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Truncated multiplication reduces part of the power required by multipliers by only computing the most-significant bits of the product. The most common approach to truncation includes physical reduction of the partial product matrix and a compensation for the reduced bits via different hardware compensation subcircuits. However, this results in fixed systems optimized for a given application at design time. A novel approach to truncation is proposed, where a full precision multiplier is implemented, but the active section of the partial product matrix is selected dynamically at run-time. This allows a power reduction tradeoff against signal degradation which can be modified at run time. Such an architecture brings together the power reduction benefits from truncated multipliers and the flexibility of reconfigurable and general purpose devices. Efficient implementation of such a multiplier is presented in a custom digital signal processor where the concept of software compensation is introduced and analyzed for different applications. Experimental results and power measurements are studied, including power measurements from both post-synthesis simulations and a fabricated IC implementation. This is the first system-level DSP core using a fine-grain truncated multiplier. Results demonstrate the effectiveness of the programmable truncated MAC (PTMAC) in achieving power reduction, with minimum impact on functionality for a number of applications. Software compensation is also shown to be effective when deploying truncated multipliers in a system.