Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation.The core of the algorithm is the replacement of a string of $1's$ with a string of $0's$ so that we have to perform fewer operations than the ordinary multiplication (a/c to my understanding).
While I understand the mathematical formulation of the algorithm , I am, not able to link it with the algorithmic form. For instance what is $P$ and how does its shifting work?
Example:
$3 \times (-4)$
$3_{10}=11_2$
$4_{10}=100_2$
$(-4)_{10}=1100_{2} \text{two's complement } (-4=-2^{3}+2^2+0+0)$
Now a/c to the algorithm $11$ can be weritten as
$100_2-1_2$, hence;
$1100 \times 11=1100\times (100-1)$
$\implies 1100 \times 100 +1100=110000+(1100)^{'}=110000+100=110100$
$=(-2^{5}+2^{4}+0+2^2+0+0)=-12_{10}=3 \times (-4)$
Is my approch equivalent to this?