a cartesian to polar coordinate converter using a cordic magnitude circuit for estimating the magnitude and angle of a vector from its known orthogonal components . the vector is described in cartesian coordinates by the complex number i + jq . the magnitude of the vector and its angle are approximated by an iterative process of successively rotating the vector toward one of the orthogonal axes and the cordic magnitude circuit is implemented in one very large scale integrated complementary metal - oxide semiconductor chip . in systems using a typical cordic magnitude circuit , accuracy increases in direct proportion to the number of rotations . the increase is accompanied by a need for an increased word size which results in a slower operating speed . the improved cordic magnitude circuit achieves higher precision without the need for a larger word size . the q processing portion of the improved circuit takes advantage of the fact that each value of q is reduced by one - half with each succeeding rotation after the first rotation , thereby vacating the most significant bit position . by doubling the resultant value of q , the msb is refilled and the least significant bit is vacated making room to accommodate the precision growth of one lsb associated with the next rotation . for small magnitude vectors , the i processing portion of the magnitude circuit left shifts the i and q components by two bit positions at each rotation to accommodate two additional bits of precision in both the i and q words .