Senary

As senär (Latin: senarius, " each containing six " ) are objects or structures composed of six parts and composed of these elements, or can be broken down into it. Are used language unary (1), binary (2), ternary (3), quaternary (4), quinary (5), Senär (6) and Denär (10).

Senäres number system

As Senärsystem is called a numbering system that is based on the basis of 6 (see also place value system ). As a name synonymous in use, the concept Hexal system (from Greek: Hexa = "Six "). However, it must be given to the likelihood of confusion with the very common and for the computer science fundamentally important hexadecimal system that uses the base 16. This figures are often shown abbreviated as hex numbers (see also: hex editor ). In contrast to the usual decimal and hexadecimal key that uses the base 10, and historical results from the ten fingers of the human, on the other hand is the number used in Senärsystem as base 6.

Also, the sixfold speed system can be attributed to the use of the human hand. With a single source, beginning with the number zero, corresponding to the number of outstretched fingers, easily and clearly the number one, and so on are shown Two through Five. Taking the second hand adds to represent an analogous manner, the number of " half a dozen ", so can be used in representation senärer all numbers between "00" and 6 "55" 6 ( of 6 index points to the sixfold spelling out ) Show with the two hands. This corresponds in decimal representation of numbers from 0 to 35, because 5.6 5 = 35.

In contrast to the usual method of counting with the ten fingers of the two hands, which can represent only the numbers from zero to ten, you'll reach a much larger number of stocks. For example, if three fingers of one hand outstretched and four of the others, then this may in senärer representation of the number " 34 " 6 represent. This corresponds to 3.6 4 = 22 in decimal representation.

To avoid confusion in the order of Senärziffern, of course, it must be clear which hand and which is the units digit of the six- point. Usually one uses the left from the perspective of the other person 's hand, so the own right hand to represent the six- point. This is the view of the deflector ends then analogous to the written representation in which the more significant digit is also always on the left.

The Senärsystem further includes an interesting feature in relation to the theory of numbers. If, namely, the primes senär is so, all prime numbers (except for 2 and 3) the number " 1" is 6 or "5" to 6 as a final number.

The first primes in senärer representation are as follows (the index 6 again has the sixfold spelling out ):

Sophie Germain primes greater than 3 to " 5" border 6 only because more is divisible by 3.

This is because only 1 and 5 are relatively prime to the base 6 of the possible digits (in any number system are exactly the prime numbers to base the final digits of prime numbers, except for the divisor of the base itself).

The general rules for determination of divisibility in value systems manifest themselves here as: A divisibility by 2, 3, and 6 can be identified by the last digit. A divisibility by 4 ( as well as 9, 12, 18, 36) is given if the last two digits are composed by 4 ( 9, 12, 18, 36 ) divisible. By 5, the number is divisible if the sum of the digits is divisible by 5. A divisibility by 7 can be determined with the alternating sum of the digits.

Senärsystem in Languages

In some languages, it can be seen that number of words - were formed by the Hexal system, suggesting suggesting that (also) was counted using the method described above in the respective cultures may initially - at least partially. Worth mentioning here is the Central American tribe of the Miskito, read the number words as follows, and " usual" next to the bases 5 and 10 are based on a system that is based on the repeated use of the base 6:

Password generation with Senärzahlen

Using ( six-sided ) dice and a special word list can be generated by a designated Diceware method passwords, offer in comparison to the usual self-created ( such as " EVA11 " ) a significantly higher level of security against unauthorized guessing. To generate the passwords sixfold random numbers are used in the Diceware method.

Sixfold encryption

In cryptography, encryption is based on an alphabet of exactly six characters, referred to as sixfold encryption. A famous example is used by the German military in World War I on the Western Front ADFGVX procedure that an alphabet of only the six letters " A", " D", " F ", "G ", "V " and "X "used.