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Computer Logic, Logic Gates, and Building Circuits

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Title: Computer Logic, Logic Gates, and Building Circuits


1
Computer Logic, Logic Gates,and Building Circuits
  • Matt HuenerfauthCSE 100Lab Session 1September
    2003U. of Pennsylvania

Image Intel Museum
2
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

3
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 waters in the kettle,
    then we will make steam.
  • If either part isnt there, then the result wont
    be true.

4
What does AND mean in Logic?
  • AND takes two inputs and produces the value TRUE
    if both inputs are TRUEs.
  • 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.)

5
A Truth Table
  • A truth table is a convenient way to write down
    the definition of a logic operation.
  • Lets use 1s for True and 0s for False
  • Heres 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.
6
Truth Table for OR and NOT
  • OR NOT
  • input input output input output
  • 1 1 1 1 0
  • 1 0 1 0 1
  • 0 1 1
  • 0 0 0

This just givesthe opposite.
We only need one of the inputsto be true, but if
both are true,thats ok, too.
7
A Logic Gate
  • A logic gate is a small computer circuit that
    simulates one of the logic operators weve 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.

8
Logic Gates
  • When drawing diagramsof logic circuits, weuse
    some traditionalshapes for each one.

A
C
NOT
If A is off, turn on C.
AND
AND
A
A
C
C
OR
B
B
If A and B are on, turn on C.
If A or B is on, turn on C.
9
The Logic Gate Demo (1)
  • Explore how AND, OR, and NOT work.
  • http//www.seas.upenn.edu/cse100/labs/01/

10
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.

11
But whats 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
12
OR Gate from Tinker Toys
spring
Pushing a pole to the right means TRUE.
moveable
Push either one of theseto make the output
polemove.
Not moveable
13
Building Gates from Wires
Lighting-up means TRUE for output.
Flipping a switch means TRUE for input.

-
AND
OR

-
How many switches must you turn on in
eachcircuit in order for the light bulb to light
up?
14
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.

15
Whats a Transistor
Image Intel Museum
16
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.

ControlSignal
Image Intel Museum
17
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.
  • Thats what we have laptop and handheld
    computers nowadays.

Image Van Pelt Library ENIAC Exhibit
18
Sizes of Transistors
  • Look at the transistors samples in class.
  • Moores 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
19
A Transistor
  • A transistor controlswhether a switch ison or
    off.
  • It turns off its switch when its given an
    electric signal.
  • When there is no power on the signal line, the
    transistor turns the switch on.

Transistor
signal
20
A Transistor
  • A transistor controlswhether a switch ison or
    off.
  • It turns off its switch when its given an
    electric signal.
  • When there is no power on the signal line, the
    transistor turns the switch on.

TransistorOFF
signalON
21
A Transistor
  • A transistor controlswhether a switch ison or
    off.
  • It turns off its switch when its given an
    electric signal.
  • When there is no power on the signal line, the
    transistor turns the switch on.

TransistorON
signalOFF
22
Logic Gates from Transistors
  • For example, we will build a NOT gate from a
    transistor.

extrapowersource
Transistor
Output fromNOT gate.
Input toNOT gate.
23
Logic Gates from Transistors
  • For example, we will build a NOT gate from a
    transistor.

extrapowersource
TransistorOFF
Output fromNOT gateis OFF.
Input toNOT gateis ON.
NOT 1 ? 0
24
Logic Gates from Transistors
  • For example, we will build a NOT gate from a
    transistor.

extrapowersource
TransistorON
Output fromNOT gateis ON.
Input toNOT gateis OFF.
NOT 0 ? 1
25
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?

26
The Logic Gate Demo (2)
  • Explore how to combine logic gates together.
  • http//www.seas.upenn.edu/cse100/labs/01/
  • What if we want to build a circuit that can
    calculate either one or the other but not both ?

27
Building Exclusive OR
  • One or the other but not both.
  • Different than OR.
  • _

28
Building Exclusive OR
  • One or the other but not both.
  • Different than OR.
  • Want output TRUE when eitherInput 1 is TRUE
    and Input 2 is FALSE orInput 1 is FALSE and
    Input 2 is TRUE

29
Building Exclusive OR
  • One or the other but not both.
  • Different than OR.
  • Want output TRUE when eitherInput 1 is TRUE
    and Input 2 is FALSE orInput 1 is FALSE and
    Input 2 is TRUE

Can replace False with NOT TRUE.
30
Building Exclusive OR
  • Want output TRUE when eitherInput 1 is TRUE and
    Input 2 is NOT TRUE orInput 1 is NOT TRUE and
    Input 2 is TRUE

AND
NOT
Input 1
OR
Output
Input 2
AND
NOT
31
If theres extra time
  • Can we build an AND circuit using only NOT and OR
    gates?

32
If theres extra time
AND should be FALSE if either Input 1 is NOT
TRUE or Input 2 is NOT TRUE.
Input 1
NOT
Output
OR
NOT
Input 2
NOT
33
Credits
  • The Intel Museum
  • http//www.intel.com/education/transworks/
  • Intel Research Website
  • http//www.intel.com/research/silicon/mooreslaw.h
    tm
  • 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/
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