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The  hexadecimal  metric  system

abbreviated internationally SMH for the french term systme mtrique hexadcimal

 
Introduction
1  The seven base units of SMH and their respective names of unit
1.1  Time, with the base unit: hexa-i-timple
1.2  Thermodynamic temperature, base unit: hexa-i-Kelvin
1.3  Length, base unit: hexa-i-metre
1.3.0  The digital foot ruler comprises onety digits
1.3.1  The main system of even magnitudes
1.3.2  The subsystem of odd magnitudes
1.3.3  The digital foot already exists as Viennese foot
1.4  Mass, base unit: hexa-a-gram
1.4.1  The main system of even magnitudes
1.4.2  The subsystem of odd magnitudes
1.4.3  The weights of an analogical balance, called stones
1.4.3.1  The eight additional stones
1.4.3.2  The named stones in several languages
1.5  Amount of substance, base unit: hexa-i-mole
1.6  Electric current, base unit: hexa-i-Ampre
1.7  Luminous intensity, base unit: hexa-i-candela
 
2  Some deduced units
2.1  The SMH velocity unit: hexa-i-Einstein
2.2  The SMH area unit: square hexa-i-metre
2.3  The SMH volume unit: hexa-a-litre
2.3.1  The main volumes
2.3.2  The "picot" serie
2.4  The SMH frequency unit: hexa-i-Hertz
2.4.1  Frequency of typical visible light
2.4.2  Frequency of the musical note Sol
2.5  The SMH information units:
2.5.1  The number of bits: names for the bit-length
2.5.2  The information quantity:
2.5.2.1  hexa-i-Byte (depreciated)
2.5.2.2  hexa-i-fit  (commendable)
2.5.3  The symbol rate: hexa-i-Baud
2.6  The SMH units of force, pressure, energy and power
 
3  Some mathematical units
3.1  The hexadecimal percentage
3.2  The hexadecimal angle units
3.2.1  The hexadecimal arc degree
3.2.2  The hexadecimal radian
 
4  Additional explications
4.1  Digits and letters
4.1.1  The omni-literal hexadecimal digits
4.1.2  A hexadecimal multiplication table with omni-literal digits
4.1.3  The rank inside magnitudes
4.1.4  The hexadecimal alphabet, in its lexicographical order
4.2  The hexadecimal number names
4.3  The hexadecimal point, the millions separator, etc.
4.4  User royalties?
 
5  Also see

New civil, historical and astronomical chronology and the Civil Calendar

 
6  References
 
7  External links

 

Introduction

The hexadecimal metric system   abbreviated internationally SMH for: "systme mtrique hexadcimal"   was developed in spring 1989 by Michael Florencetime.
This system uses the so-called "omni-literal" hexadecimal numerical system [1], also defined by  M. Florencetime, Paris.  It avoids the ambiguous IBM extension A to F.

A deliberated polemical foreword:

History

For the beginning of the year 1991, during about two years, this new proposal for a modern hexadecimal system
of weights and measures has been diffused in Paris in about eight thousand auto-edited compendium exemplars.

All the great French newspapers, as many French revues just like the French press-agency afp also received such resume exemplars. Never any French print media related it.

The therefor cause is all too obvious:

In France since more than 200 years the decimal metric system is a kind of "state religion".

Because the decimal metric system with the presuming and vain devise: "For all people, for all time." is said to have been inspired by the celebrated and adored "Goddess Reason" of the French Revolution times herself, therefore, in France, none other serious proposal can exist.

Is it necessary to remember that the first law establishing the decimal metre was adopted by the National Convention in 1793 August 1 by the regime called  Reign of Terror ?

The decimal metric system must be the final hindmost law established by this regime Reign of Terror now still applied.    Naturally, it is great time to abolish it forevermore !

Present

If however a new, better, proposed system well exists   that's the case   in France, the self-called "country of the Human Rights", it must
be denied and must be censored by any provided possibilities. That's "Raison d'tat". None French publication would ever dare to breach it.

