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[[Image:Phase Accum Graph.png|frame|Figure 2: Normalized phase accumulator output]]
The adder is designed to overflow when the sum of the [[absolute value]] of its operands exceeds its capacity (2<sup>N</sup>−1). The overflow bit is discarded so the output word width is always equal to its input word width. The remainder <math>\phi _n</math>, called the residual, is stored in the register and the cycle repeats, starting this time from <math>\phi _n</math> (see figure 2).<ref name="Grzeg"/> Since a phase accumulator is a [[finite
:<math>\mbox{GRR}=\frac{2^N}{\mbox{GCD}(\Delta F,2^N)}</math>
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