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In a digital filter realized with fixed-point arithmetic, there is a peculiar phenomenon known as limit-cycle oscillation, which is due to roundoff errors. For floating-point arithmetic, it has been conjectured that its amplitude is negligibly small, if it does exist. This paper shows that limit-cycle oscillations can exist in floating-point digital filters and that their amplitude can be large. Also, conditions for the existence of limit-cycle oscillations are derived.