doubt regarding floating point arithmetic Rounding schemes/ Truncation schemes

Rounding schemes/ Truncation schemes

The choice of schemes decides the max error and bias.

Zero bias schemes on an average cause little error but there is a large 
chance htat they might hav a bias too and not end up with an error of 
zero. Am I right or wrong

thanks a lot

What are the rounding schemes / truncation schemes in use nowadays

arun