Synthesis of parallel adders from if-decision diagrams

Abstract

Addition is one of the timing critical operations in most of modern processing units. For decades, extensive research has been done devoted to designing higher speed and less complex adder architectures, and to developing advanced adder implementation technologies. Decision diagrams are a promising approach to the efficient many-bit adder design. Since traditional binary decision diagrams does not match perfectly with the task of modelling adder architectures, other types of diagram were proposed. If-decision diagrams provide a parallel many-bit adder model with the time complexity of Ο(log2n) and area complexity of Ο(n×log2n). The paper propose a technique, which produces adder diagrams with such properties by systematically cutting the diagram’s longest paths. The if-diagram based adders are competitive to the known efficient Brent-Kung adder and its numerous modifications. We propose a blocked structure of the parallel if-diagram-based adders, and introduce an adder table representation, which is capable of systematic producing if-diagram of any bit-width. The representation supports an efficient mapping of the adder diagrams to VHDL-modules at structural and dataflow levels. The paper also shows how to perform the adder space exploration depending on the circuit fan-out. FPGA-based synthesis results and case-study comparisons of the if-diagram-based adders to the Brent-Kung and majority-invertor gate adders show that the new adder architecture leads to faster and smaller digital circuits.