A recursive algorithm for binary multiplication and its implementation

Authors:
Renato De Mori;Régis Cardin
Affiliations:
Department of Computer Science, Concordia University, 1455 De Maisonneuve, Blvd. West, Montreal, Quebec, Canada H3G 1M8;Department of Computer Science, Concordia University, 1455 De Maisonneuve, Blvd. West, Montreal, Quebec, Canada H3G 1M8
Venue:
ACM Transactions on Computer Systems (TOCS)
Year:
1985

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Abstract

A new recursive algorithm for deriving the layout of parallel multipliers is presented. Based on this algorithm, a network for performing multiplications of two's complement numbers is proposed. The network can be implemented in a synchronous or an asynchronous way. If the factors to be multiplied have N bits, the area complexity of the network is O(N2) for practical values of N as in the case of cellular multipliers. Due to the design approach based on a recursive algorithm, a time complexity O(log N) is achieved.It is shown how the structure can he pipelined with period complexity O(1) and used for single and double precision multiplication.