Fundamentals of Digital Machine Computing

The first industrial revolution was concerned with the ma­ chine solely as an alternative to human muscle. It displaced man and animal as a source of power, without appreciably affecting other human functions. The development of auto­ mation which can handle problems of programming on an automatic basis will, to a large extent, condition the entire social and technical life of the future. The picture of the auto­ matic age will be quite different from the picture of any other period. The technical revolution of automation will bring deeper and more incisive changes to man's life than did the first industrial revolution. The digital computer is the universal machine which has already revolutionized modern technology and which will be the main instrument to render factories and business places automatic. The digital computer has brought increased im­ petus and new direction to the whole field of applied mathe­ matics and to the description of problems in precisely defined and solvable relations. Since the arrival of digital computers, applied mathematics takes a place of importance at least equal to abstract mathematics. Modern engineers and scientists have become more conscious of the powerful tool of mathe­ matical analysis through the use of computers.

1 The Role and Principal Attributes of Digital Computers.- 1-1. The Universality of Digital Computers.- 1-2. Digital Computers as Logical Machines.- 1-3. Large Memory Capacity.- 1-4. Computational Rapidity.- 1-5. General Systems Configuration.- 1-6. The Computer Family Tree.- 2 Binary Numbers and Codes and their Machine Representation.- 2-1. The Binary Number System.- 2-2. The Octal System as Bridge between Decimal and Binary.- 2-3. Number Conversion.- 2-4. Binary Codes.- 2-5. Representation of Negative Numbers.- 2-6. Fixed Point Number Ranges.- 2-7. Scale Factoring.- 2-8. Floating Point Numbers.- 2-9. Initial Computer Input.- 3 The Principles of Logic in Computers.- 3-1. Relationship of Logical Concepts to Computer Circuits.- 3-2. Boolean Algebra as Symbolic Logic.- 3-3. Some Useful Theorems of Boolean Algebra.- 3-4. Basic Elements of the Computer.- 3-5. Logical Description of Basic Elements.- 3-6. Minimization of Logical Functions.- 3-7. Logical Synthesis of Combinational Circuits.- 3-8. Logical Analysis of Combinational Circuits.- 3-9. The Logic of Combinational Circuits with Several Outputs.- 3-10. Logical Synthesis of Sequential Circuits.- 3-11. Design of an Odd-Sequence Counter.- 3-12. The Logic of the Entire Computer.- 4 Arithmetic Operations of the Machine.- 4-1. The Logic of Binary Addition and Subtraction.- 4-2. Serial and Parallel Binary Addition.- 4-3. Addition with Accumulators.- 4-4. Machine Subtraction.- 4-5. BCD Addition and Complementation.- 4-6. Considerations for Machine Multiplication.- 4-7. Serial Binary Multiplication.- 4-8. Parallel Binary Multiplication.- 4-9. BCD Multiplication.- 4-10. Considerations for Machine Division.- 5 The Instruction Code of the Computer.- 5-1. Basic Computer Operations.- 5-2. Instruction Format.- 5-3. Coding of Instructions.- 5-4. General Classes of Instructions.- 5-5. Operational Instructions.- 5-6. Control Instructions.- 5-7. Instruction Modification.- 5-8. Editing Instructions.- 5-9. Instruction Execution.- 6 Principles and Examples of Programming.- 6-1. Mathematical Methods for Digital Computers.- 6-2. Diagramming the Program.- 6-3. Writing the Code.- 6-4. Simple Arithmetic Problems.- 6-5. Iterative Processes.- 6-6. Polynomial Evaluation.- 6-7. Solution of Simultaneous Linear Equations.- 6-8. Matrix Operations.- 6-9. Searching and Sorting.- 6-10. Numerical Solution of Differential Equations.- 6-11. A Complete Program for a Rocket Trajectory.- 7 Automatic Programming.- 7-1. Meaning of Automatic Programming.- 7-2. Principles of Language Design.- 7-3. The Structure of ALGOL.- 7-4. Basic Considerations for Compilers.- 7-5. The IT Compiler.- 7-6. The Listing Process.- 7-7. The Decomposition Process.- 7-8. Compiler Summary.- Appendix A. Summary of Instructions by Alphabetic Code.- Appendix B. Powers of Two.- List of References.