So currently, this dissident proposal   in France   is effectively censored.

As proof :  Since december 2003 a good referred, good frequented site in French language is constantly online.
Many Parisian and French citizens already know these consistent proposals or at least heard speaking about.

But the censorship of the whole French print media still occults this limpid, explicit and perspicacious scientific work.
Since 1991. Fifteen years.  Be it !   But not much longer.

In the world entire there must be at least one free media    excepting Wikipedia talk pages    not rendering homage
to the French bourgeois blacklisting oppression, denying this now existent contribution to science and technology.

Then " alors "  the hexadecimal metric system will not disappear de la round table
before the  S M H  is not recognised as the predominant standard measuring system.

We come back, also in sciences, to our at least five millennia old foot-based measures.
The barbarism of that decimal metre was only a bicentenarian parenthesis in metrology.

Colleagues

The revered colleague Nicolaus, as like as his pleader Gee-Gee of Pisa, died in Arcetri, now a borough of Florence, send greetings.
Or, still how many years, the lie  that Cape Dezhnev in Bering Strait belongs to the western hemisphere should be continued to be told at school ?
Our friend Albert [2]  smiles benignly, finally he repeats : " If at first the idea is not absurd, then there is no hope for it."

Devise

The own motto of the hexadecimal metric system is Two thumbs, eight other fingers. Twice eight equals onety.

Conclusion

The decisive advantage of a decimal metric system is, its capacity to express all the units in a positional arithmetic system.
Highly composite number orientated ancient systems of weights and measures don't possess this quality, nor can ever hold.
The decimal metric won exclusively for this reason. However till nowadays, it never made unanimity, for more than 200 years.    Memento Pyrrhus and his victory.

Many people still nowadays reject it. That is, because it is not foot-based like all the other systems in human civilisation for more than five millennia.
Therefore, measurement of lengths, based on the length of a human foot, must be considered as an intrinsic and essential cultural asset of humanity !

Thus, in reverse, the decimal metric system must be qualified to be a completed and consummated barbarism. The expression of a lack of culture.
The blood-thirsty political context of its introduction in France, 1793 validates convincingly this appreciation. Therefore, 200 years after, its hegemony is still uncompleted.

Howsoever, the present hexadecimal International System of Units   of course, an absolute positional system  is the gravedigger of this outdated, inferior decimal SI.
The Anglo-Saxons with their foot practised successfully lexception culturelle ;  the other way round.    Just long enough for advent of the hexadecimal metric system.

Sure, now also the English foot will perish, since it is one of 49 parts too long.  The now defined universal foot, shared into 16 digits, is objectively superior.  It will win .

PS.  It seems, that France, the other day, was the seventh country the most prosper all around the world.          Nowadays, it is the seventeenth only one...

       For this, the just cause could be the fact, that France continues to oppress the SMH for sixteen years !

 

The seven base units of SMH and their respective names of unit

 

Time, with the base unit: "hexa-i-timple"

Definition (since 1989) :

One hexa-i-timple equals exactly  675 s / 1024 ,  i.e.  0. 659 179 687 5  second. 

The current hexadecimal time format is :  BQ.QQ'q H   =  12 H 00 minute 00 s  (noon).

Thus the full circle has twice sixteen hexadecimal degrees (cf. main meridians): PQQQ'q = 360 00' 00".

