Early Computers The definition of a Ones and Zeros computer is “a device that computes, …” The abacus could be considered the first Chapter 12 computer. Its effectiveness has withstood the test of time and it is still used in some parts of the world. Lewinter & Widulski The Saga of Mathematics 1 Lewinter & Widulski The Saga of Mathematics 2 John Napier (1550 - 1617) Napier’s Bones In 1617, Scottish Napier's Bones were mathematician John multiplication tables Napier invented a inscribed on strips of technique of using wood or bone. numbering rods for Napier’s idea led to the multiplication. invention of the slide rule The rods became known in the mid 1600s by as "Napier's Bones." William Oughtred. Lewinter & Widulski The Saga of Mathematics 3 Lewinter & Widulski The Saga of Mathematics 4 The Pascaline The Pascaline In 1642, Blaise Pascal As they agonized over the columns of figures, Pascal invented his "Pascaline" decided to build a machine that would do the job much faster and more accurately. calculator. His machine could add and subtract. Pascal, a mathematician The machine used a series of toothed wheels, which and philosopher, and his were turned by hand and which could handle numbers father, a tax official, were up to 999,999.999. compiling tax reports for Pascal’s device was also called the “numerical the French government in calculator” and was one of the world’s first mechanical adding machines. Paris. Lewinter & Widulski The Saga of Mathematics 5 Lewinter & Widulski The Saga of Mathematics 6 1 Gottfried Wilhelm von Leibniz The Step Reckoner In 1671, Gottfried von This machine could add, subtract, multiply, divide and figure Leibniz invented the square roots through a series of stepped additions. "Stepped Reckoner" Although the machine did not become widely used, almost every which used a special type mechanical calculator build during the next 150 years was based of gear named the on it. stepped drum, also known as, the Leibniz Wheel. His device was not built until about 1694. Lewinter & Widulski The Saga of Mathematics 7 Lewinter & Widulski The Saga of Mathematics 8 Jacquard’s Loom Jacquard’s Loom In 1805, Joseph-Marie Jacquard built a loom controlled Jacquard’s loom emphasized three concepts by punched cards. important in computer theory. Heavy paper cards linked in a series passed over a set of rods on a loom. First, the information could be coded on punched The pattern of holes in the cards determined which rods cards. were engaged, thereby adjusting the color and pattern of the product. Second, the cards could be linked in a series of instructions – essentially a program – allowing a Prior to Jacquard’s invention, a loom operator adjusted the loom settings by hand before each glide of the machine to do work without human intervention. shuttle, a tedious and time-consuming job. Third, the programs could automate jobs. Lewinter & Widulski The Saga of Mathematics 9 Lewinter & Widulski The Saga of Mathematics 10 The Stored Program Charles Babbage (1791 - 1871) A program is a sequence of instructions for the Charles Babbage was computer to follow born in London, England. Also called “software” He entered Trinity College, Cambridge in Hardware: the chips, wires, switches, etc. on which the October 1810, and was software instructions are executed. recognized for his Primitive example: the Jacquard Loom exceptional mathematical The loom was the hardware abilities. The weaving pattern cards was the software Babbage is considered to The “program” was “stored” on punched cards be the “Father of Computing” Lewinter & Widulski The Saga of Mathematics 11 Lewinter & Widulski The Saga of Mathematics 12 2 Charles Babbage (1791 - 1871) Charles Babbage (1791 - 1871) In 1827 Babbage became Lucasian Professor of On 13 July 1823 Babbage received a gold medal from Mathematics at Cambridge, a position he held for 12 the Astronomical Society for his development of the years, although he never taught. difference engine. He had become engrossed in the main passion of his life – the development of a mechanical computer. By 1834 Babbage had completed the first drawings of Babbage began to construct a small difference engine in the analytical engine, the forerunner of the modern 1819 and had completed it by 1822. electronic computer. Babbage illustrated what his small engine was capable Babbage discussed the concept of using punched cards of doing by calculating successive terms of the sequence n2 + n + 41. to control the operation of his calculating machine, but he was never able to build a full working model. Lewinter & Widulski The Saga of Mathematics 13 Lewinter & Widulski The Saga of Mathematics 14 Charles Babbage (1791 - 1871) Charles Babbage (1791 - 1871) Babbage’s ideas embodied five key concepts of Although Babbage died before he could construct modern computers: his machine, such a computer has been built 1. Input device following Babbage's own design criteria. 