Below is the datapath for a sequential system which calculates the square root of a positive integer A$.$ It uses the Newton$-$Raphson Method $($also known as the Babylonian method$)$ that takes the following iterative form for the square root calculation:

The first value x$0$ is initialized to $1$ and then each xk$+1$ is calculated from xk based on the equation above until the difference between xk$+1$ and xk is sufficiently small.

A program for this method might look like this:

x $=1$

repeat

prev$\_$x $=$ x

x $=($ prev$\_$x $+$ A$/$prev$\_$x $)/2$

until $(|$ x $-$ prev$\_$x $|<$ e $)$

To begin, the value A is loaded into a register and the X register is initialized to $1.$ The Divider calculates A$/$X and this result is added to X$.$ Note that the Divider is started by asserting the signal SD and that the result is available when RD is high. The component DONE compares the current value X with the new value to determine whether the computation can stop $($whether xk and xk$+1$ are sufficiently close$).$ If not then the X register is loaded with the new value. The division by $2($in the component labeled $/2$ is achieved by removing the least significant bit and padding the left end with a $0.$