  Popular
Name of unit
 Multiple
 (Magn. Rank)
Scientific
Symbol
 Equivalence
 (in sexagesimal second)
  one octave
1024+2 16 0
B Mit
= 0. 691 200 Ms
  one turn
10240 16 4
B hut
= 43 200. 000 000 s
  one hour
10240 16 3
B hot
= 2 700. 000 000 s
  one maxim
10240 16 2
B hat
= 168. 750 000 s
  one minute
10240 16 1
B het
= 10. 546 875 s
  one second
10240 16 0
B hit
≤ 0. 659 180 s
  one third
1024 -2 16 4
B ut
≤ 41 198. 730 489 s

The octave unit  is not  implemented in civil calendar , where the seven-day week is
maintained as the closest integer value of a mean lunar phase, since 29.53 / 4  ≥ 7.
The octave unit as A.O.C. (Astronomical Octave Coordinated) has replaced this not
consistent Julian Day. For this new astronomical numeration TQQQQ.qqqqq A.O.C.
is arbitrarily defined at A.D. 2048, January 1st at 00 H 00 min. 00 s UTC of Florence.*

Note, that it will be due that our expectancy of life in the developed countries will
attain or even exceed thousand octaves : 
BQQQ Mega-i-timples  ≥  89.7 years.

The cinematographic cadence of images is traditionally  24 images / s. This means
one image every 41.6 ms, but every 40 ms in certain countries. So, an image every
hexadecimal third 41 407/2048 ms should be the good cinematographic cadence.

Our Earth day is accorded to the musical note Sol :  224 / 43200 = 388.361 481 Hz.
This means that the current standard pitch of 440 Hz is in excess of about 0.936 %.
The modern La is defined (224 / 43200) 21/ 6 ≥ 435.921 Hz, since the modern Sol
of the G clef is defined one hundred hexadecimal Hertz exactly one : BQQ.qqq hiHz.

* This means: DWTQQ.qqqqq A.O.C. was on 2003, February 21, at 23 H 15 UTC.G.

 

Thermodynamic temperature, base unit: "hexa-i-Kelvin"

Definition (since 1991) :

One hexa-i-Kelvin equals exactly  273.16 K / 256 ,  i.e.  1. 067 0312 5  Kelvin.

However, in everyday life the hexadecimal scale named degree Kelvin - Celsius will be used.

Symbol :   KC, (said :   kay-cee).  BQQ hiK corresponds to Q.q KCexactly  273.16 Kelvin.

So:  + BQ.q KC  corresponds to + 17. 0725 Celsius*,  respectively + 62. 7305 Fahrenheit.
Thus, water boils   depending highly on the atmosphere pressure   at less than  + SQ KC.

* actually about + 17. 0625 C, since the traditional freezing point and the modern triple point

differ by about 0.01 Kelvin. Besides : 16/15 256 = 273.066. So the mnemonic approximation :

 W Kelvin - Celsius  equal  16 Celsius  is excellent  (with an error less than 0.035 %).

 

Other remark :

 From    Q KC  to  BQ KC (about   0 C to 17 C), the ambient air temperature is rather fresh.

 From BQ KC  to  PQ KC (about 17 C to 3 4 C), the temperature is rather warm or even hot.

Above PQ Kelvin-Celsius  that is about 3 4.135 Celsius  we are really in our canicular days.

However onety-eight degrees Kay-Cee:  B T KC (about  25.6 C  or  78.1 F) are very agreeable.

 

Length, base unit: "hexa-i-metre"

Definition (conceived in 1989, defined exactly one in 1990) :

One hexa-i-metre equals exactly  19. 109 257 m / 16 ,  i.e.  1. 194 328 562 5  metre.

 
The chain value of 19. 109 257 m exactly one, was obtained by this adequate definition:

      Math.round ( r0 * Math.PI * Math.pow (10,6) / Math.pow (16,5) )      

The radius r0 is the major radius of our planet Earth (cf. World Geodetic System 1984),
scilicet the length of  6, 378 137 metres.

 

The digital foot ruler comprises onety hexadecimal digits.

The measure foot     in ancient times     was already shared into sixteen digits

by great ancient civilisations like :  Sumerians, Egyptians, Greeks and Romans.

Only during European Middle-Ages, the foot is divided into twelve parts, cf. inches.

The hexadecimal digital foot ruler equals onety digits, respectively one hundred strokes :  B milli - a - metre  =   BQ milli - e - metre  =  BQQ milli - i - metre.