2. Processor or number calculator In 1834 Babbage published his most influential 3. Control unit to direct the task to be performed and the sequence of calculations. work On the Economy of Machinery and 4. Storage place to hold number waiting to be Manufactures, in which he proposed an early processed form of what today we call operations research. 5. Output device Lewinter & Widulski The Saga of Mathematics 15 Lewinter & Widulski The Saga of Mathematics 16 Lady Augusta Ada (1815 - 1852) Lady Augusta Ada (1815 - 1852) Augusta Ada was the Ada Byron was fascinated by a demonstration of daughter of the poet, Lord Babbage's Difference Engine. Byron. Babbage found that Ada understood and could explain Her mother encouraged the workings of his machine better than anyone else. her to study mathematics Babbage later toured Europe giving lectures on his more and music. advanced concept, the Analytical Engine, a machine She was a bright which he never fully constructed. mathematician who was Extensive notes were taken of some of these lectures in introduced to Charles French. Babbage in 1833. Lewinter & Widulski The Saga of Mathematics 17 Lewinter & Widulski The Saga of Mathematics 18 3 Lady Augusta Ada (1815 - 1852) Lady Augusta Ada (1815 - 1852) Ada translated the French notes into English and When Augusta was 19, she married the wealthy Lord added a lengthy addendum. King, Baron of Lovelace. At Babbage's request, she published her notes. Her husband had some knowledge of mathematics, but it She had a unique grasp of the concepts of was Ada who urged him to provide funding to Babbage programming subroutines, loops and jumps. when his government funding ceased. Ada also had an interest in gambling, and attempted to She is often referred to as the first programmer. apply some of Babbage's technology to that end, but She was instrumental in clarifying and preserving without great success. information on Charles Babbage and his work. Lewinter & Widulski The Saga of Mathematics 19 Lewinter & Widulski The Saga of Mathematics 20 Lady Augusta Ada (1815 - 1852) Mechanical Computers In recognition of her contributions to the field of Mechanical calculators built from cogs and gears programming theory, the U.S. Department of Defense named their programming language for reducing Difference Engine software development and maintenance costs, known Analytical Engine (General Purpose) only as DoD-1 up to that point, "Ada" in her honor in May of 1979. The "Difference Engine" was massive steam powered Ada is one of the main characters in the “alternate mechanical calculator designed to print astronomical history” novel The Difference Engine by Bruce Sterling tables. and William Gibson, which imagines a world in which Babbage's machines were mass produced and the The Analytical Engine was a mechanical computer computer age started a century early. designed to run using punch cards. Lewinter & Widulski The Saga of Mathematics 21 Lewinter & Widulski The Saga of Mathematics 22 The Difference Engine The Analytical Engine Designed to solve accuracy problem First true ancestor of the modern computer would have computed tables and output results directly onto printing plates key idea: automatically feed results back into the difference engine store numbers and intermediate results for any kind of function at all 1822: partial working model Gear-based 2 orders of difference 6-figure numbers Basic components store (memory) only computing machine Babbage ever completed mill (arithmetic unit) Government research grant (1823) control barrel (primitive program control unit) abandoned support in 1842 cycle time: around 3 seconds per operation The Scheutz difference engine (Sweden, 1854) program stored on punched cards idea came from Jacquard loom irony: British government bought one planned: steam power Lewinter & Widulski The Saga of Mathematics 23 Lewinter & Widulski The Saga of Mathematics 24 4 Electromechanical Computers Electromechanical Computers Herman Hollerith Alan Turing Developed a punched card tabulating machine Computer theorist Used for the 1890 census Worked on the Colossus, used to decrypt German military messages, WW2 His company was one of several which began IBM Grace Hopper – worked as a coder on the Konrad Zuse Harvard Mark I Proposed use of vacuum tubes for switching of binary It used electrical relays circuits Sponsored by US Navy to compute navigational Hitler refused to fund his design tables Lewinter & Widulski The Saga of Mathematics 25 Lewinter & Widulski The Saga of Mathematics 26 Early Electronic Computers Early Electronic Computers The ABC computer The ENIAC The Atanasoff-Berry Computer was the world's first electronic In 1946, John Mauchly and J Presper Eckert developed the digital computer. ENIAC I (Electrical Numerical Integrator And Calculator). It was built by John Vincent Atanasoff and Clifford Berry at The ENIAC computer was intended to be a general purpose Iowa State University to do math & physics calculations. one, but it was also designed for a very specific task, namely It incorporated several major innovations in computing compiling tables for the trajectories of bombs and shells.