A circular DNA digested with 2 asymmetric sites gives:
Circular DNA cleaved at two distinct positions yields as many fragments as cuts. Asymmetric sites divide circle into two arcs of different contour lengths, producing two double-stranded fragments of unequal size. Complete digestion separates circle into those two linear pieces. Agarose gel resolves them as two distinct bands with different migration. Symmetric sites would give one band due to co-migration. One band would indicate single site, three bands would need three sites. Therefore two asymmetric sites logically generate two bands.
Ref: NCERT Biology Class XII Principles on Klenow fill-in labeling, Lehninger Chapter 9 DNA cloning techniques, and Molecular Cloning by Sambrook Chapter 10 documenting end-labeling of cohesive termini.
