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Computer Logic, Logic Gates,and Building Circuits

Image: Intel Museum

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Logic and Computers

• The technology inside of computers (and in fact all logical ideas) is based on several simple logic operations:– AND– OR– NOT

• These logical operations are related to real world equivalents…

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What does “AND” mean?

• When we say “AND,” formally we mean that something is true only when both parts of it are true.

• If the stove is on AND water’s in the kettle, then we will make steam.

• If either part isn’t there, then the result won’t be true.

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What does AND mean in Logic?

• AND takes two inputs and produces the value TRUE if both inputs are TRUE’s.

• So, with the inputs: T AND T output is: T

T AND F output is: F

F AND T output is: F

F AND F output is: F

(Just like in the real world.)

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A Truth Table

• A truth table is a convenient way to write down the definition of a logic operation.

• Let’s use 1’s for True and 0’s for False…• Here’s the table for AND:

input input output 1 1 1 1 0 0 0 1 0 0 0 0

Output of 1 onlywhen both inputsare 1.

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Truth Table for OR and NOT

OR NOTinput input output input output

1 1 1 1 0

1 0 1 0 1

0 1 1

0 0 0

We only need one of the inputsto be true, but if both are true,that’s ok, too.

This just givesthe opposite.

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A Logic Gate

• A logic gate is a small computer circuit that simulates one of the logic operators we’ve seen.

• There are one or two wires that go into the gate that represent the input.

• There is one output wire that represents the result of the logic operation.

• When the power is on, that means True.

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Logic Gates

When drawing diagramsof logic circuits, weuse some traditionalshapes for each one.

If A and B are on, turn on C. If A or B is on, turn on C.

A

B

A

BC C

If A is off, turn on C.

A C

AND ORAND

NOT

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What have we seen so far?

• We saw what a logic gate is. We saw how to use one.

• Now we will see how they work inside.

• But we will return to the LogSim program later to see how we can combine multiple logic gates together to do useful work.

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But what’s inside the box?

• How do we build an individual logic gate?

• “Pattern on the Stone” chapter 1 shows to build each logic gate from tinker toys, water pipes, or wires.

• But real computers today use logic gates built out of small electronic devices.

Image: Tinkertoy Website

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“OR” Gate from Tinker Toys

spring

moveablePush either one of theseto make the output polemove. Not moveable

Pushing a pole to the right means TRUE.

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Building Gates from Wires

+ -

+ -

AND

OR

How many switches must you turn on in eachcircuit in order for the light bulb to light up?

Lighting-up means TRUE for output.

Flipping a switch means TRUE for input.

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Real Computers

• Real computers are not built from tinker toys or any of the other wacky approaches shown in the “Pattern on the Stone.”

• Computers today use logic gates that are built out of small electronic devices called “transistors.”

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What’s a Transistor

       

                      

Transistors are miniature electronic switches.

Similar to a light switch, transistors have two operating positions, on and off.

This on/off functionality is used to build logic gates.

Image: Intel Museum

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Why are transistors special?Transistors are like real switches, but –

1. They have no moving parts.

2. They can be turned on and off by an electric signal.

3. You could hook the output of one switch to the input of another since they both use electricity!

So that means – They are small and fast.

In fact, as transistors get smaller and faster, so do computers.

Image: Intel Museum

ControlSignal

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Computers Get Smaller: ENIAC

• The tremendous size of the first electronic computer, built here at Penn, was because the transistors used to built it were the size of lightbulbs.

• Modern transistors are microscopic.

• That’s what we have laptop and handheld computers nowadays.

Image: Van Pelt Library ENIAC Exhibit

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Sizes of TransistorsLook at the transistors samples in class.

“Moore’s Law” is a famous observation that: Researchers tend to shrink transistor sizes in half every 18 months.

Transistors shrink so we can make chips smaller and fit more on a single chip.

Image: Intel Research

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A Transistor

• A transistor controlswhether a switch ison or off.

• It turns off its switch when it’s given an electric signal.

• When there is no power on the signal line, the transistor turns the switch on.

Transistor

signal

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A Transistor

• A transistor controlswhether a switch ison or off.

• It turns off its switch when it’s given an electric signal.

• When there is no power on the signal line, the transistor turns the switch on.

TransistorOFF

signalON

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A Transistor

• A transistor controlswhether a switch ison or off.

• It turns off its switch when it’s given an electric signal.

• When there is no power on the signal line, the transistor turns the switch on.

TransistorON

signalOFF

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Logic Gates from Transistors

• For example, we will build a NOT gate from a transistor.

Transistor

extrapowersource

Input toNOT gate.

Output fromNOT gate.

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Logic Gates from Transistors

• For example, we will build a NOT gate from a transistor.

TransistorOFF

extrapowersource

NOT 1 0

Input toNOT gateis ON.

Output fromNOT gateis OFF.

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Logic Gates from Transistors

• For example, we will build a NOT gate from a transistor.

TransistorON

extrapowersource

NOT 0 1

Input toNOT gateis OFF.

Output fromNOT gateis ON.

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Summary: A Hierarchy of Parts

• We started with TRANSISTORS.

• We built some LOGIC GATES.

Can we build useful stuff out of logic gates?How can we combine them?

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Building “Exclusive OR”

• One or the other but not both.

• Different than “OR.”

_

IN IN OUT1 1 11 0 10 1 10 0 0

“Normal” ORIN IN OUT1 1 01 0 10 1 10 0 0

What we want…

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Building “Exclusive OR”

• One or the other but not both.

• Different than “OR.”

• Want output TRUE when either:

Input 1 is TRUE and Input 2 is FALSEor

Input 1 is FALSE and Input 2 is TRUE

IN IN OUT1 1 11 0 10 1 10 0 0

“Normal” ORIN IN OUT1 1 01 0 10 1 10 0 0

What we want…

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Building “Exclusive OR”

• One or the other but not both.

• Different than “OR.”

• Want output TRUE when either:

Input 1 is TRUE and Input 2 is FALSEor

Input 1 is FALSE and Input 2 is TRUE

IN IN OUT1 1 11 0 10 1 10 0 0

“Normal” ORIN IN OUT1 1 01 0 10 1 10 0 0

What we want…

Can replace False with NOT TRUE.

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Building “Exclusive OR”

• Want output TRUE when either:Input 1 is TRUE and Input 2 is NOT TRUE

orInput 1 is NOT TRUE and Input 2 is TRUE

OR

NOT

AND

AND

NOT

Input 1

Input 2

Output

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If there’s extra time…

• Can we build an AND circuit using only NOT and OR gates?

IN IN OUT1 1 11 0 00 1 00 0 0

What we want…

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If there’s extra time…

NOT

NOTInput 1

Input 2

OutputNOTOR

AND should be FALSE if either Input 1 is NOT TRUEor Input 2 is NOT TRUE.

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Credits

The Intel Museum:http://www.intel.com/education/transworks/

Intel Research Website:http://www.intel.com/research/silicon/mooreslaw.htm

Van Pelt Library ENIAC Exhibit:John W. Mauchly and the Development of the ENIAC Computer

http://www.library.upenn.edu/exhibits/rbm/mauchly/jwm0-1.html

Tinker Toys Website:http://www.hasbro.com/tinkertoy/