In other words :

By definition, the hexadecimal digit is the half of the circumference of planet Earth  i.e. about 20 037.5 km   divided three times by 1024.

The hexadecimal digit equals  19, 109 257 m    1024-1  exactly one. This is a little more than 18.66 mm or just 72 / 98 English inch.

 

The main system of even magnitudes

( Cf. :  System of units, Magnitudes and Ranks )

This principal main system covers the even magnitudes and includes the magnitude zero.
In analogy to the established decimal prefixes, the binary pico, micro, mega and tera, etc.
are respectively 1024 power -4, 1024 power -2, 1024 power 2 and 1024 power 4 etc.

However, the magnitude zero, in contrast to the decimal SI, features its own prefix: hexa.
Therefore the decimal names of unit can be reused without any risk of misunderstandings.
Example :  One decimal metre equals almost  Q. ysztc kpzfp pzdbz b  hexa-i-metre.

For the meaning of the concept of the ranks inside each hexadecimal magnitude, see the
detailed explications below [3]Hexadecimal magnitudes are integer powers of 1024.

 

 The hexadecimal metre is scientifically called hexa-i-metre.
 Its popular name is the aune which designates a four-feet-ell.

 Between the megane (one mega-i-metre) and the micron (one micro-i-metre),
there are nine other measures of length belonging to this principal system:
Athlon, league, stadium, chain, aune, palm, line, point and link.

The chain is defined 19, 109 257 micrometres exactly one since 1990.

  Popular
Name of unit
 Multiple
 (Magn. Rank)
Scientific
Symbol
 Equivalence
 (in decimal metre)
  (onety meganes)
1024 2 16 1
B Mem
≥ 20. 037 508 Mm
  one megane
1024 2 16 0
B Mim
≥ 1. 252 344 Mm
  one athlon
1024 0 16 4
B hum
= 78 271. 516 672 m
  one league
1024 0 16 3
B hom
= 4 891. 969 792 m
  one stadium
1024 0 16 2
B ham
= 305. 748 112 m
  one chain
1024 0 16 1
B hem
= 19. 109 257 m
  one aune
1024 0 16 0
B him
≤ 1. 194 329 m
  one palm
1024 -2 16 4
B um
≥ 74 645. 535 156 m
  one line
1024 -2 16 3
B om
≥ 4 665. 345 947 m
  one point
1024 -2 16 2
B am
≤ 291. 584 122 m
  one link
1024 -2 16 1
B em
≤ 18. 224 008 m
  one micron
1024 -2 16 0
B im
≥ 1. 139 000 m
 (1/16 micron)
1024 -4 16 4
B pum
≤ 71 187. 529 713 pm

So  by definition   the circumference of the Earth measured at the equator

is two thousand (=  8192) hexadecimal leagues exactly one, i.e. PQQQ hom.

Thus :  One thousand hexadecimal leagues are the antipodal distance.

Even if the 64-digital-feet-chain is the defined unit, however the aune is the base unit.

 

The subsystem of odd magnitudes

Next to the system of even magnitudes, a secondary deduced system of odd magnitudes
exists. The relative importance of this easy understanding subsystem depends on the
real use with the concerned units of measure. With the units of length, the system of odd
magnitudes is not less important than the main system of the even magnitudes.

 

The hexadecimal or digital foot is the quarter of one hexa-i-metre.
Seven named measures of length belong to this important subsystem:
 Mile, arpent length, perch, digital foot, digit, stroke and foil.
There are 1024 hexadecimal points (micro-a-metres) in a digital foot.
There are also 1024 digital feet (milli-a-metres) in the modern stadium.
  Popular
Name of unit
 Multiple
 (Magn. Rank)
Scientific
Symbol
 Equivalence
 (in decimal metre)
  one mile
1024 1 16 0
B kim
≥ 1. 222 992 km
  one arpent
1024-1 16 4
B mum
= 76 437. 028 000 mm
  one perch
1024-1 16 3
B mom
= 4 777. 314 250 mm
  one foot
1024-1 16 2
B mam
≤ 298. 582 141 mm
  one digit
1024-1 16 1
B mem

