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Non-Adjacent Form (NAF) is a canonical form of signed binary representation of integers. Joye-Yen proposed a left-to-right analogue of NAF (FAN). It is known that NAF and FAN can be generated by applying a sliding window method with width-2 to the Booth encoding in right-to-left and left-to-right direction, respectively. In this article, we derive some properties of Booth encoding such as pattern, classification, extension, adjacency, and length. 1doi:10.14257/ijsia.2013.7.6.27 fatcat:7uqqjkr74nhczerlewyeyeakii