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In many signal processing applications it is desirable to maintain constant word size through the basic arithmetic operations of add, subtract, multiply and divide. Of these operations, multiply is the biggest concern as multiplying two n-bit data yields a 2n-bit product. Forming the full product and rounding it to the desired precision is mathematically attractive, but the complexity is high. Forming a portion of the bit product matrix would reduce the complexity, but this incurs potentially large errors. A compromise approach has been developed that represents a reasonable (in many applications) compromise. The complexity is slightly above that of a truncated bit product multiplier, but the accuracy is close to that of a rounded full precision multiplier.