The architecture of computer hardware and systems software an information technology approach suplement 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 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 Digital Computer Logic S1-2 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 Digital Computer Logic S1-3 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 Digital Computer Logic S1-4 Boolean Algebra  Rules that govern constants and variables that can take on values  True/false; on/off; yes/no; 0/1  Boolean logic  Rules for handling Boolean constants and variables  fundamental operations: AND, OR and NOT  Truth Table: specifies results for all possible input combinations Supplementary Chapter Digital Computer Logic S1-5 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 Digital Computer Logic A B C 0 0 1 0 1 A B C 0 0 1 1 1 S1-6 Boolean Operators  NOT A C 1  Result TRUE if single input value is FALSE  C=A Supplementary Chapter Digital Computer Logic S1-7 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 ⊕ B = (A + B)  ( A  B ) A xor B equals A or B but not both A and B A ⊕ B = (A  B ) + ( B  A ) A xor B = either A and not B or B and not A Supplementary Chapter Digital Computer Logic S1-8 A B C 0 0 1 1 1 Boolean Algebra Operations  Valid for INCLUSIVE-OR, AND, XOR  Associative  A + ( B + C ) = ( A + B ) + C  Distributive  A  ( B + C ) = A  B +A  C  Commutative  A + B =B + A  DeMorgan’s Theorems  A + B =A  B  A  B =A + B Supplementary Chapter Digital Computer Logic S1-9 Gates and Combinatorial Logic  Many computer functions defined in terms of Boolean equations  Example: sum of single binary digit numbers  Truth table for sum Truth table for carry XOR AND A B C A B C 0 0 0 1 1 1 0 1 1 Supplementary Chapter Digital Computer Logic S1-10 Computer Implementation  Gates or logical gates  Integrated circuits constructed from transistor switches and other electronic components  VLSI: very large-scale integration Supplementary Chapter Digital Computer Logic S1-11 Boolean Algebra Implementation  Single type of gate appropriately combined  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 Digital Computer Logic S1-12 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 Digital Computer Logic S1-13 Half-Adder Supplementary Chapter Digital Computer Logic S1-14 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 Digital Computer Logic S1-15 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 Digital Computer Logic S1-16 Flip-Flop Types with State Tables Supplementary Chapter Digital Computer Logic S1-17 Register COPY Operation  Uses both sequential and combinatorial logic Supplementary Chapter Digital Computer Logic S1-18 Steps in a LOAD Instruction Supplementary Chapter Digital Computer Logic S1-19 ... and variables that can take on values  True/false; on/off; yes/no; 0 /1  Boolean logic  Rules for handling Boolean constants and variables  fundamental operations: AND, OR and NOT  Truth Table:... both the inputs to the operation and the result of the previous operation  Uses: counter Supplementary Chapter Digital Computer Logic S1-4 Boolean Algebra  Rules that govern constants and variables... B  A ) A xor B = either A and not B or B and not A Supplementary Chapter Digital Computer Logic S1-8 A B C 0 0 1 1 1 Boolean Algebra Operations  Valid for INCLUSIVE-OR, AND, XOR  Associative