{"id":330,"date":"2007-12-10T00:00:00","date_gmt":"2007-12-10T00:00:00","guid":{"rendered":"https:\/\/test.simple-talk.com\/uncategorized\/numeral-systems-and-numbers-conversion-in-sql\/"},"modified":"2021-09-29T16:22:14","modified_gmt":"2021-09-29T16:22:14","slug":"numeral-systems-and-numbers-conversion-in-sql","status":"publish","type":"post","link":"https:\/\/www.red-gate.com\/simple-talk\/databases\/sql-server\/t-sql-programming-sql-server\/numeral-systems-and-numbers-conversion-in-sql\/","title":{"rendered":"Numeral Systems and Numbers Conversion in SQL"},"content":{"rendered":"
\n

My fascination with\u00a0numbers started\u00a0when I was about two years old.<\/p>\n

One of my parents used to bend my fingers, saying “One, Two, Three…” and all our guests smiled, when I\u00a0 tried to repeat “Four, Five, Six…”<\/p>\n

At that time, I believed that people need the numbers in order to count their fingers and to make their parents and relatives laugh.<\/p>\n

When I grew up, I discovered that numbers could be helpful in a few more situations, for example to identify time and count money. However, I did not pay much attention to the fact that the counting rules for time and money are different.<\/p>\n

In one day, among the old documents, stored in our family, I found my grandfather’s watch. The watch had a beautiful watch face with strange symbols on it, instead of numbers. My mother told me that these symbols are the Roman numbers.<\/p>\n

That fact, however, did not make me curious about the Roman numbers. In my mind, they were associated with the old, broken watch – both, the numbers and the watch were not in use.<\/p>\n

I got my first hints of other numeral system\u00a0at university.<\/p>\n

The computers were built of transistors – small electronic devices with two physical states: opened and closed. These states, being coded as 0 and 1, perfectly fitted into binary numeral system. Based on that system and supported by the powerful mathematical apparatus, the computers changed human life.<\/p>\n

If you carefully look around, you will find many signs of different numeral systems. Some of them are not relevant anymore; the other ones we still use and develop. Time, and angles, for example, are still\u00a0based on sexagesimal systems.<\/p>\n

This article is about the numeral systems. It will also demonstrate interesting SQL techniques that can be used, when you need to convert the numbers from one numeral system to another.<\/p>\n

A Brief History of Numeral Systems<\/h3>\n

The numbers and numeral systems are very old. The simple counting systems appeared when people started to develop speech, but even before, the first primitive people had notion of counting and could enumerate similar objects, using their fingers, pabbles, knotted roups or notches on sticks or bones.<\/p>\n

When alphabets and written languages appeared, the simple counting systems transformed into quite complicated ways of writing numbers.<\/p>\n

About 3000 – 3500 B.C,. number systems have developed spontaneously in different isolated cultures and so almost each civilization created its own language and numeral system.<\/p>\n

There is no an official classification of the numeral systems. However, many researchers (especially a French mathematician Genevi\u00e8ve Guitel in her “Compared History of written numerations”, 1975) agree that written numeral systems should be divided into two main groups – additive and positional.<\/p>\n

Georges Ifrah in his important work “The Universal History of Numbers: From Prehistory to the Invention of the Computer” gives more detailed classification of the numeral systems:<\/p>\n