  In this paper, we find all sums of two Fibonacci numbers which are close to a
power of 2. As a corollary, we also determine all Lucas numbers close to a
power of 2. The main tools used in this work are lower bounds for linear forms
in logarithms due to Matveev and Dujella-Peth\"{o} version of the
Baker-Davenport reduction method in diophantine approximation. This paper
continues and extends the previous work of Chern and Cui.
