Logic Basics Lus Oliveira Original slides by: Jarrett Billingsley - - PowerPoint PPT Presentation

CS 0447 Introduction to Computer Programming Luís Oliveira

Fall 2020

Logic Basics

Original slides by: Jarrett Billingsley Modified with bits from: Bruce Childers, David Wilkinson

#C

What's electric icity?

(E (EE-ish sec ection)

2

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In In your orb rbit

p+

e-

here's a proton. it has a positive charge here's an electron. it has a negative charge it kinda goes around the proton in an orbit*

*it actually doesn’t… it’s way more complex than that! Waves, teleportation and other black magic!

protons sit still while electrons can move around

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Opposites att ttract…

p+ e- p+ e-

• pposite charges

attract two of the same charge repel here's electricity. here it is but protons are kinda stuck, so…

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Lots ts of f fis fish ele lectrons in in th the sea

here's a solid piece of metal the atoms are in a fixed structure but some of the electrons are free to move around right now, the charges are balanced: same number of positive and negative let's knock it out of whack

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Two mole les is is company, th three's 's a cro rowd

let's shove more electrons in packing more electrons in leads to two things:

• 1. this metal is now

negatively charged

• 2. the electrons are

now closer together meaning they're less happy

aaa noo

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Caro rousel of f unhappiness

and then give them a (difficult) way out and then have something which will squeeze them back together again well now you have electricity if we shove some down a wire

wire

we'd like to get off mister bones wild ride

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Watch em em go go

voltage measures electron unhappiness current measures how many electrons per second are moving past a point low high low high and that's electricity

Logic ic Basic ics

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• Why is a vacuum tube called like that?
• They are also called thermionic valves (or simply valves)

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Valv lves (o (or tu tubes) – more fu fun?

https://en.wikipedia.org/wiki/Vacuum_tube

• a transistor is like a little valve

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Tra ransis istors

MOSFET BJT There are multiple types of transistors

common

• utput

input

• utput

common input

• utput

common input

Can be used many different ways!

• The ones we’ll focus on MOSFET transistors
• Metal-Oxide Semiconductor Field-Effect Transistor
• Commonly used just as switches (digital electronics)

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Tra ransis istors

D S G 9V D S G 0V

The positive terminal (e.g. 9V) The negative/ground terminal (0V)

• Used as an electrically controlled switch
• The input is connected to G (Gate)

▪ controls the switch state

• The output is D (drain) is connected to S (source)
• The voltages represent bits! (maybe 9V = 1, 0V = 0)

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Tra ransis istors

Input Output D S G

• MOSFETs come in two varieties:

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Tra ransis istors

D S G “N” Type Work when connected to 0 G=1 G=0 ON OFF S D G “P” Type Work when connected to 1

This means inverted

G=0 G=1 ON OFF

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Tra ransis istors – Overly ly sim implifie ied

1 D S G 1 S D G “N” Type “P” Type

The current must flow!!

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Tra ransis istors

Now just put 3 billion

• f them together! who

said EE was hard?

• We can combine transistors in interesting ways to make gates
• A gate implements one of the basic boolean logic functions
• Let's start with the simplest: the NOT gate

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Gate tes

this little bubble means "invert"

A Q

A is the input Q is the output

• if we want to, say, NOT a 32-bit value, we can draw it like:

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Tim ime to to bundle up

32 32

• it's a lot nicer than drawing 32 wires with 32 NOT gates
• Logisim calls these wire bundles
• it doesn't draw the slashes and numbers though…

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NOT with ith MOSFETs

A Q “N” Type “P” Type

A Q

A Q 1 1

A=0

1

A=1

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NAND with ith MOSFETs

A Q B

A B Q 1 1 1 1 1 1 1

A A B Q B

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AND with ith MOSFETs

A Q B

A B Q 1 1 1 1 1

A A B B Q

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NOR with ith MOSFETs

A B Q 1 1 1 1 1

A A B Q B A Q B

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OR with ith MOSFETs

A B Q 1 1 1 1 1 1 1

A A B B A Q B Q

• we know about AND and OR, but what's XOR?

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AND, OR, , and… XOR?

A Q B

AND gate

A Q B

OR gate

A Q B

XOR gate

A B Q 1 1 1 1 1 1 A B Q 1 1 1 1 1 1 1

eXclusive OR means "one or the other, but NOT BOTH."

A B Q 1 1 1 1 1

AB A+B A⊕B

• If you have more than 2 inputs…

you can just concatenate:

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AND (m (multiple le in inputs)

A Q’ B

AND gate

Q’ Q C

AND gate

A B C Q 1 1 1 1 1 1 1 1 1 1 1 1 1

AND and/or r OR

• Combining logic is just a matter of

combining logic gates:

• Look at the truth entries on the truth-table
• when Q is “1”
• AND each entry variable
• Then, OR each entry:

ABC + ABC

• In English:

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A B C Q 1 1 1 1 1 1 1 1 1 1 1 1 1 1

It’s truth when “A is false” and “B is true” and “C is false” OR “A is false” and “B is true” and “C is true”

ABC + ABC

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AND and/or OR

B A Q C

A B C Q 1 1 1 1 1 1 1 1 1 1 1 1 1 1

• if you stick a NOT gate after an AND gate, you get a NAND gate

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If If you giv ive an ele lectrical l engineer a NAND gate…

• this kind of gate has a cool property: it's universal
• in other words, you can build an entire computer with NANDs
• but this isn't how real circuits are designed, at least anymore
• digital logic courses use them cause NAND gate chips are cheap
• but in Logisim, we have infinite gates for free :D
• use the kind of gate you need for the situation at hand