Complexity of basic boolean operators for digital circuit design

Abstract

This article provides a survey of circuit complexity bounds for basic boolean transforms exploited in digital circuit design and efficient methods for synthesizing such circuits. The exposition covers structurally simple functions and operators, such as counters, adders, encoders, and multiplexors, and excludes more complex algebraic operations with numbers, polynomials, and matrices. Several applications to implementing more specific operations are also discussed.

Figures (3)

• Figure 1: Ofman's (Brent---Kung) prefix circuit
• Figure 2: Standard circuit for summing $n$ bits
• Figure 3: Computational scheme of the weight-preserving counting circuit