The base 10 number 0.03841 has the value
$$0 \times 10 ^ { - 1 } + 3 \times 10 ^ { - 2 } + 8 \times 10 ^ { - 3 } + 4 \times 10 ^ { - 4 } + 1 \times 10 ^ { - 5 } = 0.03841$$
Similarly, the base 2 number 0.01101 has the value
$$0 \times 2 ^ { - 1 } + 1 \times 2 ^ { - 2 } + 1 \times 2 ^ { - 3 } + 0 \times 2 ^ { - 4 } + 1 \times 2 ^ { - 5 } = \frac { 13 } { 32 }$$
What is the value of the recurring base 2 number $0 . \dot { 0 } 01 \dot { 1 } = 0.001100110011 \ldots$ ?
A $\frac { 1 } { 3 }$
B $\frac { 1 } { 5 }$
C $\frac { 1 } { 15 }$
D $\frac { 2 } { 15 }$
E $\frac { 4 } { 15 }$
F $\frac { 3 } { 16 }$
G $\frac { 5 } { 16 }$
H $\frac { 6 } { 31 }$