Introduction

All digital computers are built with the basic components shown on this page. All other circuits, including the Xor Gate shown below, can be constructed with Inverter Gates, Or Gates, and And Gates.

What makes computers so complicated is that they are composed of millions of these basic gates, interconnected in very intricate ways.

When you have finished studying these concepts, you can cement your comprehension with a companion page, Digital Logic Primer Exam, an on-line, interactive test of this material.

Contents

• Introduction
• Definitions
• Basic Circuits
  • Switch and LED
  • Inverter Gate
  • And Gate
  • Or Gate
• Combinational Gates
  • Xor Gate
  • Xor Circuit
  • Nand Gate
  • Nor Gate
  • Xnor Gate
• Tripple Input Gates
  • 3-Input And Gate
  • 3-Input Or Gate
  • 3-Input Xor Gate
• Negative Tripple Input Gates
  • 3-Input Nand Gate
  • 3-Input Nor Gate
  • 3-Input Xnor Gate
• Examination Link
• More Detail Link
• Credits

Definitions

As you study this page, here are some things to consider:

• A State is a way of being..
• An Input is a pin, connection, or electrical signal that goes INTO a device that affects its current state in some way.
• An Output is a pin, connection, or electrical signal that comes OUT of a device and reflects its current state.
• For Binary Digital Computers:

  Binary States
  Inputs and Outputs	Off	On
  	0	1
  	False	True
  Switches on this page	Down	Up
  LED's on this page	Dark	Lit

• In general, Outputs are connected to Inputs.
• The Switches are Input Devices. On this page, all switches have ONE OUTPUT. which can be connected to ONE OR MANY INPUTS
• The LED's are Output Devices. On this page, all LED's have ONE INPUT which can be connected to just ONE OUTPUT.
• All Logic Gates on this page have either ONE or TWO or THREE INPUTS, with only ONE OUTPUT.
• A Truth Table is a list of all the possible input states of a device along with the resulting output states.

You are invited to experiment with the switches on this page. Clicking them will change their state -- that is, from a "Down / 0" to a "Up / 1", and vise versa. Then watch what happens to the LED's in the same box.

Basic Circuits
Name	Schematic Symbol	Truth Table	Description
Switch and LED		Switch LED Down / 0 Dark / 0 Up / 1 Lit / 1	The most basic of all circuits. The switch on the left will turn the LED (Light Emitting Diode) on the right on. Click it and see.
Inverter Gate		Switch LED 0 Lit / 1 1 Dark / 0	The most basic gate. It changes its input from a "1" to a "0", and vise versa.
And Gate		Switches LED 0 0 Dark / 0 0 1 Dark / 0 1 0 Dark / 0 1 1 Lit / 1	This gate will output a "1" only if both its inputs are a "1"
Or Gate		Switches LED 0 0 Dark / 0 0 1 Lit / 1 1 0 Lit / 1 1 1 Lit / 1	The output of this gate is a "1" if either of its inputs is a "1"

Combinational Gates
Name	Schematic Symbol	Truth Table	Description
Xor Gate		Switches LED 0 0 Dark / 0 0 1 Lit / 1 1 0 Lit / 1 1 1 Dark / 0	Xor is short for Exclusive Or. This gate can be implemented with Inverter Gates, And Gates, and Or Gates (See below). The output of this gate is a "1" only if one of its inputs is a "1"
Xor Circuit
Nand Gate		Switches LED 0 0 Lit / 1 0 1 Lit / 1 1 0 Lit / 1 1 1 Dark / 0	Nand is ahort for Negative And. This gate combines an And Gate with its output connected through an Inverter Gate in one device. It will output a "0" only if both its inputs are a "1"
Nor Gate		Switches LED 0 0 Lit / 1 0 1 Dark / 0 1 0 Dark / 0 1 1 Dark / 0	Nor is short for Negative Or. This gate combines an Or Gate with its output connected through an Inverter Gate in one device. It will output a "0" if either its inputs are a "1"
Xnor Gate		Switches LED 0 0 Lit / 1 0 1 Dark / 0 1 0 Dark / 0 1 1 Lit / 1	Xnor is short for Exclusive Nor. This gate combines an Xor Gate with its output connected through an Inverter Gate in one device. The output of this gate is a "0" only if one of its inputs is a "1"

Triple Input Gates
Name	Schematic Symbol	Truth Table	Description
3-Input And Gate		Switches LED 0 0 0 Dark / 0 0 0 1 Dark / 0 0 1 0 Dark / 0 0 1 1 Dark / 0 1 0 0 Dark / 0 1 0 1 Dark / 0 1 1 0 Dark / 0 1 1 1 Lit / 1	This gate will output a "1" only if all of its inputs are a "1"
3-Input Or Gate		Switches LED 0 0 0 Dark / 0 0 0 1 Lit / 1 0 1 0 Lit / 1 0 1 1 Lit / 1 1 0 0 Lit / 1 1 0 1 Lit / 1 1 1 0 Lit / 1 1 1 1 Lit / 1	This gate will output a "1" if any of its inputs are a "1"
3-Input Xor Gate		Switches LED 0 0 0 Dark / 0 0 0 1 Lit / 1 0 1 0 Lit / 1 0 1 1 Dark / 0 1 0 0 Lit / 1 1 0 1 Dark / 0 1 1 0 Dark / 0 1 1 1 Lit / 1	Xor is short for Exclusive Or. This gate will output a "1" if only one or all of its inputs are a "1"

Negative Triple Input Gates
Name	Schematic Symbol	Truth Table	Description
3-Input Nand Gate		Switches LED 0 0 0 Lit / 1 0 0 1 Lit / 1 0 1 0 Lit / 1 0 1 1 Lit / 1 1 0 0 Lit / 1 1 0 1 Lit / 1 1 1 0 Lit / 1 1 1 1 Dark / 0	This gate will output a "0" only if all of its inputs are a "1"
3-Input Nor Gate		Switches LED 0 0 0 Lit / 1 0 0 1 Dark / 0 0 1 0 Dark / 0 0 1 1 Dark / 0 1 0 0 Dark / 0 1 0 1 Dark / 0 1 1 0 Dark / 0 1 1 1 Dark / 0	This gate will output a "0" if any of its inputs are a "1"
3-Input Xnor Gate		Switches LED 0 0 0 Lit / 1 0 0 1 Dark / 0 0 1 0 Dark / 0 0 1 1 Lit / 1 1 0 0 Dark / 0 1 0 1 Lit / 1 1 1 0 Lit / 1 1 1 1 Dark / 0	Xnor is short for Exclusive Nor. This gate will output a "0" if only one or all of its inputs are a "1"

Examination Link

Now that you have familiarized yourself with these concepts, you can cement your comprehension with a companion page, Digital Logic Primer Exam, an on-line, interactive test of this material.

Here is a link to a much more thorough treatment of logic gates and other more complex devices: http://www.play-hookey.com/digital/

Credits

These gates, plus many other devices, are part of a software package called Multimedia Logic, a free program which simulates digital logic circuits. It will run under Microsoft Windows '95 and up.

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