Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation.
The block diagram for the implementation of the Booth's algorithm for determining the product of two 8-bit signed numbers is as shown below.
The Multiplier and Multiplicand are placed in the $Q$ and $M$ registers, respectively. There is also a $1$-bit register placed logically to the right of the least significant bit($Q_0$) of the $Q$ register and designated $Q_{-1}$.
The results of the multiplication will appear in the $A$ and $Q$ registers. $A$ and $Q_{-1}$ are initialized to $0$. The control logic scans the bits of the multiplier one at a time. Now, as each bit is examined, the bit to its right is also examined. If the two bits are the same ($11$ or $00$), then all of the bits of the $A,Q,$ and $Q_{-1}$ registers are shifted to the right $1$ bit. If the two bits differ, then the multiplicand is added to or subtracted from the $A$ register, depending on whether the two bits are $01$ or $10$. Following, the addition or subtraction, the right shift occurs.
In either case, the right shift is such that the leftmost bit of $A$, namely $A_{n-1}$, not only is shifted into $A_{n-2}$,but also remains in $A_{n-1}$. This is required to preserve the sign of the number in $A$ and $Q$. It is known as an arithmetic shift, because it preserves the sign bit.
