IMAGE PROCESSING I Computer Technology Michael Habeck November 11, 2020 [email protected] Microscopic Image Analysis University Hospital Jena OVERVIEW ∙ An abridged history of computers ∙ Computer systems organization ∙ Logic gates and Boolean algebra ∙ Radix number systems ∙ Operators and data types in Python 1 AN ABRIDGED HISTORY OF COMPUTERS∗ Year Name Made by Comments 1623 Calculating clock Schickard Sketches of two mechanical calculators 1642 Pascaline Pascal Operated by rotating wheels 1673 Step reckoner Leibniz First true four-function calculator 1822 Difference engine Babbage Mechanical calculator for tabulating polynomials 1834 Analytical Engine Babbage First attempt to build a digital computer 1936 Z1 Zuse First working relay calculating machine 1943 COLOSSUS British gov’t First electronic computer 1944 Mark I Aiken First American general-purpose computer 1946 ENIAC Eckert/Mauchley Modern computer history starts here 1949 EDSAC Wilkes First stored-program computer 1951 Whirlwind I M.I.T. First real-time computer 1952 IAS Von Neumann Most current machines use this design 1960 PDP-1 DEC First minicomputer (50 sold) 1961 1401 IBM Enormously popular small business machine 1962 7094 IBM Dominated scientific computing in the early 1960s 1963 B5000 Burroughs First machine designed for a high-level language 1964 360 IBM First product line designed as a family 1964 6600 CDC First scientific supercomputer from: A. S. Tannenbaum & T. Austin: Structured Computer Organization, 6th edition ∗ See wikipedia entry on the history of computing hardware for more information 2 AN ABRIDGED HISTORY OF COMPUTERS∗ Year Name Made by Comments 1965 PDP-8 DEC First mass-market minicomputer (50,000 sold) 1970 PDP-11 DEC Dominated minicomputers in the 1970s 1974 8080 Intel First general-purpose 8-bit computer on a chip 1974 CRAY-1 Cray First vector supercomputer 1978 VAX DEC First 32-bit superminicomputer 1981 IBM PC IBM Started the modern personal computer era 1981 Osborne-1 Osborne First portable computer 1983 Lisa Apple First personal computer with a GUI 1985 386 Intel First 32-bit ancestor of the Pentium line 1985 MIPS MIPS First commercial RISC machine 1985 XC2064 Xilinx First field-programmable gate array (FPGA) 1987 SPARC Sun First SPARC-based RISC workstation 1989 GridPad Grid Systems First commercial tablet computer 1990 RS6000 IBM First superscalar machine 1992 Alpha DEC First 64-bit personal computer 1992 Simon IBM First smartphone 1993 Newton Apple First palmtop computer (PDA) 2001 POWER4 IBM First dual-core chip multiprocessor from: A. S. Tannenbaum & T. Austin: Structured Computer Organization, 6th edition ∗ See wikipedia entry on the history of computing hardware for more information 3 AN ABRIDGED HISTORY OF COMPUTERS from: www.computerhistory.org 4 AN ABRIDGED HISTORY OF COMPUTERS from: www.computerhistory.org 5 ZEROTH GENERATION—MECHANICAL COMPUTERS Wilhem Schickard Sketch of his machine Replica of Schickard’s machine from: https://commons.wikimedia.org 6 ZEROTH GENERATION—MECHANICAL COMPUTERS Blaise Pascal Replica of Pascal’s machine, the Pascaline from: https://commons.wikimedia.org 7 ZEROTH GENERATION—MECHANICAL COMPUTERS Gottfried Leibniz Replica of Leibniz’s stepreckoner ... it is beneath the dignity of excellent men to waste their time in calculation when any peasant could do the work just as accurately with the aid of a machine. from: www.computerhistory.org 8 ZEROTH GENERATION—MECHANICAL COMPUTERS Charles Babbage Replica of the analytical engine from: wikipedia and www.computerhistory.org 9 FIRST GENERATION—RELAY BINARY ADDER George Stibitz Stibitz’s Model K binary adder from: M. M. Irvine: IEEE Annals of the History of Computing (2001) 23:22–42 10 FIRST GENERATION—VACCUM TUBES Colossus Mark 2 from: wikipedia 11 FIRST GENERATION—VACCUM TUBES ENIAC (Electronic Numerical Integrator and Computer) from: wikipedia 12 SECOND GENERATION—TRANSISTORS TX-0 (Transistorized eXperimental computer 0) from: wikipedia 13 THIRD GENERATION—INTEGRATED CIRCUITS IBM System/360 from: wikipedia 14 FOURTH GENERATION—VERY LARGE SCALE INTEGRATION VLSI Chip Today’s computers from: wikipedia and http://www.bytemods.com/mods/54/beer-case-mediacenter 15 SEC. 1.1 STRUCTURED COMPUTER ORGANIZATION 5 1.1.2 Contemporary Multilevel Machines Most modern computers consist of two or more levels. Machines with as many as six levels exist, as shown in Fig. 1-2. Level 0, at the bottom, is the ma- chine’s true hardware. Its circuits carry out the machine-language programs of level 1. For the sake of completeness, we should mention the existence of yet an- other level below our level 