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The two's complement fractional fixed-point number system is widely used to implement digital signal processing on VLSI chips. It has a range of values from −1 to one least significant bit below +1. Either the multiplication of −1 • −1 or taking the absolute value of −1 produces a result (+1) that cannot be represented. A new system, the negative two's complement number system, is described here that has a range of one least significant bit above −1 to +1 which eliminates the problem. This paper presents the new number system and describes algorithms for the basic arithmetic operations.