Decide the Winner

$Alice$ and $Bob$ were fond of playing. One day, $Alice$ came up with a game of power of two. The game is as follows: 1. $Alice$ starts the game. 2. $Bob$ gives Alice a number. 3. If the number is a power of $2$, divide it by $2$ and change the turn, else subtract the highest power of $2$ and change the turn. 4. Continue until $1$ is left. The person who cannot move further $loses$ the game.