04-2021-1000-109_Lecture3_Combinational_Logic_Design_I
Lecture Overview
Course: CSCI 150 Introduction to Digital and Computer System Design
Topic: Combinational Logic Design I
Materials:
Textbook v4: Chapter 3, Section 3.1;
Textbook v5: Chapter 3, Section 3.1
Focus
This lecture focuses on the methodology and architecture of combinational logic circuits, which are fundamental components in digital systems that provide outputs based solely on the current inputs without memory.
Review of Lectures 1 & 2
Lecture 1: Introduction to Digital Circuits
Overview of digital (logic) circuits and their importance in computer systems.
Examination of how information is represented in digital circuits using binary values (0s and 1s) and the significance of this representation for data processing and storage.
Lecture 2: Atomic Components of Digital Circuits
Identification of essential components within digital circuits, such as:
Gates: Basic building blocks (AND, OR, NOT) that perform logical operations.
Inputs/Outputs (I/O): Mechanisms through which information enters and leaves the digital system.
Review and application of Boolean Algebra concepts, which are crucial for designing and simplifying digital circuits.
Design Procedure
A structured approach to designing digital circuits involves several key steps:
Know the Problem: Understand the requirements and constraints of the design task at hand.
Specification of the Problem: Clearly define the desired functionality and goals for the circuit design, including performance metrics and resource limitations.
Basic Design: Create a preliminary version (beta implementation) of the circuit to verify initial concepts.
Optimization: Enhance the performance of the design by reducing latency, power consumption, or resource usage.
Systematic Design Procedures
Specification: Develop a detailed specification document outlining all functional and non-functional requirements of the circuit.
Formulation: Analyze and derive relationships between inputs and outputs using truth tables or Boolean expressions to elucidate the circuit's behavior.
Optimization: Minimize the quantity of logic gates and literals utilized in the design, promoting efficiency and potentially reducing cost.
Technology Mapping: Convert the design into a usable schematic using available technology components (e.g., specific types of gates).
Verification: Conduct tests to ensure the final design adheres to all specified requirements and functions as intended.
Example: Curtain Motor Control
Input Definitions
Sensors:
Sensor1: Outputs 1 when the curtain is fully closed.
Sensor2: Outputs 1 when the curtain is fully open.
Buttons:
Button1: Outputs 1 to signal intent to open the curtain.
Button2: Outputs 1 to signal intent to close the curtain.
Outputs:
Output1: Activates the motor to open the curtain (outputs 1).
Output2: Activates the motor to close the curtain (outputs 1).
Light: An indicator that shows whether the motor is currently active.
Example's Key Functions
The motor must automatically stop when the curtain is fully opened or fully closed to prevent mechanical damage or operational errors.
Formulation and Logic Expressions
Formulation:
Light: Light = Output1 + Output2
FullyClosed: FullyClosed = Sensor1
FullyOpened: FullyOpened = Sensor2
Logic Expressions for Control:
Output1: Output1 = Button1 ⋅ FullyOpened ⋅ BothPressed
Output2: Output2 = Button2 ⋅ FullyClosed ⋅ BothPressed
BothPressed: BothPressed = Button1 ⋅ Button2
Optimization of Design
To increase efficiency, combine logic expressions:
Light = Output1 + Output2
Where Output1 = Button1 ⋅ FullyOpened ⋅ BothPressed
Where Output2 = Button2 ⋅ FullyClosed ⋅ BothPressed
Technology Mapping
Implementable Components: Use of AND, NAND, OR gates, and others as needed.
Mapped Logic Expressions:
Output1 = Button1 ⋅ Sensor2 ⋅ Button1 ⋅ Button2
Output2 = Button2 ⋅ Sensor1 ⋅ Button1 ⋅ Button2
Verification of Design
Create comprehensive test cases to verify design functionality:
Test various combinations of sensor and button activations to ensure outputs are accurate and align with expected behavior. This step is critical to ensure the reliability of the circuit in practical applications.
