SUPLEMENTARY CHAPTER 1: An Introduction to Digital Logic

1. The Architecture of Computer Hardware and Systems Software: An Information Technology Approach 3rd Edition, Irv Englander John Wiley and Sons 2003 SUPLEMENTARY CHAPTER 1:An Introduction to Digital Logic

2. Integrated Circuits • The building blocks of computers • Designed for specialized functions • Examples: the CPU, bus interface, memory management unit • Transistors: primary components of ICs • Motorola MPC 7400 PowerPC modules: 6.5 million transistors in less than ½ in2 Supplementary Chapter 1 Digital Computer Logic

3. Transistors • Boolean algebra: basis for computer logic design • Transistors: means for implementing Boolean algebra • Switches: on/off to represent the 0’s and 1’s of binary digital circuits • Combined to form logic gates Supplementary Chapter 1 Digital Computer Logic

4. Digital Circuits • Combinatorial logic • Results of an operation depend only on the present inputs to the operation • Uses: perform arithmetic, control data movement, compare values for decision making • Sequential logic • Results depend on both the inputs to the operation and the result of the previous operation • Uses: counter Supplementary Chapter 1 Digital Computer Logic

5. Boolean Algebra • Rules that govern constants and variables that can take on 2 values • True/false; on/off; yes/no; 0/1 • Boolean logic • Rules for handling Boolean constants and variables • 3 fundamental operations: AND, OR and NOT • Truth Table: specifies results for all possible input combinations Supplementary Chapter 1 Digital Computer Logic

6. Boolean Operators • AND • Result TRUE if and only if both input operands are true • C = A  B • INCLUSIVE-OR • Result TRUE if any input operands are true • C = A + B Supplementary Chapter 1 Digital Computer Logic

7. Boolean Operators • NOT • Result TRUE if single input value is FALSE • C = A Supplementary Chapter 1 Digital Computer Logic

8. Boolean Operators • EXCLUSIVE-OR • Result TRUE if either A or B is TRUE but not both • C = A ⊕ B • Can be derived from INCLUSIVE-OR, AND and NOT A xor B equals A or B but not both A and B A xor B = either A and not B or B and not A Supplementary Chapter 1 Digital Computer Logic

9. Boolean Algebra Operations • Valid for INCLUSIVE-OR, AND, XOR • Associative • Distributive • Commutative • DeMorgan’s Theorems Supplementary Chapter 1 Digital Computer Logic

10. Gates and Combinatorial Logic • Many computer functions defined in terms of Boolean equations • Example: sum of 2 single binary digit numbers • Truth table for sum Truth table for carry XOR AND Supplementary Chapter 1 Digital Computer Logic

11. Computer Implementation • Gates or logical gates • Integrated circuits constructed from transistor switches and other electronic components • VLSI: very large-scale integration Supplementary Chapter 1 Digital Computer Logic

12. Boolean Algebra Implementation • Single type of gate appropriately combined • 2 possibilities • NAND gate: AND operation followed by a NOT operation • NOR gate: INCLUSIVE-OR followed by a NOT operation Note:  indicates a NOT operation Supplementary Chapter 1 Digital Computer Logic

13. Selector or Multiplexer • Switch input back and forth between inputs • Logic circuits that make up a computer • are relatively simple but • look complicated because many circuits required Supplementary Chapter 1 Digital Computer Logic

14. Half-Adder Supplementary Chapter 1 Digital Computer Logic

15. Full Adder • Handles possible carry from previous bit • Half adder shown as block to simplify (portion of half adder in Fig. S1.11 enclosed in dotted line) • 2-bit adder contains 32 circuits • Also called ripple adder because the carry ripples through 32 bits Supplementary Chapter 1 Digital Computer Logic

16. Sequential Logic Circuits • Output depends on • Input • Previous state of the circuit • Flip-flop: basic memory element • State table: output for all combinations of input and previous states • Cf. Truth Table Supplementary Chapter 1 Digital Computer Logic

17. Flip-Flop Types with State Tables Supplementary Chapter 1 Digital Computer Logic

18. Register COPY Operation • Uses both sequential and combinatorial logic Supplementary Chapter 1 Digital Computer Logic

19. Steps in a LOAD Instruction Supplementary Chapter 1 Digital Computer Logic