Stepped Reckon (1672 - 1694)

In 1671 the German mathematician-philosopher Gottfried Wilhelm von Leibniz designed a calculating machine called the Step Reckoner. It was first built in 1673. The Step Reckoner expanded on Pascal's ideas and did multiplication by repeated addition and shifting.
Leibniz was a strong advocate of the binary system. Binary numbers are ideal for machines because they require only two digits, which can easily be represented by the on and off states of a switch. When computers became electronic, the binary system was particularly appropriate because an electrical circuit is either on or off. This meant that on could represent true, off could represent false, and the flow of current would directly represent the flow of logic.
Leibniz was prescient in seeing the appropriateness of the binary system in calculating machines, but his machine did not use it. Instead, the Step Reckoner represented numbers in decimal form, as positions on 10-position dials.

It is unclear how many different variants of the calculator were made. Some sources, such as the drawing to the right, show a 12 digit version.[4] This section describes the surviving 16 digit prototype in Hannover.

The machine is about 67 cm (26 inches) long, made of polished brass and steel, mounted in an oak case.[1] It consists of two attached parallel parts; an accumulator section to the rear, which can hold 16 decimal digits, and an 8 digit input section to the front. The input section has 8 dials with knobs to set the operand number, a telephone-like dial to the right to set the multiplier digit, and a crank on the front to perform the calculation. The result appears in the 16 windows on the rear accumulator section. The input section is mounted on rails and can be moved along the accumulator section with a crank on the left end that turns a worm gear, to change the alignment of operand digits with accumulator digits. There is also a tens-carry indicator and a control to set the machine to zero. The machine can:

· add or subtract an 8 digit number to / from a 16 digit number

· multiply two 8 digit numbers to get a 16 digit result

· divide a 16 digit number by an 8 digit divisor

Addition or subtraction is performed in a single step, with a turn of the crank. Multiplication and division are performed digit by digit on the multiplier or divisor digits, in a procedure equivalent to the familiar long multiplication and long division procedures taught in school. Sequences of these operations can be performed on the number in the accumulator; for example it can calculate roots by a series of divisions and additions.

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