there is a question saying that,
"Represent these unsigned numbers in both Base-Complement and using Booth’s representation. For each number you also need to state how many shifts and additions (these include potential subtractions)are needed if this number is used as a multiplier in both the usual algorithm and Booth’s algorithm.
As an example, 7 is represented as 111, or 1001 in Booth’s representation. Considering 4 bits for the usual multiplication algorithm, 7 would be represented as 0111 and would require 3 additions, and 4 shifts (3 from the 1’s and 1 from the 0); and for the Booth’s algorithm we would require 1 more bit, to represent 7 as 01110 so we can go through the multiplier 2 bits at a time: 10 to detect we are entering a sequence; 11 to detect where are in the sequence; and 01 to detect we are leaving the sequence. Using Booth’s Algorithm we have 2 additions (with one being a subtraction) and 4 shifts."
Could someone explain this to me why "1001" is the booth representation, I know exactly what booth algorithm is, but shouldn't it be like "01110"... Or for instance, to represent 1, could someone exlain why and when we should have an "addition" or "shift" operation? Thanks!