**
ALGORITHM FOR SQUARE ROOT IMPLEMENTATION:**

Consider X is an N bit number whose square root is to be determined. X can be expressed as

(1)

, (2)

Considering to be the nearest perfect square number of. Now assume that the square root of is . Then equation (2) can be rewritten as

(3)

Now consider, (4)

Where Q is the quotient and R is the remainder. Inserting equation (4), equation (3) can be reformulated as

(5)

Equation (5) can be rewritten as

(6)

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 Q^{2} 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.