You are given ten rings numbered from $1$ to $10$, and three pegs labeled $A$, $B$, and $C$. Initially all the rings are on peg $A$, arranged from top to bottom in ascending order of their numbers. The goal is to move all the rings to peg $B$ in the minimum number of moves obeying the following constraints:
- In one move, only one ring can be moved.
- A ring can only be moved from the top of its peg to the top of a new peg.
- At no point can a ring be placed on top of another ring with a lower number.
How many moves are required?
- $501$
- $1023$
- $2011$
- $10079$
- None of the above.