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 Linda Senne, Bentley College Wilson Wong, Bentley College

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

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

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

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

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 ABC

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

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 A ⊕ B = (A+B) (A B) A ⊕ B = (A B)+(B A)

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

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 ABC

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

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

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

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

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

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

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

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

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

Supplementary Chapter 1 Digital Computer Logic S1-20 Copyright 2003 John Wiley & Sons All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the permissions Department, John Wiley & Songs, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein.