1. CPS3340 COMPUTER ARCHITECTURE Fall Semester, 2013 09/05/2013 Lecture 4: Basics of Logic Design Instructor: Ashraf Yaseen DEPARTMENT OF MATH & COMPUTER SCIENCE CENTRAL STATE UNIVERSITY, WILBERFORCE, OH 1

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

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 3

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 4

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 5

6. Boolean Logic -- AND  AND (Logical Product)  Its output = 1, only if both inputs are 1  Truth table ABA·B 000 010 100 111 6

7. Boolean Logic -- OR  OR (Logical Sum)  Its output = 1 if either input = 1  Truth table ABA+B 000 011 101 111 7

8. Boolean Logic -- NOT  NOT (Logical Inversion) or ~A  The output is the opposite of the input  Truth Table A~A 0 1 1 0 8

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

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 10

11. Truth Table  Example from the book: 11

12. Answer 12  In class exercise : Show the logic equations for the logic functions, D, E, and F Implement D and F

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

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

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

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 16

17. Simplification of NOT Gate 17

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

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. ABC 001 011 101 110 19

20. NOR  NOR  Its output = 1, only if no inputs are not 1  Boolean Expression: A + B  Truth Table ABC 001 010 100 110 20

21. XOR  XOR is EXCLUSIVE-OR  Its output = 1 if the inputs are different and equal 0 if all are the same. Boolean Expression: A  B  Truth Table Equivalent to (AB) + (AB) = C A C B ABC 000 011 101 110 21

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 22

23. What I want you to do  Review Chapter 1  Work on your assignment 1 23