A Computer Story:Complexity from Simplicity

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Lehigh University andParkland High School

Gary DeLeo, Amanda Weidenhammer, and Kristen Wecht

“Series” PlumbingFaucet 1 Faucet 2 Water?

off offoff onon offon on

“Series” PlumbingFaucet 1 Faucet 2 Water?

off off nooff on noon off noon on yes

Series CircuitSwitch 1 Switch 2 Light

0 00 11 01 1

0 = Off 1 = On

battery light

switch 1 switch 2

Series CircuitSwitch 1 Switch 2 Light

0 00 11 01 1

0 = Off 1 = On

battery light

switch 1 switch 2

Series CircuitSwitch 1 Switch 2 Light

0 0 00 11 01 1

0 = Off 1 = On

battery light

switch 1 switch 2

Series CircuitSwitch 1 Switch 2 Light

0 0 00 11 01 1

0 = Off 1 = On

battery light

switch 1 switch 2

Series CircuitSwitch 1 Switch 2 Light

0 0 00 1 01 01 1

0 = Off 1 = On

battery light

switch 1 switch 2

Series CircuitSwitch 1 Switch 2 Light

0 0 00 1 01 01 1

0 = Off 1 = On

battery light

switch 1 switch 2

Series CircuitSwitch 1 Switch 2 Light

0 0 00 1 01 0 01 1

0 = Off 1 = On

battery light

switch 1 switch 2

Series CircuitSwitch 1 Switch 2 Light

0 0 00 1 01 0 01 1

0 = Off 1 = On

battery light

switch 1 switch 2

Series CircuitSwitch 1 Switch 2 Light

0 0 00 1 01 0 01 1 1

0 = Off 1 = On

battery light

switch 1 switch 2

Switch 1 Switch 2 Light0 0 00 1 01 0 01 1 1

0 = Off 1 = On

X Y Z

battery light

switch 1 switch 2X Y

Z

Series Circuit

Series CircuitX Y Z0 0 00 1 01 0 01 1 1

0 = Off 1 = On

battery Z

X Y

Truth Table for X AND YX Y Z

0 0 00 1 01 0 01 1 1

Z = X AND YOutputInput

X Y

“Parallel” PlumbingFaucet 1 Faucet 2 Water?

off offoff onon offon on

“Parallel” PlumbingFaucet 1 Faucet 2 Water?

off off nooff on yeson off yeson on yes

Parallel CircuitSwitch 1 Switch 2 Light

0 00 11 01 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 00 11 01 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 0 00 11 01 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 0 00 11 01 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 0 00 1 11 01 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 0 00 1 11 01 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 0 00 1 11 0 11 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 0 00 1 11 0 11 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 0 00 1 11 0 11 1 1

0 = Off 1 = On

battery light

switch 1

switch 2

Parallel CircuitSwitch 1 Switch 2 Light

0 0 00 1 11 0 11 1 1

0 = Off 1 = On

battery light

switch 1

switch 2

X Y Z

X

Y Z

Parallel CircuitX Y Z0 0 00 1 11 0 11 1 1

0 = Off 1 = On

battery Z

X

Y

Truth Table for X OR YX Y Z

0 0 00 1 11 0 11 1 1

Z = X OR YOutputInput

X Y

X Y Z0 0 00 1 11 0 11 1 0

X XOR Y

X YXORTruth Table

for

“XOR” Means X or Y, but Not Both (“Exclusive OR”)

XNOTTruth Table

forX X

0 1

1 0

NOT X (= X)

XNOT

Electrical Circuit ElementsX X )(

X AND YXY

XY X OR Y

XY X XOR Y

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D

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eg

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Seven-Segment Display Converter

A B C D Number0123456789

0 = Off1 = On

Binary Coded Decimal (BCD)

A B C D Number0 0 0 0 0

123456789

0 = Off1 = On

Binary Coded Decimal (BCD)

A B C D Number0 0 0 0 00 0 0 1 1

23456789

0 = Off1 = On

Binary Coded Decimal (BCD)

A B C D Number0 0 0 0 00 0 0 1 10 0 1 0 2

3456789

0 = Off1 = On

Binary Coded Decimal (BCD)

A B C D Number0 0 0 0 00 0 0 1 10 0 1 0 20 0 1 1 3

456789

0 = Off1 = On

Binary Coded Decimal (BCD)

A B C D Number0 0 0 0 00 0 0 1 10 0 1 0 20 0 1 1 30 1 0 0 4

56789

0 = Off1 = On

Binary Coded Decimal (BCD)

A B C D Number0 0 0 0 00 0 0 1 10 0 1 0 20 0 1 1 30 1 0 0 40 1 0 1 50 1 1 0 60 1 1 1 71 0 0 0 81 0 0 1 9

0 = Off1 = On

Binary Coded Decimal (BCD)

A

B

C

D

G1

G2

G3

G4

G5

G6

G7

G8

G9

G10

G11

G12

G13

G14

G15

b

a

c

d

f

g

e

b

c

a

d

f

eg

B

C

D

Seven-Segment Display Converter

Seven-Light DisplayNumber

(0-9)

A B C D

abcdefg

Seven-Light DisplayNumber

(0-9)

A B C D

abcdefg

b

c

a

d

f

eg

Number(3)

A B C D

abcdefg

b

c

a

d

f

eg

0 0 1 1

0 0 1 1

Seven-Light Display

Number(3)

A B C D

abcdefg

b

c

a

d

f

eg

0 0 1 1

b

Seven-Light Display