This paper defines a new distance measurement for binary strings called the extended Hamming distance. Using this measurement we prove that the binary decoding method in the simple genetic algorithm satisfies the demand of certain continuity. Based on this continuity, we propose a new selection mechanism called the driven selection mechanism. This selection mechanism computes the expected number of copies of each string in the population based on the difference of fitness values between the best string and the current string, i.e. if a string is close to the best string, it has more chance to survive. A distinct improvement of this new selection mechanism is that the impact of the sign of the fitness value disappears, and the comparing experiment verifies that the driven selection mechanism can prevent premature termination more effectively.