On the probability distribution of fixed-point multiplication

The area, delay and power consumption of functional units all are dependent on the word-length of the processed data. Since choosing an optimum word-length is a tradeoff between design costs and accuracy, it is essential to have an accurate model of computational errors for each operation. Errors resulting from the output rounding or truncation of the functional units is generally considered as uniformly distributed over the error limits regardless to the functionality of the unit. This work presents an analysis of the probability distribution of a fixed-point multiplier and its output truncation error. Simulations show that the uniform distribution assumption is violated in the case of truncation of a multiplication result of less than 8 bits.