Excess-N is simply a means of representing negative integers in a fixed-width weighted binary system. It is taught both because it is one of several ways of representing negative integers and is therefore useful in introducing and discussing the pros and cons of such representations and also because it is very widely used -- anyone that uses floating point variables (that use IEEE-754 representation) since that is how the exponent is represented.Anyone know why colleges seem to want to teach excess-3 codes so often? I know why they were important in the fifties and sixties, but there's really no need now. I think it would be more important to teach ASCII, maybe EBCDIC, and newer expanded character codes. Maybe that comes later.
The use of excess-3 is common not so much because of the historical advantages it has in a BCD system, but rather because it is something that is very easy for students to understand and to work with on paper. Any excess-N representation with N < 7 can represent the positive digits. For the basics I tend to use a 3-bit representation using either excess-3 or excess-4 in part because 3-bits doesn't take as much time to enumerate on the board and also because I want to divorce the conversation from any kind of BCD notions, which students have a very hard time doing.