Radix-4 square root without initial PLA

A systematic derivation of a radix-4 square root algorithm using redundance in the partial residuals and the result is presented. Unlike other similar schemes, the algorithm does not use a table-lookup or programmable logic array (PLA) for the initial step. The scheme can be integrated with division. It also performs on-the-fly conversion and rounding of the result, thus eliminating a carry-propagate step to obtain the final result. The selection function uses 4 b of the result and 8 b of the estimate of the partial residual.