Combinational Logic An Overview Digital Electronics Combinational Logic
Combinational Logic An Overview Digital Electronics
Combinational Logic This presentation will • Introduce the basics of combinational and sequential logic. • Present the logic symbol, logic expression, and truth table for the AND gate, OR gate, and INVERTER gate. • Review the design for a simple combinational logic circuit. 2
Combinational & Sequential Logic Combinational Logic Sequential Logic Inputs . . Clock Combinational Logic Gates Memory Elements (Flip-Flops) . . . Outputs 3
General Form for All Logic Gates Logic Symbol Output X Y Z=X Y Inputs Logic Expression X Y Z 0 0 1 Truth Table 0 1 0 1 1 Lists the output condition for all possible input combinations. PS – There’s no such thing as a smiley face gate. 4
The AND Gate X Y Z 0 0 1 1 1 Three ways to write the AND symbol Z is TRUE whenever X AND Y are TRUE 5
The OR Gate X Y Z 0 0 1 1 1 0 1 1 Z is TRUE whenever X OR Y are TRUE 6
The INVERTER Gate The NOT symbol or bar X X Z 0 1 1 0 Z is TRUE whenever X is NOT TRUE 1 0 The inverter is sometimes called the NOT gate. 7
AOI Logic • Combinational logic designs implemented with AND gates, OR gates, and INVERTER gates are referred to as AOI designs. A ND O R I NVERT • AOI Logic is just one type of combinational logic. Unit 2 of this course will spend a significant amount of time exploring other forms of combinational logic and their applications. • The purpose of this introduction is to provide a basis of understanding for the combinational logic subsection of the Board Game Counter design. 8
Combinational Logic Design Example The following is a review of the design and operation of a combinational logic circuit using AOI logic. This design controls the safety buzzer in a car and was designed to the following specifications: The buzzer is On whenever the door is open OR the key is in the ignition AND the seat belt is NOT buckled. 9
Design Example: Truth Table The buzzer is On whenever • the door is open • OR • the key is in the ignition AND the seat belt is NOT buckled. Car Buzzer – Truth Table Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 Seat Belt 0 : Seat Belt is NOT Buckled 1 : Seat Belt is Buckled Key 0 : Key is NOT in the Ignition 1 : Key is in the Ignition Door Buzzer 0 : Door is NOT Open 1 : Door is Open 0 : Buzzer is OFF 1 : Buzzer in ON 10
Design Example: Circuit Design 11
Design Example: Functional Test (1 of 8) Logic ‘ 1’ Logic ‘ 0’ Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 12
Design Example: Functional Test (2 of 8) Logic ‘ 1’ Logic ‘ 0’ Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 13
Design Example: Functional Test (3 of 8) Logic ‘ 1’ Logic ‘ 0’ Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 14
Design Example: Functional Test (4 of 8) Logic ‘ 1’ Logic ‘ 0’ Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 15
Design Example: Functional Test (5 of 8) Logic ‘ 1’ Logic ‘ 0’ Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 16
Design Example: Functional Test (6 of 8) Logic ‘ 1’ Logic ‘ 0’ Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 17
Design Example: Functional Test (7 of 8) Logic ‘ 1’ Logic ‘ 0’ Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 18
Design Example: Functional Test (8 of 8) Logic ‘ 1’ Logic ‘ 0’ Seat Belt Key Door Buzzer 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 19
Design Example: IC Component View 1 2 3 20
Design Example Using LEDs LED – Light Emitting Diode 21
LED – Light Emitting Diode To Turn an LED ON • The ANODE must be at a higher voltage potential ( 1. 5 v) than the CATHODE. • The amount of current flowing through the LED will determine how bright it is. • The amount of current is controlled by a series resistor. (not shown) CATHODE (‒) (+) ANODE ← Current Flow 22
LED Examples Logic 1 ANODE CATHODE 5 volts The ANODE is at a higher voltage potential than the CATHODE; the LED is ON. Logic 0 ANODE The 180 resistor controls the current that flows through the LED. This in turn controls its brightness. CATHODE 0 volts The ANODE is NOT at a higher voltage potential than the CATHODE; the LED is OFF. 23
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