The 2´s Complement and Other Semi-Systematic Binary Codes

The class of semi-systematic weight codes is presented. To this class belong 2´s complement and minus two code. Properties of semi-systematic codes are considered. Some of these properties are shown on the representation diagram, and the semi-systematic codes used in the real computers are listed. One of the semi-systematic codes called 2´s complement (neg. 2´s complement) is described in detail. This code has the same useful properties as conventional 2´s complement code and, in addition, multiplication in the 2´s complement code is closed. The algorithms for arithmetical operations in 2´s complement are shown and proved. It follows that the arithmetic unit in 2´s complement does not require any additional equipment compared with a conventional 2´s complement arithmetic unit.