The coordinate rotation digital computer (CORDIC) algorithm is used in numerous special-purpose systems for real-time signal processing applications. It is desirable to use fixed-point CORDIC units in such systems, since the low complexity, compared to floating-point, allows multiple CORDIC units and additional hardware to be integrated on the same chip. However, an analysis of fixed-point CORDIC in the Y-reduction mode, which allows computation of the inverse tangent function, shows that unnormalized input values can result in large numerical errors. This paper describes two approaches to tackle the numerical accuracy problem. The first approach builds on a fixed-point CORDIC unit and eliminates the problem by including additional hardware for normalization. This paper presents a method to integrate the normalization operation with the CORDIC iterations for efficient implementation in "0(n1.5)" hardware. The second solution to the accuracy problem is to use a floating-point CORDIC unit but reduce the implementation complexity by using a hybrid architecture. We present arguments to support the use of such an architecture in certain special purpose arrays.