Truncated multiplications and divisions for the negative two's complement number system
Park, Hyuk, 1973-
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In the design of digital signal processing systems, where single-precision results are required, the power dissipation and area of parallel multipliers can be significantly reduced by truncating the less significant columns and compensating to produce an approximate rounded product. This dissertation presents the design of truncated multiplications of signed inputs utilizing a new number system, the negative fractional two's complement number system which solves an inherent problem of the conventional two's complement number system. This research also presents a new truncated multiplication method to reduce the errors with only slightly more hardware. Error, area, delay and dynamic power estimates are performed at the structural HDL level. The new method is also applied to various conventional number systems. For division, which is the slowest and most complex of the arithmetic operations, a new truncated division method is described that yields the same errors as those of true rounding without additional execution time that is normally required for true rounding. The new method is also applied to various conventional number systems.