  Within the quantum computing, there are two ways to encode a normalized
vector $\{ \alpha_i \}$. They are one-hot encoding and binary coding. The
one-hot encoding state is denoted as $\left | \psi_O^{(N)} \right
\rangle=\sum_{i=0}^{N-1} \alpha_i \left |0 \right \rangle^{\otimes N-i-1} \left
|1 \right \rangle \left |0 \right \rangle ^{\otimes i}$ and the binary encoding
state is denoted as $\left | \psi_B^{(N)} \right \rangle=\sum_{i=0}^{N-1}
\alpha_i \left |b_i \right \rangle$, where $b_i$ is interpreted in binary of
$i$ as the tensor product sequence of qubit states. In this paper, we present a
method converting between the one-hot encoding state and the binary encoding
state by taking the Edick state as the transition state, where the Edick state
is defined as $\left | \psi_E^{(N)} \right \rangle=\sum_{i=0}^{N-1} \alpha_i
\left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle ^{\otimes i}$.
Compared with the early work, our circuit achieves the exponential speedup with
$O(\log^2 N)$ depth and $O(N)$ size.
