Difference between revisions of "Logic Gates"
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== | [[File:7400.jpg|thumb|right|link=|The 7400 chip contains four logical NAND gates.]] | ||
== Curriculum == | |||
{{MerlinCurriculumData|{{ROOTPAGENAME}}}} | |||
== Introduction == | |||
A logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces one or more binary outputs. | |||
== Symbols == | |||
The table below provides the symbols that are used to represent common gates. | |||
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Additionally, a '''multiplexer''' is a device which selects from <math>n</math> digital inputs and forwards the signal to a single output line. Given <math>n</math> inputs, there are <math>log_2 n</math> selector pins. Conversely, a '''demultiplexer''' forwards the signal from a single line to one of multiple outputs. | |||
{| class="wikitable" | |||
! Formal Name | |||
! Abbreviated Name | |||
! Symbol | |||
! Gate | |||
! Truth Table | |||
|- | |||
| Multiplexer | |||
| MUX | |||
| <math>{A \cdot \overline{S}} \lor {B \cdot S}</math> | |||
| [[File:Multiplexer-ABSQ.png ]] | |||
| | |||
{| class="wikitable" style="text-align: center;" | |||
!colspan="3"| Inputs | |||
! Outputs | |||
|- | |||
! <math>S</math> | |||
! <math>A</math> | |||
! <math>B</math> | |||
! <math>Q = {A \cdot \overline{S}} \lor {B \cdot S}</math> | |||
|- | |||
| 0 || 0 || 0 || 0 | |||
|- | |||
| 0 || 0 || 1 || 0 | |||
|- | |||
| 0 || 1 || 0 || 1 | |||
|- | |||
| 0 || 1 || 1 || 1 | |||
|- | |||
| 1 || 0 || 0 || 0 | |||
|- | |||
| 1 || 0 || 1 || 1 | |||
|- | |||
| 1 || 1 || 0 || 0 | |||
|- | |||
| 1 || 1 || 1 || 1 | |||
|} | |||
|- | |||
| Demultiplexer | |||
| DEMUX | |||
| | |||
| [[File:Demultiplexer-ABSQ.png ]] | |||
| | |||
{| class="wikitable" style="text-align: center;" | |||
!colspan="2"| Inputs | |||
!colspan="2"| Outputs | |||
|- | |||
! <math>S</math> | |||
! <math>A</math> | |||
! <math>Q = {\overline{S} \cdot A}</math> | |||
! <math>R = {S \cdot A}</math> | |||
|- | |||
| 0 || 0 || 0 || 0 | |||
|- | |||
| 0 || 1 || 1 || 0 | |||
|- | |||
| 1 || 0 || 0 || 0 | |||
|- | |||
| 1 || 1 || 0 || 1 | |||
|} | |||
|} | |||
== The Special Role of NAND and NOR Gates == | |||
Both NAND and NOR gates exhibit a property known as '''functional completeness'''. ''Any Boolean function'' can be implemented using one or more of either of these gates. This is a very powerful principal because it enables us, using only one type of logic gate, to implement systems of arbitrary complexity. | |||
== Exercises == | |||
{{Exercises| | |||
* {{MMMAssignment|M1014-10}} | |||
}} | |||
== References == | |||
* [https://en.wikipedia.org/wiki/NAND_gate NAND Gate] (Wikipedia) | |||
* Schocken, Simon and Nisan, Noam. The Elements of Computing Systems. MIT Press, 2005. | |||
{{Experience | |||
|experienceID=W1014 | |||
|experienceUnit=Boolean algebra | |||
|knowledgeAndSkills=§10.325 | |||
|topicAreas=Boolean algebra | |||
|classroomTime=45 minutes | |||
|studyTime=2 hours | |||
|acquiredKnowledge=understand the symbology of common logic gates | |||
|acquiredSkill=demonstrate proficiency in using the symbols of logic gates to document Boolean functionality | |||
}} |
Latest revision as of 18:04, 27 November 2021
Curriculum[edit]
Coder Merlin™ Computer Science Curriculum Data | |
Unit: Boolean algebra Experience Name: Logic Gates (W1014) Next Experience: () Knowledge and skills:
Topic areas: Boolean algebra Classroom time (average): 45 minutes Study time (average): 120 minutes Successful completion requires knowledge: understand the symbology of common logic gates Successful completion requires skills: demonstrate proficiency in using the symbols of logic gates to document Boolean functionality |
Introduction[edit]
A logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces one or more binary outputs.
Symbols[edit]
The table below provides the symbols that are used to represent common gates.
Additionally, a multiplexer is a device which selects from digital inputs and forwards the signal to a single output line. Given inputs, there are selector pins. Conversely, a demultiplexer forwards the signal from a single line to one of multiple outputs.
Formal Name | Abbreviated Name | Symbol | Gate | Truth Table | ||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Multiplexer | MUX |
| ||||||||||||||||||||||||||||||||||||||||||
Demultiplexer | DEMUX |
|
The Special Role of NAND and NOR Gates[edit]
Both NAND and NOR gates exhibit a property known as functional completeness. Any Boolean function can be implemented using one or more of either of these gates. This is a very powerful principal because it enables us, using only one type of logic gate, to implement systems of arbitrary complexity.
Exercises[edit]
- M1014-10 Complete Merlin Mission Manager Mission M1014-10.
References[edit]
- NAND Gate (Wikipedia)
- Schocken, Simon and Nisan, Noam. The Elements of Computing Systems. MIT Press, 2005.
Experience Metadata
Experience ID | W1014 |
---|---|
Next experience ID | |
Unit | Boolean algebra |
Knowledge and skills | §10.325 |
Topic areas | Boolean algebra |
Classroom time | 45 minutes |
Study time | 2 hours120 minutes <br /> |
Acquired knowledge | understand the symbology of common logic gates |
Acquired skill | demonstrate proficiency in using the symbols of logic gates to document Boolean functionality |
Additional categories |