≤

18. 661 384 mm
  one stroke
1024-1 16 0
B mim
≥ 1. 166 336 mm
  one foil
1024-3 16 4
B num
≥ 72 896. 030 426 nm

An other informal unit of length, the so-called "sester" merits to be mentioned:
In Roman times the sixth of the volume unit congius, it is now a unit of length,
the sixth of the hexadecimal metre. C.c milli-e-metres (digits) equal 2/3 foot.
This natural span is very practical for rough measures without metering rule.

Six English feet equal six hexadecimal feet plus two digits.

The new digital foot and the anglo-saxon foot maintain the exact ratio  49 to 48.

However, the current definition of the anglo-saxon compromise foot, 1959  is contested.

 
 English  foot :   1764 0.1728    fc  =  304. 8192    fc     ≤     304. 8 02 601 888  mm  
 Digital  foot :   1728 0.1728    fc  =  298. 5984    fc        298. 5 82 140 625  mm  

The correction factor fc is :  Ten digital chains divided by 640 idealistic digital feet :   

  (10   19,109 257)   /   (10  64   298 598.4)      ≤     0.999 945 548    

Thus, the English foot   in its new scientific definition  is about 0. 000 854 % larger

  than the inconsistent anglo-saxon compromise foot of 1959, with its exact 304. 8 mm. 

In conclusion:

The English yard  is  4910 ( = VBH )  universal digits  =  0. 914 4 07 805 664 0625 m.

 The English mile is now  1. 373 796 875 cm longer, since it is exactly  B.zqx kim.

Nevertheless:

The idealistic

  Roman foot  

equals 

35    

840  

  10080  

  =  

 296, 352 000  nm.

The idealistic

  English foot  

equals 

36    

840  

  10080  

  =  

 304, 819 200  nm.

The  idealistic

  digital foot  

equals 

 100    

1728  

  1728  

  =  

 298, 598 400  nm.

 

The digital foot already exists :  This is the Viennese foot !

When in 1990  M. Florencetime defined the digital foot, he ignored the Viennese foot.

However, the cathedral of Vienna possesses two related, public standards of length :

The linen ell  896 mm  and the drapery ell 776 mm, like it measured Franz Twaroch,

an Austrian engineer who demonstrated how the drapery ell is related to the linen ell.

This linen ell is obviously deduced from the raw Nippur cubit, via Greek measures.

The ratio of the Nippur cubit to the linen ell is 1000 : 1728,

since 518. 4 millimetres    1. 728  =  895. 7952 millimetres.

Franz Twaroch clearly proofed: this Viennese linen ell is a three-feet-measure, a yard.

So, the Viennese foot equals  895. 7952 mm  3  =   298. 5984 mm,  the idealistic foot.

 The concurrence of the new digital and the Viennese foot must be a coincidence.

Self-evidence :

All hypothetical speculations of a former deduction of the Viennese foot it-self

by the circumference of the Earth are unfounded, would be pseudo-scientific.

For more details, please see this special page.

 

Mass, base unit: "hexa-a-gram"

Attention, an exception:  The base unit is well the hexa-a-gram, not the hexa-i-gram.

Definition (since 1990) :

One hexa-a-gram equals  10 3 19. 109 257 3 16 -6  ≥  0. 415 921 631 423 095  kg.

