1 / 23

Introduction to Computer Architecture and Logic Design Principles

This course, led by Instructor Yaohang Li, reviews essential concepts in computer architecture and operations. Key topics include the power wall, basic logic design principles, and the fundamental laws of Boolean logic. Students will explore combinational and sequential logic, truth tables, and the implementation of logical expressions using basic gates (AND, OR, NOT) and universal gates (NAND, NOR). Course objectives include reviewing foundational concepts and completing Assignment 1. Students will gain skills necessary for understanding modern digital computers.

konala
Télécharger la présentation

Introduction to Computer Architecture and Logic Design Principles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Instructor: Yaohang Li Computer Architecture & Operations I

  2. Review • Last Class • Assignment 1 • Power Wall • IC manufacture • Amdahl’s Law • This Class • Basic of Logic Design • Next Class • Combinational Logic

  3. 0s and 1s • Modern Computers are Digital • 1 • Corresponding to a high voltage • Signal • Asserted • Logical • True • 0 • Corresponding to low voltage • Signal • Deasserted • Logical • False • 0s and 1s are complimentary • 0’s inverse is 1 • 1’s inverse is 0

  4. Units • Bit • 0 or 1 • Byte (B) • 8 bits (00101010) • Kilo (KB) • 1024 bytes • Mega (MB) • 1,048,576 bytes • Giga (GB) • 1,073741,824 bytes • Tera (TB) • 1,099,511,628,000 bytes

  5. Combinational Logic and Sequential Logic • Combinational Logic • A logic system whose blocks do not contain memory and hence compute the same output given the same input • Sequential Logic • A group of logic elements that contain memory and hence whose value depends on the inputs as well as the current contents of the memory

  6. Boolean Logic -- AND • AND (Logical Product) • Its output = 1, only if both inputs are 1 • Truth table

  7. Boolean Logic -- OR • OR (Logical Sum) • Its output = 1 if either input = 1 • Truth table

  8. Boolean Logic -- NOT • NOT (Logical Inversion) or ~A • The output is the opposite of the input • Truth Table

  9. Order of Precedence • Precedence Rule • Parentheses (Highest) • NOT • AND • OR • Example

  10. Boolean Logic • Any Boolean Logic function can be implemented with only NOT, AND, OR functions • NOT, AND, OR functions are the basic logic functions • Others can be implemented by the basic logic functions NOT, AND, OR

  11. Truth Table • Example from the book:

  12. Answer

  13. Boolean Logic Laws • Identity Law • Zero and One Law • Inverse Law • Commutative Law

  14. Boolean Logic Laws (cont.) • Associative Laws • Distributive Laws • De Morgan’s Laws

  15. How to prove a logical law? • One approach: Truth table Truth table for de Morgan Laws

  16. Gates • Gates • basic digital building blocks which correspond to and perform the basic logical functions • AND • OR • NOT • Complex digital functions that make up a computer are built from these basic digital building blocks

  17. Simplification of NOT Gate

  18. In Class Exercise • Design a Combinational Logic to implement the following logical expression

  19. NAND • NAND • Its output = 1, only if both inputs are not 1 • Boolean Expression: A • B • Truth Table • The NAND functions has traditionally been the universal gate in digital circuits. It is simple to implement in hardware and can be used to construct the other gates.

  20. NOR • NOR • Its output = 1, only if no inputs are not 1 • Boolean Expression: A + B • Truth Table

  21. A C B XOR • XOR is EXCLUSIVE-OR • Its output = 1 if the inputs are different and equal 0 if all are the same. Boolean Expression: A Å B • Truth Table Equivalent to (A•B) + (A•B) = C

  22. Summary • 0s and 1s in Computer • Boolean Logic • NOT, AND, OR • Boolean Logic Laws • Truth Table • Gates • Basic Gates • NOT, AND, OR • Other Gates • NAND, NOR, XOR

  23. What I want you to do • Review Chapter 1 • Review Appendix C • Work on your assignment 1

More Related