How to get a pure bias value with zero-order holder

Question

A bias value 2 is given to sinwave, T is 0.5, and i want to get it using ZOH with a sample time 0.25, but the error is bigger with time,why? and how to get the pure bias value?

the simple example is attached.

Answer 1

The error here is on the order of 1e-15 in the first 2 seconds and will increase as the time increases.  For example, at 200 seconds the error is on the order of 1e-13. 

The reason the value you're observing in the scope is close-to, but not exactly, 2 is because of limitations of floating point arithmetic.