# Need a relation between additions/ subtractions performed and the number of bit switching in multiplier in Booth Algorithm

This is my home work assignment.

Establish a relation between the number of bit-switching in multiplier and the number of addition/subtraction operations performed in Booth’s algorithm.

Now Booth Algorithm is shown below, I understand that addition or subtraction will be performed when the LSB of Q and Q-1 are different. But how do I come up with a relation?

Notice that $Q_{-1}$ is not $Q-1$. It is the bit next to $Q_0$, which is the LSB (least significant bit). So there's a strong connection between sign changes in $Q$ and which path is taken after querying $(Q_0,Q_{-1})$. –  Yuval Filmus Aug 28 '11 at 19:53