Optimization of one-bit full adders embedded in regular structures

Abstract

We study the problem of optimizing the transistor sizes in the one-bit nMOS full adder either isolated or embedded in a regular array. A local optimization method that we call the critical-path optimization method is developed. In this method, two parameters at a time are changed along the critical path until a locally optimal choice of transistor sizes is found. The critical-path optimization method uses the Berkeley VLSI tools and the hierarchical layout language ALLENDE developed at Princeton. First, we optimize the isolated one-bit full adder implemented in three ways: as a PLA, data selector, and with random logic. The details of the critical-path optimization method and power-time tradeoff curves are illustrated here. Second, we optimize the one-bit full adder embedded in a simple array multiplier. The entire 3 × 3, 4 × 4, 8 × 8, and 10 × 10 multipliers are optimized and their local optima are compared. Because the optimization of the entire circuit becomes less practical when the circuit becomes larger, we develop a method that makes use of circuit regularity. We prove that some small array of one-bit full adders, called the canonical configuration, has the same local optima as the n × n multiplier for large n, with the criterion of minimizing the delay time T. Hence, we can greatly reduce the computation load by optimizing this canonical configuration instead of optimizing the entire circuit. Experimental results confirm the effectiveness of this approach.