ALGORITHM FOR SQUARE ROOT IMPLEMENTATION:
Consider X is an N bit number whose square root is to be determined. X can be expressed as
Considering to be the nearest perfect square number of. Now assume that the square root of is . Then equation (2) can be rewritten as
Now consider, (4)
Where Q is the quotient and R is the remainder. Inserting equation (4), equation (3) can be reformulated as
Equation (5) can be rewritten as
If then X is a perfect square number whose square root is (Z+Q).
If then X is not a perfect square number whose nearest integral
square root is (Z+Q). The procedure to calculate the square root by division method can be described in the following steps:
Step 1: Obtain the nearest square root of the N/2 Most Significant Bits (MSB). Assume that the output is Z.
Step 2: Determine the square of Z by combining Yavadunam and Duplex methodology.
Step 3: Subtract the squared output from N/2 MSB.
Step 4: Obtain the double of Z.
Step 5: Combine the output of the subtractor and the next N/4 bits. Divide the combination by 2Z. Assume the quotient as Q and the remainder as R.
Step 6: Determine the square of Q and subtract Q2 from. If the residue is zero then Z+Q is the perfect square root otherwise Z+Q is the square root of nearest perfect square.
Step 7: Divide the residue by the double of (Z+Q) and the quotient is the floating point part of the square root.