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Most suns or bodies large enough to potentially have become suns are in motion, themselves orbiting around others of like size. This is not by accident, but is a factor of their size in proportion to the other clumps of matter that form coming out of a big bang. Suns are monstrous in proportion to their planets, and the planets are monstrous in proportion to their moons, and all are monstrous in proportion to the dust and meteor fragments haplessly caught in the web of all the larger bodies. Just as the planets in a solar system orbit their sun because it is the largest voice around them, just so suns themselves hear the voices of the other suns around them. If suns are not peers a different dance ensues, but if peers neither sun dominates the other and they remain at a distance from each other depending on the balance point between their gravity attraction to each other and the force of repulsion that develops as they move toward each other. If they are in motion as this balance is achieved they will remain in motion, if all other factors are also a settled issue at that time - binary suns.
If suns are not of an equal size they are not likely to become binaries, especially if there are other suns in the vicinity vying to be dominant. The smaller sun may dither, perpetually, first approaching one larger brother and when turned away by the repulsion force approaching the other brother and likewise being turned away. This scenario can entail any number of large and small suns. Do not these suns of unequal size begin to orbit each other? Indeed they do, when the size is greatly disproportional, but most suns are not that disproportional. Therefore, either a dither or more often a dance between peers develops. The dance that binaries do can be rapid and complex, if other suns are nearby and influence the dance, or the dance can be a dead stand still, as is the case between your Sun and its dead twin.