Essay About Complement Notation And Count Of Bits Of The Multiplicand

Booths Algo
Essay title: Booths Algo
Booths multiplication algorithm
Procedure
If x is the count of bits of the multiplicand, and y is the count of bits of the multiplier :
Draw a grid of three lines, each with squares for x + y + 1 bits. Label the lines respectively A (add), S (subtract), and P (product).
In twos complement notation, fill the first x bits of each line with :
A: the multiplicand
S: the negative of the multiplicand
P: zeroes
Fill the next y bits of each line with :
A: zeroes
S: zeroes
P: the multiplier
Fill the last bit of each line with a zero.
Do both of these steps |y| (the Absolute Value of y) times :
If the last two bits in the product are

00 or 11: do nothing.

01: P = P + A. Ignore any overflow.

10: P = P + S. Ignore any overflow.
Arithmetically shift the product right one position.
Drop the last bit from the product for the final result.
Example
Find 3 Ч -4:
A = 0011 0000 0
S = 1101 0000 0
P = 0000 1100 0
Perform the loop four times :
P = 0000 1100 0. The last two bits are 00.
P = 0000 0110 0. A right shift.
P = 0000 0110 0. The last two bits are 00.
P = 0000 0011 0. A right shift.
P = 0000 0011