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Computer Architecture & Operations I

Instructor: Yaohang Li. Computer Architecture & Operations I. Review. Last Class Assignment 1 Power Wall IC manufacture Amdahl’s Law This Class Basic of Logic Design Next Class Combinational Logic. 0s and 1s. Modern Computers are Digital 1 Corresponding to a high voltage Signal

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Computer Architecture & Operations I

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  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

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