An exercise weight system includes an exercise weight bar, a plurality of weights selectively connectable to the exercise weight bar, and a cradle for holding the exercise weight bar and weights. The exercise weight bar has a rod having a longitudinal axis and a selector positioned on the rod such that the selector is rotatable about the longitudinal axis of the rod. The exercise weight bar includes an engagement system that permits a user to selectively secure one or more weights to the rod. The engagement system includes one or more weight engagement members and a binary cam system that selectively moves the one or more weights engagement members between a first position and a second position to selectively engage or disengage various combinations of the one or more weights when the selector is rotated about the longitudinal axis of the rod.