Logic Minimization

Boolean Algebra

Boolean algebra is perhaps the oldest method used to minimize logic equations. It provides a formal algebraic system to manipulate logic equations so that the minimum can be found. A basic understanding of this system is indispensable to the study and analysis of logic circuits.

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Logic Minimization

K-maps with Don't Cares

Situations can arise where a circuit has N input signals, but not all 2N combinations of inputs are possible. Or, if all 2N combinations of inputs are possible, some combinations might be irrelevant.

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Logic Minimization

Multiple Outputs

Circuits that have more complex inputs and outputs then we have previously discussed require less tedious and error prone methods of analysis. Here we will discuss how multiple output systems are analyzed.

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Multi-Button Input

This topic page describes how you can set up a multi-button input circuit.

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Resistance and Ohm's Law

In 1827, George Ohm demonstrated through a series of experiments that voltage, current, and resistance are related through a fundamental relationship: Voltage (V) is equal to Current (I) times resistance (R).

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Voltage-Current Characteristics

In any electric circuit, our typical goal is to move charges around to perform some useful task. This involves both voltage differences and currents. We create voltage differences in the circuit, which provides energy differences (or electromotive forces) which move charges around, creating currents.

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Parallel Circuit Elements

This topic page will cover parallel circuit elements. Circuit elements are said to be connected in parallel if all of the elements share the same pair of nodes.

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Series Circuit Elements

How to Identify a Series

Series circuit elements share the same current. Elements in series can be recognized in two ways: If two and only two elements are connected to a single node, the elements are in series. If applying KCL at a node results in the conclusion that the currents in two elements are identical, the elements are in series.

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Parallel Resistors

Equivalent Resistance

Circuits which consist of resistors connected in parallel can be simplified. This topic page will explain how.

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Series Resistors

Equivalent Resistance

When resistors are connected in series, a simplification of the circuit is possible.

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Ohm's Law

Design Challenge 3: Choosing Resistance

A common problem in designing electric circuits is having to pick a resistance that provides the desired amount of current. In this project, we will create a circuit (i.e. choose a resistor) which results in a specified current being provided by a 5V source.

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Ohm's Law

Design Challenge 4: Current-Limiting Resistor

Resistors in electrical circuits are commonly used to provide other components in the circuit with the voltages and currents they require in order to function properly. For example, in this exercise, we will design our circuit (i.e. choose a resistance value) to ensure that an LED receives the voltage necessary for it to light up without allowing excessive current, which could burn out the LED.

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Voltage Dividers

Design Challenge 1: Temperature Measurement

Design a circuit whose output voltage provides a crude temperature measurement.

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Voltage Dividers

Design Challenge 2: Temperature Measurement

Design a circuit so that the output voltage of the system to be zero at room temperature, increase as temperature increases, and decrease as temperature decreases.

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Diode Protection Circuit

This topic provides background information on diode protection circuits.

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Introduction to Electronic Circuits

Real Digital Project 1

This project presents a brief, non-rigorous introduction to electronic circuits and systems. Only the most essential concepts are presented, with emphasis on topics used in later projects. As with all projects in this module, a companion “Exercise1” document is available for further understanding.

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Logic Circuit Structure with an Introduction to Computer Aided Design (CAD) tools

Real Digital Project 3

This module presents the basic structure of combinational logic circuits, and introduces the use of computer aided design (CAD) tools in modern circuit design.

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Logic Minimization

Real Digital Project 4

The requirements for new logic circuit designs are often expressed in some loose, informal manner. For an informal behavioral description to result in an efficient, well designed circuit that meets the stated requirements, appropriate engineering design methods must be developed.

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Logic Circuit Structure

Project 3, Exercise 1

This Exercise is based on the material covered in Real Digital Project 3.

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Logic Minimization

Project 4, Exercise 2

This project exercise presents several worded problems that serve as behavioral specifications for digital circuits. Your job is to design, simulate, and download those circuits to your board. The topics from this exercise are based off of the material presented in Real Digital Project 4.

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