0. This level, not shown in Fig. 1-2 because it falls within the realm of electrical engineering (and is thus outside the scope of this book), is called the device level. At this level, the designer sees individual transis- CONTEMPORARYtors, which are the MULTILEVEL lowest-level primitives MACHINES for computer designers. If one asks how transistors work inside, that gets us into solid-state physics. Level 5 Problem-oriented language level Translation (compiler) Level 4 Assembly language level Translation (assembler) Level 3 Operating system machine level Partial interpretation (operating system) Level 2 Instruction set architecture level Interpretation (microprogram) or direct execution Level 1 Microarchitecture level Hardware Level 0 Digital logic level Figure 1-2. A six-level computer. The support method for each level is indicated from: A. S. Tannenbaumbelow & T. it Austin: (along Structured with the Computer name ofOrganization, the supporting 6th edition program). 16 At the lowest level that we will study, the digital logic level, the interesting ob- jects are called gates. Although built from analog components, such as transistors, gates can be accurately modeled as digital devices. Each gate has one or more dig- ital inputs (signals representing 0 or 1) and computes as output some simple func- tion of these inputs, such as AND or OR. Each gate is built up of at most a handful of transistors. A small number of gates can be combined to form a 1-bit memory, which can store a 0 or a 1. The 1-bit memories can be combined in groups of (for example) 16, 32, or 64 to form registers. Each register can hold a single binary LOGIC GATES AND BOOLEAN ALGEBRA Logic gates are physical implementations of Boolean functions with two inputs 퐴, 퐵 and an output 푋1 Boolean functions can be represented by truth tables Input 퐴 Input 퐵 Output 푋 0 0 푋1 0 1 푋2 1 0 푋3 1 1 푋4 1 represents TRUE, ON, etc. 0 represents FALSE, OFF, etc. 1General situation: 푛 input pins and 푚 output pins 17 LOGIC GATES AND BOOLEAN ALGEBRA OR function Hydraulic OR gate Input 퐴 Input 퐵 Output 푋 0 0 0 0 1 1 1 0 1 1 1 1 Mechanical OR gate Electrical OR gate from: W. D. Hillis: The Pattern on the Stone 18 LOGIC GATES AND BOOLEAN ALGEBRA NOT AND OR 퐴 퐴 퐴 푋 푋 푋 퐵 퐵 퐴 퐵 푋 퐴 퐵 푋 퐴 푋 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 19 LOGIC GATES AND BOOLEAN ALGEBRA Any logical function can be constructed from NOT, OR, and AND gates 퐴 퐵 퐶 퐷 ⋯ 푋 0 0 0 0 ⋯ 0 ⋮ ⋮ ⋮ ⋮ ⋯ ⋮ 0 0 0 1 ⋯ 1 ⟶ 퐴 퐵 퐶 퐷 ⋯ ⋮ ⋮ ⋮ ⋮ ⋯ ⋮ 0 1 1 0 ⋯ 1 ⟶ 퐴 퐵 퐶 퐷 ⋯ ⋮ ⋮ ⋮ ⋮ ⋯ ⋮ 푋 = ⋯ + ( 퐴 퐵 퐶 퐷 ⋯ ) + ⋯ + ( 퐴 퐵 퐶 퐷 ⋯ ) + ⋯ where 퐴 ↔ NOT(퐴), 퐴 퐵 ↔ AND(퐴, 퐵), 퐴 + 퐵 ↔ OR(퐴, 퐵) 20 LOGIC GATES AND BOOLEAN ALGEBRA Another way to see that NOT, AND, OR suffice to represent any Boolean function is by recursion 푋 = 푓(퐴, 퐵, 퐶, 퐷, …) = 퐴 푓(0, 퐵, 퐶, 퐷, …) + 퐴 푓(1, 퐵, 퐶, 퐷, …) = 퐴 퐵 푓(0, 0, 퐶, 퐷, …) + 퐴 퐵 푓(0, 1, 퐶, 퐷, …) + 퐴 퐵 푓(1, 0, 퐶, 퐷, …) + 퐴 퐵 푓(1, 1, 퐶, 퐷, …) = … 21 NAND AND NOR Can we simplify NOT, AND, OR any further? NAND NOR 퐴 퐴 푋 푋 퐵 퐵 퐴 퐵 푋 퐴 퐵 푋 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 0 22 SEC. 3.1 GATES AND BOOLEAN ALGEBRA 149 In Fig. 3-1(b) two transistors are cascaded in series. If bothV 1 andV 2 are high, both transistors will conduct andV out will be pulled low. If either input is low, the corresponding transistor will turn off, and the output will be high. In other words,V out will be low if and only if bothV 1 andV 2 are high. In Fig. 3-1(c) the two transistors are wired in parallel instead of in series. In this configuration, if either input is high, the corresponding transistor will turn on and pull the output down to ground. If both inputs are low, the output will remain high. These three circuits, or their equivalents, form the three simplest gates. They are called NOT, NAND, and NOR gates, respectively. NOT gates are often called inverters; we will use the two terms interchangeably. If we now adopt the conven- tion that ‘‘high’’ (Vcc volts) is a logical 1, and that ‘‘low’’ (ground) is a logical 0, we can express the output value as a function of the input values. The symbols used to depict these three gates are shown in Fig. 3-2(a)–(c), along with the func- CONSTRUCTINGtional behavior LOGICAL for FUNCTIONS each circuit. FROM In these NAND figures, OR NORA andB are inputs andX is the output. Each row specifies the output for a different combination of the inputs. 154 THE DIGITAL LOGIC LEVEL CHAP. 3 NOT NAND NOR AND OR A A A A AX X X X X A A B B B B A X A B X A B XA A B X A B X 0 1 0 0 A 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 (a) 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 from: A.