Binary adder architectures for cell-based VLSI and their synthesis

TLDR: It is found that the ripple-carry, the carry-lookahead, and the proposed carry-increment adders show the best overall performance characteristics for cell-based design.

Abstract: The addition of two binary numbers is the fundamental and most often used arithmetic operation on microprocessors, digital signal processors (DSP), and data-processing application-specific integrated circuits (ASIC). Therefore, bi¬ nary adders are crucial building blocks in very large-scale integrated (VLSI) circuits. Their efficient implementation is not trivial because a costly carrypropagation operation involving all operand bits has to be performed. Many different circuit architectures for binary addition have been proposed over the last decades, covering a wide range of performance characteristics. Also, their realization at the transistor level for full-custom circuit implemen¬ tations has been addressed intensively. However, the suitability of adder archi¬ tectures for cell-based design and hardware synthesis both prerequisites for the ever increasing productivity in ASIC design — was hardly investigated. Based on the various speed-up schemes for binary addition, a compre¬ hensive overview and a qualitative evaluation of the different existing adder architectures are given in this thesis. In addition, a new multilevel carryincrement adder architecture is proposed. It is found that the ripple-carry, the carry-lookahead, and the proposed carry-increment adders show the best overall performance characteristics for cell-based design. These three adder architectures, which together cover the entire range of possible area vs. delay trade-offs, are comprised in the more general prefix adder architecture reported in the literature. It is shown that this universal and flexible prefix adder structure also allows the realization of various customized adders and of adders fulfilling arbitrary timing and area constraints. A non-heuristic algorithm for the synthesis and optimization of prefix adders is proposed. It allows the runtime-efficient generation of area-optimal adders for given timing constraints.