Some of them are even used within computers, for example when dealing with long integers not to mention non integer numerals. A first remark is that when people count in thousands, or millions as a unit, this is still considered decimal, because these are powers of So one might wonder why octal or hexadecimal should not be considered just a variation on binary.
One possible reason may be the number of symbols used to represent numbers though that is disputable issue, as we shall see with other systems. Then, regarding humans, they using several system in base 5, called quinary systems.
Actually, most of these system are with two bases, the second one being 2 or 4, alternating with the base five, which makes them equivalent to base 10 decimal or base 20 vigesimal.
Guess where that comes from :. These double-base systems are called bi-quinary or quadri-quinary systems. Pure quinary is rarely used. Roman numeral may be seen as bi-quinary system which is an indication on how to do arithmetics with them. Chinese and Japanese abacus use bi-quinary. Quadri-quinary was used by the Mayas. The reason for using a system are probably many. One good reason is that it was the first local design, and people are now used to it. For example, one might wonder as well why English speaking people are still using an extremely weird numeration system when trying to measure distances.
You could argue thet it is a matter of multiple units, not numbering, but that is a very weak remark. Numbers are used mainly to measure things. Other reasons for keeping a system is convenience in a given context.
There may be a trade-off between the number of different symbols, or positions on an abacus, and the number of symbol occurencess required to form sufficiently large numbers.
Base 2 works with 2 distinct symbols, but has lots of occurences, which may be inconvenient for a material representation. Vigesimal base 20 would require twenty symbols, and very big multiplication tables that people would not remember. But a bi-quinary or quadri-quinary system is a lot more manageable, especially to build abacus.
Pure quinary system would probably be even better, but it goes against physiology based habits and intuition. And it is always nice to be able to use our fingers to count with, when we do not know any better. One very old and very common system is the sexagesimal system used to measure time and angles but we know they are related, through Earth rotation. It uses base 60, but does not use 60 symbols as that is far too many.
So it relies on another system to represent its synbols such as the decimal system. The circle can be divided in 6 parts corresponding to 60 degrees angles, which are the simplest to build with equilateral triangles. Then Each degree is 60 minutes of arc, each divided in 60 seconds. It originated with the ancient Sumerians in the 3rd millennium BC, it was passed down to the ancient Babylonians, and it is still used —in a modified form —for measuring time, angles, and geographic coordinates.
Considering the origin it was a pretty convenient system, at a time when mathematics were hardly entering infancy. Physiologically, it can be related to a duodecimal-quinary system, base 12 and 5. Or do you Read more. Ana Hoffman - September 30, 0. Living and competing are intrinsically linked.
In nature and society, living objects interact daily to compete for capital, a better quality of life, and Most Popular. You have developed a new product, and you are eager to launch it to market. We understand your excitement. But, hold on! Do you Are you searching for the best careers? Are you in a dilemma on which career path you should choose? If you're a newbie in the cycling world, buying the ideal; bicycle can be overwhelming.
With innumerable and versatile choices, it's hard to pick Load more. Recent Comments. For each additional digit in base 8, we need up to three spaces to represent it in base 2. For hexadecimal base 16 , we need up to four digits in binary to represent each single digit. You may want to print out copies of these worksheets to help you with your conversions between binary and octal or hexadecimal:. Privacy Policy. Skip to main content. Module 3: Numeration System.
Search for:. Thus, the number two in binary would be represented as a 0 in the ones place and a 1 in the twos place, i. Three would be 11, a 1 in the ones place and a 1 in the twos place. No numeral greater than 1 is ever used in binary notation.
Because binary notation can be cumbersome, two more compact notations are often used, octal and hexadecimal. Octal notation represents data as base-8 numbers.
Each digit in an octal number represents three bits. Similarly, hexadecimal notation uses base numbers, representing four bits with each digit. Octal numbers use only the digits , while hexadecimal numbers use all ten base digits and the letters a-f representing the numbers The number 42 is written in octal as:.
0コメント