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Charles Babbage designed a machine that was essentially an automated adding machine (Skilled manipulation of addition can perform any mathematical function). Babbage's machine performed polynomial functions using the method of divided differences. He called the machine a difference engine. Babbage worked on a prototype for his difference engine, but it never completed it due to lack of funding.

In 1837, Inspired by his difference engine, Babbage went on to design a more complex machine he called the analytical engine. The analytical engine would have used a series of punched cards as a list of instructions to perform a series of operations.

The design for Babbage's analytical engine introduced two more fundamentals of the digital computer, bringing the total up to five:

4. the
conditional branch, and;

5. the conditional loop.

A computer performs a conditional branch when it is following a program and comes to a point where it must either step on to the next instruction or jump ahead to other instructions. The decision to jump forward or not depends on whether two pieces of information elsewhere in the memory are equal. A conditional loop is the same as a conditional branch except the computer jumps to a previous instruction and repeats instructions that have already been performed. Each time the computer loops changes are made to data stored elsewhere in memory. At the end of each iteration the computer checks the conditions of the data. It then decides whether to loop again or to go on to the next instruction.

In 1989 through 1991 the London Science Museum constructed two difference engines according to Babbage's design for his Difference Engine No. 2. They used construction techniques that were available to Babbage. This was to demonstrate that Babbage could have completed the project given sufficient funds and time. The builders corrected some flaws in the design but noted that the defects were obvious and Babbage would have certainly discovered and corrected them during the building process.

A modern construction of Babbage's Difference Engine No. 2 on display at the London Science Museum |

Babbage built parts of his analytical engine as proofs of concept devices but never built full machine. In 2010, an organization called Plan28 began fundraising to build a computer model of Babbage's analytical engine. If this is successful, they plan to build a real-world working model.

Babbage built parts of his analytical engine as proofs of concept devices but never built full machine. In 2010, an organization called Plan28 began fundraising to build a computer model of Babbage's analytical engine. If this is successful, they plan to build a real-world working model. As of 2017 Plan 28 finished their initial review of Babbages's voluminous Scribbling Books and has a searchable database of available materials.

Thanks to his work on these early computing machines, Charles Babbage is considered by many historians to be the father of the modern computer.

In the mid-1800s, George Boole developed mathematics for logic called Boolean algebra. The Boolean functions of "AND," "OR" and "NOT" are the basis for most computer operations.

In electronics, the Boolean AND function is like two switches in one wire. In this circuit, both switches must be in the "on" position for the bulb to light.

Boolean AND function, both switches must be on for the light to be on |

The Boolean OR function is like two switches in separate wires running to the same light bulb. If either switch is in the "on" position, the lamp will light.

Boolean OR function, if either switch is on the light will be on |

The Boolean NOT function is like a switch that works backward; when the switch is on the light is off and when the switch is off the light is on.

As discussed previously, the states of the switches can be used to represent binary numbers. The Boolean functions can be combined to give the algebraic sum of two such numbers. Simple addition is the basis for all calculations done by computers. These three Boolean functions are the basis for all mathematics and other functions done by computers.

In 1884, Herman Hollerith
patented a system that used punched cards and an electromechanical counter to
tabulate statistics.^{[1]} The U.S. Census Bureau contracted with Hollerith to
tabulate the 1890 census. It took eight years to tabulate the 1880 census by
hand. Hollerith's machines did the 1890 census in one year.

Hollerith's punched card reader/tabulator |

Hollerith didn't introduce any new fundamentals of computing. His system was based on previous work by Jacquard and Babbage. However, it was the first major use of a machine to do the work that most computers so today. That is, manipulate and present information.

A woman transferring data to Hollerith's punched cards |

In 1911, Hollerith's company merged with three other companies to form the Computing Tabulating Recording Corporation. In 1924, under the presidency of Thomas Watson, the company changed its name to International Business Machines. Today the company is known simply as IBM.

—————————^{1} | To ''tabulate'' means to put into columns and rows, like a spreadsheet |

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