Adders and Their Design (UMAP)

This module involves elementary group theory and abstract algebra as applied to adders and their design. It discusses the logic behind adders, and looks at the circuitry used in their realization and the various design methods for creating fast-adders.

Table of Contents:

INTRODUCTION
Binary System
Two-element Boolean Algebra
Switching Functions

DESIGN FOR COLUMN ADDITION
Half Adder
Full Adder

THREE-COLUMN ADDITION
Parallel Adder
Serial Adder
Circuitry Comparison

MINIMIZING ADDITION TIME
Effect of Network Design on Speed
Ripple-carry Addition
Carry-lookahead Addition
A Good Compromise

UNCONVENTIONAL METHODS AND REPRESENTATIONS
Conditional-sum Addition
Residue Representation

THE THEORETICALLY BEST FAST ADDER

SOLUTIONS TO EXERCISES

REFERENCES