04-2021-1000-109_Lecture3_Combinational_Logic_Design_I
Lecture Overview
Course: CSCI 150 Introduction to Digital and Computer System Design
Topic: Combinational Logic Design I
Materials:
Textbook v4: Chapter 3, Section 3.1;
Textbook v5: Chapter 3, Section 3.1
Focus
This lecture focuses on the methodology and architecture of combinational logic circuits, which are fundamental components in digital systems that provide outputs based solely on the current inputs without memory.
Review of Lectures 1 & 2
Lecture 1: Introduction to Digital Circuits
Overview of digital (logic) circuits and their importance in computer systems.
Examination of how information is represented in digital circuits using binary values (0s and 1s) and the significance of this representation for data processing and storage.
Lecture 2: Atomic Components of Digital Circuits
Identification of essential components within digital circuits, such as:
Gates: Basic building blocks (AND, OR, NOT) that perform logical operations.
Inputs/Outputs (I/O): Mechanisms through which information enters and leaves the digital system.
Review and application of Boolean Algebra concepts, which are crucial for designing and simplifying digital circuits.
Design Procedure
A structured approach to designing digital circuits involves several key steps:
Know the Problem: Understand the requirements and constraints of the design task at hand.
Specification of the Problem: Clearly define the desired functionality and goals for the circuit design, including performance metrics and resource limitations.
Basic Design: Create a preliminary version (beta implementation) of the circuit to verify initial concepts.
Optimization: Enhance the performance of the design by reducing latency, power consumption, or resource usage.
Systematic Design Procedures
Specification: Develop a detailed specification document outlining all functional and non-functional requirements of the circuit.
Formulation: Analyze and derive relationships between inputs and outputs using truth tables or Boolean expressions to elucidate the circuit's behavior.
Optimization: Minimize the quantity of logic gates and literals utilized in the design, promoting efficiency and potentially reducing cost.
Technology Mapping: Convert the design into a usable schematic using available technology components (e.g., specific types of gates).
Verification: Conduct tests to ensure the final design adheres to all specified requirements and functions as intended.
Example: Curtain Motor Control
Input Definitions
Sensors:
Sensor1: Outputs 1 when the curtain is fully closed.
Sensor2: Outputs 1 when the curtain is fully open.
Buttons:
Button1: Outputs 1 to signal intent to open the curtain.
Button2: Outputs 1 to signal intent to close the curtain.
Outputs:
Output1: Activates the motor to open the curtain (outputs 1).
Output2: Activates the motor to close the curtain (outputs 1).
Light: An indicator that shows whether the motor is currently active.
Example's Key Functions
The motor must automatically stop when the curtain is fully opened or fully closed to prevent mechanical damage or operational errors.
Formulation and Logic Expressions
Formulation:
Light: Light = Output1 + Output2
FullyClosed: FullyClosed = Sensor1
FullyOpened: FullyOpened = Sensor2
Logic Expressions for Control:
Output1: Output1 = Button1 ⋅ FullyOpened ⋅ BothPressed
Output2: Output2 = Button2 ⋅ FullyClosed ⋅ BothPressed
BothPressed: BothPressed = Button1 ⋅ Button2
Optimization of Design
To increase efficiency, combine logic expressions:
Light = Output1 + Output2
Where Output1 = Button1 ⋅ FullyOpened ⋅ BothPressed
Where Output2 = Button2 ⋅ FullyClosed ⋅ BothPressed
Technology Mapping
Implementable Components: Use of AND, NAND, OR gates, and others as needed.
Mapped Logic Expressions:
Output1 = Button1 ⋅ Sensor2 ⋅ Button1 ⋅ Button2
Output2 = Button2 ⋅ Sensor1 ⋅ Button1 ⋅ Button2
Verification of Design
Create comprehensive test cases to verify design functionality:
Test various combinations of sensor and button activations to ensure outputs are accurate and align with expected behavior. This step is critical to ensure the reliability of the circuit in practical applications.
