Basics of Booth's Multiplication Booth Re-coding

Theory:

Mr. Booth observed that multiplier can be written in many different ways, this is the basics of Booth Multiplications.

In Booth multiplication algorithm signed and unsigned numbers are treated the same.

In gate Exam, Questions are generally asked from this topic.

They may ask the number of additions and subtraction needed in particular Booth Algorithm.

Booth Recoding:

Step1:  We have to always take the multiplier.If we say multiply 2 by 3 So 3 is a multiplier.

Step 2:  Append 0 in the multiplier. Appending 0 means writing one extra 0 at the rightmost or least significant bit side.

let us say our multiplier is

, after appending  0 at the rightmost side

Step 3:

From right-hand side observe two consecutive bit patterns

 1st Bit 2nd Bit Action 0 0 Write 0 1 1 Write 0 0 1 Write -1 1 0 Write +1

Our Multiplier is

Now Booth Re-Coding is  like this:

Now the number of Subtraction Required is just one because in encoded multiplier we have only one "-1".

Now the number of Addition Required is just one because in encoded multiplier we have only one "1".

Booth Algorithm has a large number of addition and subtraction involved when Multiplier pattern is like 0101010101010. It means a lot of 01 or 10 pairs.