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Steering Gates, Timing Diagrams & Combinational Logic Technician Series ©Paul Godin Created Jan 2014 Steering 1.1 Timing Diagrams Steering 1.2 Timing ◊ Timing diagrams are the best means of comparing the input and output logic values of a digital circuit over time, such as would be found in a functioning circuit. ◊ The output of digital circuit analysis tools such as oscilloscopes and logic analyzers essentially display timing diagrams. Steering 1.3 Timing Diagram sample: AND A Y B Logic 1 Logic 0 The output Y is determined by looking at the input A and B states and comparing them to the truth table for the gate. A B Y Steering 1.4 Timing Diagram sample: OR A Z B A B Z 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 Steering 1.5 Complete the Timing Diagram: Exercise 1 A Z B A B Z Steering 1.6 Complete the Timing Diagram: Exercise 2 A Z B A B Z Steering 1.7 Steering or Control Gates Steering 1.8 Introduction ◊ An application for a logic circuit is to control one digital signal with another digital signal. ◊ The AND and the OR gates can function as signal Control, or Steering Gates. Steering 1.9 Steering Gates ◊ Digital gates can be used to control the flow of one digital signal with another. 1 0 Signal Output Control 1 Signal Output Control 1 Animated Steering 1.10 Steering Gates Signal 1 0 0 Output Control 0 Signal 0 Output Control 0 Animated Steering 1.11 Exercise: Control Gates Worksheet (AND, OR) Control Y Z Z’ Signal Control Signal 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 Control Signal 0 Y Status Z Z’ Status Steering 1.12 Combinational Logic Steering 1.13 Combinational Logic ◊ Combinational logic describes digital logic circuits that are based on arrays of logic gates. Combinational logic circuits have no retention of states. ◊ Combinational logic circuits can be described with: ◊ ◊ ◊ ◊ ◊ English Terms Boolean equations Truth Tables Logic diagrams Timing Diagrams Steering 1.14 Combinational Logic Example 1 The circuit below is a combinational logic circuit. A B C Y Steering 1.15 Combinational Logic Example 1 It can be described in English terms: A AND B, OR C equals output Y A B Y C A AND B Steering 1.16 Combinational Logic Example 1 It can be described using a Boolean equation: (A ● B) + C = Y A B Y C A●B Steering 1.17 Combinational Logic Example 1 It can be described using a Truth Table: A A B C Y B 0 0 0 0 Y C If C is 1, Y is 1 0 0 1 1 0 1 0 0 (A ● B) + C = Y 0 1 1 1 1 0 0 0 1 0 1 1 Only instances where the output of the AND gate = 1 1 1 0 1 1 1 1 1 Steering 1.18 Combinational Logic Example 1 It can be described using a Timing Diagram: A B C (A ● B) + C = Y Y A B C Y 0 0 0 0 0 0 1 1 A 0 1 0 0 B 0 1 1 1 C Y 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Steering 1.19 Combinational Logic Example 2 This is a combinational Logic equation: A●B●C=Y It can be described as “NOT A AND B AND C equals Y”. It can be drawn this way: A A B C Y Steering 1.20 Combinational Logic Example 2 The Truth Table and Timing diagram describes its function A●B●C=Y A A A’ B C Y 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 A 0 1 1 1 1 B 1 0 0 0 0 C 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 A B C Y Y Steering 1.21 Boolean from a Circuit Diagram ◊ A step-by-step process is used to determine the Boolean equation from a circuit diagram. ◊ Begin at the inputs and include the logic expressions while working toward the outputs. Steering 1.22 Example 1: Circuit to Boolean Step 1: AB Step 2: AB Step 3: AB+C Steering 1.23 Circuit to Boolean Exercise 1: Convert the following circuit to its Boolean Expression Step 1: Step 2: Steering 1.24 Circuit to Boolean Exercise 2: Convert the following circuit to its Boolean Expression Step 1: Step 2: Step 3: Step 4: Steering 1.25 Circuit to Boolean Exercise 3: Convert the following circuit to its Boolean Expression Step 1: Step 3: Step 2: Steering 1.26 Circuit to Boolean Exercise 4: Convert the following circuit to its Boolean Expression Steering 1.27 Boolean to Circuit Conversion Example ◊ Take a step-by-step approach when converting from Boolean to a circuit. Work outward from the expression that brings together groupings found within the expression. ◊ Example: Convert (ABC) + BC = Y Step 1: ABC is OR’d with BC ABC BC Y Steering 1.28 Boolean to Circuit Conversion Example Step 3: Other side, BC Step 2: One side, ABC A B C B C ABC BC Step 4: Put it all together (ABC) + BC = Y Steering 1.29 Boolean to Circuit Conversion Example Step 5: Tidy up the circuit (inputs on left, outputs on right) A B C B C ABC (ABC) + BC = Y BC Steering 1.30 Boolean to Circuit Conversion Example Step 6: Common the B and the C inputs A B C ABC (ABC) + BC = Y BC Done Steering 1.31 Boolean to Circuit Exercise 1: Draw the circuit whose expression is: (AB)+(CD) Steering 1.32 Boolean to Circuit Exercise 2: Draw the circuit whose expression is: (A+B)•(BC) Steering 1.33 Boolean to Circuit Exercise 3: Draw the circuit whose expression is: (AB) + (AC) Steering 1.34 The Resistor and his Ohmies END ©Paul R. Godin prgodin°@ gmail.com Steering 1.35