Truncated Binary Multipliers With Variable Correction and Minimum Mean Square Error

Truncated multipliers compute the $n$ most-significant bits of the $n \times n$ bits product. This paper focuses on variable-correction truncated multipliers, where some partial-products are discarded, to reduce complexity, and a suitable compensation function is added to partly compensate the introduced error. The optimal compensation function, that minimizes the mean square error, is obtained in this paper in closed-form for the first time. A sub optimal compensation function, best suited for hardware implementation, is introduced. Efficient multipliers implementation based on sub-optimal function is discussed.