A self-compensation fixed-width booth multiplier and Its 128-point FFT applications

This paper presents a method for compensating the truncation error of fixed-width Booth multipliers which keep the input and the output the same bit-width. The truncated part that produces the carry-out bits is replaced with a carry-estimation equation. In order to reduce the truncation error, different input-width multipliers will have different carry-estimation equations. Simulation results show that our self-compensation method can lead to 85% reduction of truncation errors while compared with direct-truncated multipliers, as well as 40% reduction in area of a multiplier while compared with traditional Booth multipliers. In contrast with the 128-point fast fburier transform (FFT) using traditional Booth multipliers, our approach has 10% area reduction but only 1dB SQNR loss.