Binary scaling always a valid angle in the range of −180° degrees (−π radians) to +180° degrees (+π radians). In some cases, it is convenient to use unsigned multiplication (rather than signed multiplication) on a binary angle, which gives the correct angle in the range of 0 to +360° degrees (+2π radians or +1 turn). Compared to storing angles in a binary angle format, storing angles in any other format inevitably results in some bit patterns giving "angles" outside that range, requiring extra steps to range-reduce the value to the desired range, or results in some bit patterns that are not valid
Degrees of freedom (statistics) degrees of freedom. In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions. Comparison of sum-of-squares with degrees-of-freedom is no longer meaningful, and software may report certain fractional 'degrees of freedom' in these cases. Such numbers have no genuine degrees-of-freedom interpretation, but are simply providing an "approximate" chi-squared distribution for the corresponding sum-of-squares. The details of such approximations are beyond the scope of this page. Several commonly encountered statistical distributions (Student's t, Chi-Squared, F) have parameters that are commonly referred to as "degrees of freedom". This terminology simply reflects that in many applications