Stephen Bucaro - Basic Digital Logic Design: Use Boolean Algebra, Karnaugh Mapping, or an Easy Free Open-Source Logic Gate Simulator

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Boolean Algebra

karnaugh Map Logic Simplification

Binary Number Representation

Binary Mathematics Circuits

Sequential Systems

Digital Circuits

Interfacing to the Real World

Memory Circuits

Logic Devices

State Macines

Digital Electrons lab

Appendices

Digital design is based on the binary principle, where everything is either 0 or 1, either low or high.Few people realize that digital logic existed before the advent of the computer. Digital logic was usedfor control and communications systems even before semiconductors where invented. They worked usingswitches, relays and solenoids.

If you search the internet you will not find the phrase digital logic separate from computers. It's likethe only purpose for digital logic was to invent the computer. I'm sorry, but as an electronics engineerbefore computers, I designed all kinds of control systems for transportation, farming, manufacturing,and many other industries, using digital logic. In fact it was a heck of a lot more fun than programmingtoday's microprocessors.

Now days, much of the work of a system is accomplished in programs, but the programs must have a digitaldevice to execute on. Today, almost all systems work using a microcontroller or microprocessor runninga software. But that's not always the most efficient way to do it. In a system there is always a trade-offbetween accomplishing a task with software or hardware (digital logic), each has its advantages.

Software is usually cheaper because increasing its functionality does not require adding more physicalmaterial other than possibly more memory to store the code in. Hardware, like digital logic, is fasterand in some circumstances more reliable. At some point the system has to interface with the real world.Software can't do the job. That's where hardware comes in.

With digital design you are involved with problem solving. You have a set of inputs and you must designthe logic that will turn that into the desired output or outputs. To accomplish that task you can useBoolean algebra or Karnaugh mapping. All the advanced features of the most powerful computers, suchas mulicore and parallel processing are done with digital logic. This book will give you the basicprinciples you need to design digital logic circuits.

Lets look at a simple electric circuit with a battery, a light bulb, and a switch. This circuit is shown below.

With the switch open, the light bulb does not illuminate.

With the switch closed, the light bulb illuminates.

Lets designate the situation where the light is off as "0". Lets designate the situationwere the light is illuminated as "1". What we have is a system with two possible situations,referred to as a "binary" system.

It doesn't matter what voltage the battery is, as long as its high enough to illuminate the light.Light off is binary 0. Light on is binary 1.

Lets make a slightly more complex circuit.

In the circuit shown above, switch A is open, but the light is still illuminated. That's becauseswitch B is closed, providing a path from the battery to the light.

The idea behind this circuit is - if switch A OR switch B is closed, the light is illuminated.If both switches are open, the light will not be illuminated. Of course if both switched are closedthe light will be illuminated.

This circuit functions as what we call a logical OR gate.

In the circuit shown above, switch A is closed, but the light is not illuminated. This is because switchB is open, breaking the path to the battery. If switch B were to be closed, the light would be illuminatedbecause then there would be a closed path from the battery to the light.

If either switch is open, the light will not be illuminated. Both switch A AND switch B must be closedfor the light to be illuminated.

This circuit functions as a logical AND gate.

These circuits demonstrate the fundamental concept of logic circuits.

Logical OR Gate

Let's substitute the symbol shown below for the logical OR gate function.

If voltage is applied (a logical 1) to either A OR B (or both), voltage (a logical 1) willappear at the output. If neither input is 1, the output will be 0. The following table describesthe logical OR function.

This table is called a "truth table". It is the truth table for a 2-input OR gate.

Logical AND Gate

Let's substitute the symbol shown below for the logical AND gate function.

If a logical 1 is applied only to input A, or only to input B, the output will be 0.Both inputs must be 1 for the output to be 1. The following table describes the logical AND function.

This is the truth table for a 2-input AND gate.

Logical NOT Gate

Let's introduce a very simple gate shown below.