Chapter 4: Boolean Machine Architectures

Chapter 4: Boolean Machine Architectures

Joseph P. Damico

Sandia National Laboratories, Livermore, CA

Overview

LabVIEW?s basic Boolean functions (AND, OR, NOT, etc.) have the same behavior and schematic symbols as their hardware equivalents. These software functions can be combined to emulate many digital logic components and circuits. This chapter discusses several basic digital components and the VIs that emulate them. Many of the VIs can be coded using other LabVIEW structures and functions, but the emphasis is on emulating circuits with schematically equivalent software diagrams.

The NAND, NOR, and NOT gates are the primitive circuits used to build modern computers. The NOT, or inverter, can be fabricated with a single transistor if you use the simple (but obsolete) resistor-transistor logic (RTL) circuit. Two transistors in series can form a NAND gate. Two transistors in parallel can form a NOR gate. While we think of the AND and OR as the fundamental logic components, they are more commonly built from the NAND and NOR gates with inverters on their outputs. The NOT, NAND, and NOR gates combine in many ways to build higher-level circuits and components. Corresponding software functions combine to build emulations of higher-level logical operations.

Basic Logic Functions

A Boolean function with n inputs has at most 2 ⁿ distinct input states. These states and the corresponding outputs can be described with a truth table . A truth table typically lists the input states in (base 2) numerical order. Table 4.1 displays the truth tables for...

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Chapter 4: Boolean Machine Architectures

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