Modulo-2 addition (or exclusive-OR) is one of fundamental operations for binary variables. In this paper, we discuss statistical properties of sequences obtained by modulo-2 addition of two binary sequences. Firstly, we theoretically evaluate statistics of sequences obtained by modulo-2 addition of two general binary random variables. Secondly, we consider statistics of modulo-2 added chaotic binary sequences generated by a class of one-dimensional chaotic maps. Furthermore, we consider synthesis of an aperiodic binary sequence and a periodic one by modulo-2 addition with the purpose of generating aperiodic sequences with good statistical properties. We also perform computer experiments about such sequences.