BOOTH ALGORITHM IN SIGNED-DIGIT REPRESENTATION

The algorithm given by Andrew Donald Booth in 1950 for multiplication, can be interpreted in the classic way: a way to reduce existing sequences consecutive 1s in the binary representation of a number. Or you can look more from the prism they do techniques such as NAF representation: where it is understood that instead of opting for a binary representation of the number, it is a ternary representation, which meets the property (or is expected to meet) having more 0s than classical binary representation. In both approaches, the performance increase is achieved because, in the algorithmic scheme Booth, when the number against which it has a 0 in the ith position operates in the i-th algorithmic step, we saved the calculations (or part thereof). Hence in this paper we are going to optimize those cases where, according to the prism through which we look, we compact sequences of consecutive 1s or 0s ternary representation has more than binary.