How could be proved that the following language is decidable?

$\{\langle G\rangle|G\ \text{is a CFG over}\ \{0,1\}\ \text{and}\ 1^* \subseteq L(G)\}$

P.S. 
It's the problem 4.15 of the third edition of the "Introduction to the Thoery of Computation" by Michael Sipser.