Thanks to comment by @gIS, I realized that I was mixing up the order. If I write $j$ as $|j1\cdots j_t\rangle$$|j_1\dots j_t\rangle$, of course it will be equal to $j_12^{t-1} \dots j_12^0$$j_12^{t-1} \cdots j_t2^0$. I was confused about the numbering of the qubits.