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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 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