose denominator is a power of two has a finite <binary expansion>. Leading <integer> zeroes and trailing fractional zeroes do not change its value.
Back to article page
