Logic Gates
Logic Gates
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•
•
•
•
•
•
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Digital Signals
Logic Gates
NOT (Inverter) Gate
AND Gate
OR Gate
NAND Gate
NOR Gate
XOR Gate
Digital Signals
Digital 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
1 (3V)
1
0
0
1
0
1
0 (0V)
Each column represents a
small amount of time
1
0
Logic Gates
An electronic system that performs
a 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) Gate
A logic gate that changes its input logic
level to the opposite state
Symbol
0
1
A
Y
Truth Table: A table listing all possible inputs to a circuit and
the corresponding outputs
Truth Table
NOT Gate
Input (A)
Output (Y)
0
1
1
0
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
Symbol
A logic circuit whose:
Inputs both = 1 then,
Output = 1
If I am hungry AND it is 5:00 p.m., then I will eat dinner.
AND Gate
A
B
Truth Table
AND Gate
0
1Y
Input (A)
Input (B)
Output (Y)
0
0
1
0
1
0
0
0
0
1
1
1
OR Gate
Symbol
A logic circuit when:
Either Input = 1 then,
Output = 1
If I pedal harder OR go downhill, then my bike will go faster.
OR Gate
A
B
Truth Table
OR Gate
1
0Y
Input (A)
Input (B)
Output (Y)
0
0
1
0
1
0
0
1
1
1
1
1
NAND Gate
Symbol
A logic circuit whose:
Inputs both = 1 then,
Output = 0
If it is windy AND cold, then I am NOT going to walk home.
NAND Gate
A
B
Truth Table
NAND Gate
1Y
0
Input (A)
Input (B)
Output (Y)
0
0
1
0
1
0
1
1
1
1
1
0
NOR Gate
Symbol
A logic circuit when:
Either Input = 1 then,
Output = 0
If my battery is dead OR I forget headphones, then I will
NOT listen to my music.
NOR Gate
A
B
Truth Table
NOR Gate
0
1Y
Input (A)
Input (B)
Output (Y)
0
0
1
0
1
0
1
0
0
1
1
0
XOR Gate
A logic circuit when:
If A or B = 1, but not both,
then Output = 0
Symbol
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.
Possible Inputs (conditions)
Outputs
First Friend wants to
go to dinner (T or F)
Second friend wants
to go to dinner (T or F)
We will go to dinner
(T or F)
F
F
F
F
T
T
T
F
T
T
T
F
XOR Gate
A
B
Truth Table
XOR Gate
1Y
0
Input (A)
Input (B)
Output (Y)
0
0
1
0
1
0
0
1
1
1
1
0
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