Circuitry for calculating the square root of a binary number iterates the equation E(K+1)=E(K)+(S-E(K).sup.2) where E(K+1) is the current estimate of the square root of the sample S and E(K) is the previous estimate. The value E(K).sup.2 is estimated in order to reduce the complexity of the hardware. An application is described for real time processing of digital audio signals in serial-bit format.