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

2. Supplementary Chapter 1 Digital Computer Logic S1-2 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 in 2

3. Supplementary Chapter 1 Digital Computer Logic S1-3 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

4. Supplementary Chapter 1 Digital Computer Logic S1-4 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

5. Supplementary Chapter 1 Digital Computer Logic S1-5 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

6. Supplementary Chapter 1 Digital Computer Logic S1-6 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 ABC 000 010 100 111 ABC 000 011 101 111

7. Supplementary Chapter 1 Digital Computer Logic S1-7 Boolean Operators  NOT  Result TRUE if single input value is FALSE  C = A AC 01 10

8. Supplementary Chapter 1 Digital Computer Logic S1-8 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 ABC 000 011 101 110 A ⊕ B = (A+B) (A B) A ⊕ B = (A B)+(B A)

9. Supplementary Chapter 1 Digital Computer Logic S1-9 Boolean Algebra Operations  Valid for INCLUSIVE-OR, AND, XOR  Associative   Distributive   Commutative   DeMorgan’s Theorems  A + ( B +C)=(A+B)+C A ( B +C)=A B+A C A+B = B+A A+B = A B A B = A+B

10. Supplementary Chapter 1 Digital Computer Logic S1-10 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 XORAND ABC 000 010 100 111 ABC 000 011 101 110

11. Supplementary Chapter 1 Digital Computer Logic S1-11 Computer Implementation  Gates or logical gates  Integrated circuits constructed from transistor switches and other electronic components  VLSI: very large-scale integration

12. Supplementary Chapter 1 Digital Computer Logic S1-12 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

13. Supplementary Chapter 1 Digital Computer Logic S1-13 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

14. Supplementary Chapter 1 Digital Computer Logic S1-14 Half-Adder

15. Supplementary Chapter 1 Digital Computer Logic S1-15 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

16. Supplementary Chapter 1 Digital Computer Logic S1-16 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

17. Supplementary Chapter 1 Digital Computer Logic S1-17 Flip-Flop Types with State Tables

18. Supplementary Chapter 1 Digital Computer Logic S1-18 Register COPY Operation  Uses both sequential and combinatorial logic

19. Supplementary Chapter 1 Digital Computer Logic S1-19 Steps in a LOAD Instruction