logic gates. digital signals logic gates not (inverter) gate and gate or gate nand gate nor gate xor...

Logic Gates

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Logic Gates

• Digital Signals • Logic Gates• NOT (Inverter) Gate• AND Gate• OR Gate• NAND Gate• NOR Gate• XOR Gate

Digital SignalsDigital signals 0 (false) or 1 (true)Digital signal 1 is represented by a small voltage.Digital signal 0 is represented by no voltage.

Digital Waveforms

Each column represents a small amount of time

1 (3V)

0 (0V)

1 0 0 1 0 1 1 0

Page 4: Logic Gates. Digital Signals Logic Gates NOT (Inverter) Gate AND Gate OR Gate NAND Gate NOR Gate XOR Gate

Logic GatesAn electronic system that performsa logical operation on an input signal

Gates process digital inputs to produce digital outputs.

How do computer processors make decisions? How do they do math? Display images? Etc.?

LOGIC

NOT (Inverter) GateA logic gate that changes its input logic level to the opposite state

Symbol

01Truth Table: A table listing all possible inputs to a circuit and the corresponding outputs

Truth Table

NOT Gate

Input (A) Output (Y)

A Y

0 1

1 0

Page 6: Logic Gates. Digital Signals Logic Gates NOT (Inverter) Gate AND Gate OR Gate NAND Gate NOR Gate XOR Gate

Logic Word Problems

• If I am hungry and it is 5:00 p.m., then I will eat dinner.

• If I pedal harder or go downhill, then my bike will go faster.

• If it is windy and cold, then I am not going to walk home.

• If my battery is dead or I forget headphones, then I cannot listen to my music.

Each word problem uses the same logic as a common gate.

AND Gate

If I am hungry AND it is 5:00 p.m., then I will eat dinner.

A logic circuit whose:Inputs both = 1 then,Output = 1Symbol

0010

AND Gate

Truth Table

AND Gate

Input (A) Input (B) Output (Y)

0 00

0 01

1 00

1 11

OR Gate

If I pedal harder OR go downhill, then my bike will go faster.

A logic circuit when:Either Input = 1 then,Output = 1Symbol

0111

OR Gate

Truth Table

OR Gate

Input (A) Input (B) Output (Y)

0 00

0 11

1 10

1 11

NAND Gate

If it is windy AND cold, then I am NOT going to walk home.

A logic circuit whose:Inputs both = 1 then,Output = 0Symbol

1110

NAND Gate

Truth Table

NAND Gate

Input (A) Input (B) Output (Y)

0 10

0 11

1 10

1 01

NOR Gate

If my battery is dead OR I forget headphones, then I will NOT listen to my music.

A logic circuit when:Either Input = 1 then,Output = 0Symbol

1000

NOR Gate

Truth Table

NOR Gate

Input (A) Input (B) Output (Y)

0 10

0 01

1 00

1 01

XOR Gate

I only have enough money for one friend to go to dinner with me. If either one (but not both) want to go to dinner, we’ll go to dinner.

A logic circuit when:If A or B = 1, but not both,then Output = 0Symbol

Possible Inputs (conditions) Outputs

First Friend wants to go to dinner (T or F)

Second friend wants to go to dinner (T or

We will go to dinner (T or F)

F F F

F T T

T F T

T T F

XOR Gate

Truth Table

XOR Gate

Input (A) Input (B) Output (Y)

0 00

0 11

1 10

1 01

0011A

Logic Gates

• Digital Signals • Logic Gates• NOT (Inverter) Gate• AND Gate• OR Gate• NAND Gate• NOR Gate• XOR Gate

Image Resources

Microsoft, Inc. (2008). Clip Art. Retrieved September 10, 2008, from http://office.microsoft.com/en-us/clipart/default.aspx

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logic gates. digital signals logic gates not (inverter) gate and gate or gate nand gate nor gate xor...

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