ELEC3020 - Lecture 1

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ELEC3020 - Lecture 0
Introduction - Slides

Digital vs Analog

• Digital $-$ information is represented by signals which take on values that correspond to a finite number of discrete information values
• Analogue $-$ a continuous range of signal values correspond to a continuous range of information values

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Transistor

• Can act as an amplifier or a rapid switch
• Three pins:
  • Collector
  • Base
  • Emitter

Transistors can be used to make logic gates:

Logic Gates Review

De Morgan’s Theorem

• The complement of the logical AND of two or more variables is equal to the logical OR of the complements of those variables
• The complement of the logical OR of two or more variables is equal to the logical AND of the complements of those variables

(x + y)' = x'y'$$$$(x\ y)' = x' + y'

• Complement $f=(x^{\prime }y{z}^{\prime })+(x{y}^{\prime }{z}^{\prime })$?
  Answer: $f^{\prime }=(x+y^{\prime }+z)\cdot (x^{\prime }+y+z)$

Boolean algebra allows us to simplify a function so that it contains the smallest number of literals

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ELEC1303 - Lecture 4

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Universal Gates

• Universal gates can implement any Boolean function
• NAND/NOR gates are universal gates because one can implement any logic function using only NOR or only NAND

Universal Gate - NOR

• NOR is a universal gate because one can implement any logic function using only NOR gates

• NOR gate is preferred to OR gate because it can be implemented more efficiently in CMOS technology

Universal Gate - NAND

• NAND is a universal gate because one can implement any logic function using only NAND gates

• NAND gate is preferred to AND gate because it can be implemented more efficiently in CMOS technology

Remember that inverters cancel each other out and this can help with trying to find the most efficient circuit using NAND/NOR gates

e.g. two AND gate formations running into an OR gate formation becomes just two NAND gates!

Recall: $\overline{A\cdot B}=\bar{A}+\bar{B}$

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Embedded Systems

• An embedded system is:

  • Connected to sensors and actuators
  • Real-time operation
  • Programmed once

• Embedded systems are built to be resilient/reliable

  • Increased temperature resistance -> lower performance

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ELEC3020 - Lecture 2