logic gates. digital signals logic gates not (inverter) gate and gate or gate nand gate nor gate xor...
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Logic Gates
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
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
10
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
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)
A
B
0 00
Y
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)
A
B
0 00
Y
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)
A
B
0 10
Y
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)
A
B
0 10
Y
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
F)
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
BY
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