Leonardo Torres Y Quevedo, the scientist who first applied floating-point arithmetic to computers, was born in the Spanish town of Santa Cruz on December 28, 1852. He was educated at the Institute of Bilbao and School of Engineers in Madrid, before embarking on a career as an engineer and inventor.

His powers of invention reached their heights in later part of his life, He designed the Niagara Transport Bridge and cable car, which are still in use today at Niagara Falls. Torres was a child of his times and his main interest was n electro mechanical devises. In 1906, he demonstrated a radio controlled model boat in the habour of Bilbao before the King of Spain. In 1911 he invented the first automatic chess player. The machine used electromagnets beneath the table to move pieces, and was programmed to win a simple game against a human opponent.

Torres’ interests in automata derived from his experience of assembly lines in the industrial plants of early 20th century. Through out his life he sought to separate the types of problems that require human thought from those that could be done automatically.

In 1914, he published a paper showing the feasibility of building Babbage’s Analytical Engine using electromechanical techniques. It was this paper that first suggested the use of floating-point arithmetic in future computer. In 1920, he constructed an electromechanical calculator that used an adapted typewriter for entering the numbers and printed the results automatically. The typewriter was connected by telephone wires to the calculator and Torres foresaw the possibility of many terminals attached to a central calculator, (= today’s term- processing units)

Torres was honoured by French Academy of Sciences for his work, and later became the President of his country’s own Academy of Sciences. Torres died in Madrid on December 18, 1936.


What is floating point Arithmetic

A cash register displays in the totals of rupees and cents. (Rs 12.25 for example), in such machine there are only need for two decimal places, after the decimal point. But in a computer greater accuracy is often required and the number of decimal places is allowed to vary or “float” according to the need of the problem. This is known as “floating point Arithmetic”.

Any number can be written in a variety of ways. For example 0.8752 meters can be expressed as 875.2 millimeters, or 0.8752x1000millimeters or simply 0.8752x10power3. This last method lends itself to an economical method of encoding for a computer. If a computer has  only allocated six digit spaces to represent each number (and for the sake of clarity the decimal system is used instead binary) then the above number can be stowed as 875203: where the last two digits on the right hand side are called the “index” and represent the power of 10(in this case 3) and the leading four digits are called “mantissa”

The mantissa and the index are usually “normalized” to remove any leading zeros from the mantissa. For number 41.83 could be written as 004104, but would be normalized to 418302- thus including more significant digits in the mantissa.

The index/mantissa form of floating-point arithmetic has the advantage that a wide that a wide range of numbers can be represented.  For the computer suggested above , which allocates two digits for the index , a number as large as 0.9999x10power99 can be dealt with – or a number so small that there are 98 zeros after the decimal point before any non zero digit is encountered.

However, the accuracy of this system remains limited to digits allocated in the mantissa. Consequently, some numbers can be only approximately represented. A great care and ingenuity must be put into the techniques of arithmetic programming to stop errors arising. This is the reason why (1/3)*3 will give 0.9999999 on some computers rather than the true answer of 1.