Logic Gates

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The 7400 chip contains four logical NAND gates.

Curriculum[edit]

ExercisesIcon.png
 Coder Merlin™  Computer Science Curriculum Data

Unit: Boolean algebra

Experience Name: Logic Gates (W1014)

Knowledge and skills:

  • §10.325 Demonstrate understanding and proficiency in the use of logic gates

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.

Formal Name Abbreviated Name Symbol Gate Truth Table
Buffer Gate Buffer.png
Inputs Outputs
0 0
1 1
Conjunction AND Gate AND.png
Inputs Outputs
0 0 0
0 1 0
1 0 0
1 1 1
Disjunction OR Gate OR.png
Inputs Outputs
0 0 0
0 1 1
1 0 1
1 1 1
Exclusive OR XOR Gate XOR.png
Inputs Outputs
0 0 0
0 1 1
1 0 1
1 1 0
Inverter NOT Gate Inverter.png
Inputs Outputs
0 1
1 0
Negated Conjunction NAND Gate NAND.png
Inputs Outputs
0 0 1
0 1 1
1 0 1
1 1 0
Negated Disjunction NOR Gate NOR.png
Inputs Outputs
0 0 1
0 1 0
1 0 0
1 1 0
Negated Exclusive OR NOT XOR Gate NOT XOR.png
Inputs Outputs
0 0 1
0 1 0
1 0 0
1 1 1

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 Multiplexer-ABSQ.png
Inputs Outputs
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 Demultiplexer-ABSQ.png
Inputs Outputs
0 0 0 0
0 1 1 0
1 0 0 0
1 1 0 1

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]

ExercisesIcon.png
Exercises
  •  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
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


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