<p><b>Abstract</b>—This paper presents a new fast RNS converter for the 3 moduli set of the form <tmath>$\{2^n-1,2^n,2^n+1 \}$</tmath>. A new property of the CRT is also presented and this property is used to develop a fast converter for this <tmath>$3$</tmath> moduli set. The resulting implementation is based on carry-save adders and one carry-propagate adder stage, without the need for any look-up tables. The new design is faster and smaller than existing designs.</p>