VLSI Digital Signal Processing Systems: Design and Implementation

14.8    CONCLUSIONS

This chapter has presented the basic concepts of redundant number systems and redundant arithmetic, which leads to carry-free addition property. Algorithms and architectures for hybrid radix-2 and radix-4 addition/subtraction, as well as signed-digit addition/subtraction have been developed. Two msd-first serial hybrid radix-2 redundant multipliers have been designed, which are also suitable for on-line computations. Finally, the design of data format converters including conversion from nonredundant to redundant in radix-2 and redundant to nonredundant in lsd-first and msd-first modes has been addressed. Fast redundant to nonredundant converters can be designed by using variations of known fast carry generation schemes such as carry-select and/or binary-tree configurations (see Appendix E). Interested readers may refer to [21] for a detailed description of the design of fast low-power redundant to nonredundant converters, and their application to perform fast binary addition.

Fig. 14.22    Dependence graph for a radix-2 redundant to nonredundant converter for a wordlength of 4 digits operating in the msd-first mode.