Answer from cs61c-es (Meng Chang Bruce Lin 16075852) for Question 3
Programmer used to base their design according to the hardware specification. So, for single and double precisions, the missing guard bits has created many problems in terms of precision and accuracies. The format of writing (0.5-x)+0.5 is a way to compensate the missing guard bits to avoid the errors. This method were used in the older machines such as S/360 7090,7094 and Cray's. So, the main idea here is they had to deal with the guard bit issues.