 

The main system of even magnitudes

The hexadecimal ton, the pound and the ace are respectively the masses
of pure water in the digital aune cube, the palm cube and the line cube.
  Popular
Name of unit
 Multiple
 (Magn. Rank)
Scientific
Symbol
 Equivalence
 (in decimal gram)
  one ton
10242 16 0
B Mig
≥ 1. 703 615 Mg
  one quintal *
10240 16 4
B hug
≥ 106 475. 937 644 g
  one stone
10240 16 3
B hog
≤ 6 654. 746 103 g
  one pound
10240 16 2
B hag
≥ 415. 921 631 g
  one florin
10240 16 1
B heg
≤ 25. 995 102 g
  one drachm
10240 16 0
B hig
≤ 1. 624 694 g
  one ace
1024-2 16 4
B ug
≤ 101 543. 367 047 g

The word ounce, cf. latin uncia, etymologically means: "shared into twelve parts".
Thus a hypothetical hexadecimal "ounce" doesn't exist. This mass is the florin.

 * Or that is the same one hundredweight

 

The subsystem of odd magnitudes

These units are used for the evaluation of human body's weight.
One arbitrary, discretionary example like another one:
If any President of the French Republic incidentally weights 79.857 kg,
so he weights three talents or thirty mines or just three hundred francs.
  Popular
Name of unit
 Multiple
 (Magn. Rank)
Scientific
Symbol
 Equivalence
 (in decimal gram)
  one charge
1024 1 16 2
B kag
≤ 425. 903 751 kg
  one talent
1024 1 16 1
B keg
≥ 26. 618 984 kg
  one mine
1024 1 16 0
B kig
≤ 1. 663 687 kg
  one franc
1024-1 16 4
B mug
≤ 103 980. 407 856 mg
  one shekel
1024-1 16 3
B mog
≤ 6 498. 775 491 mg
  one obol
1024-1 16 2
B mag
≥ 406. 173 468 mg

Exactly-like in ancient times :  One talent is the mass of water in a foot cube.

If the mine is much appreciated since ancient times, the shekel is devalued a little.

In the sexagesimal Babylonian system of weights the mine is 1/ 60, like the shekel

 (sicilicus)  is 1/ 3600 of the talent.  Now, the ratios are 1 : 16 and 1 : 4096 respectively.

One mark has ever been half-a-pound. The franc is now half-a-mark or two escudos.

 

The weights of an analogical balance are called stones

The eight additional stones

An analogical balance needs a completed set of weights ; called : stones of the balance .
Some ponderous stones are simply named, for example, half-a-talent or the double-mine.
From the pistole to the hexadecimal grain, the necessary weights have their own names:

one pistole
P hag ≤ 832 g
one escudo
P heg ≤ 52 g
one dinar
P hig ≤ 3.2 g
one carat
P ug ≥ 0.2 g
t hag ≤ 208 g
one mark
t heg ≤ 13 g
one peso
t hig ≥ 0.8 g
one penny
t ug ≥ 50.8 mg
one grain

 

The named stones in several languages :
one talent
un talent
ein Talent
one mine
une mine
eine Mine
one franc
un franc
ein Franken
one shekel
un sicle
ein Schekel
one obol
une obole
ein Obolus
≥  26.6 kg ≤  1664 g ≤  104 g ≤  6.5 g ≥  0.4 g
 

 
one pistole
une pistole
eine Pistole
one escudo
un cu
ein Escudo
one dinar
un denier
ein Dinar
one carat
un carat
ein Karat
≥  13.3 kg ≤  832 g ≤  52 g ≤  3.25 g ≥  0.2 g
one stone
une pierre
ein Stein
one pound
une livre
ein Pfund
one florin
un florin
ein Gulden
one drachm
une drachme
eine Drachme
one ace
un as
ein As
≥ 6.65 kg ≤ 416 g ≤ 26 g ≤ 1.625 g ≥ 0.1 g
 

 
one mark
un marc
eine Mark
one peso
un peson
ein Peso
one penny
un fennigue
ein Pfennig
one grain
un grain
ein Grain
≤  3.33 kg ≤  208 g ≤  13 g ≥  0.8 g ≥  0.05 g

 So, one of the weights, the mass of 104 g, in German language, is the Frankenstein  ;-)

Remark: Binary analogical balances need two exemplars of the lightest weight.

Example: A balance with a capacity weight of one mine may have these twelve stones:
Pistole, pound, mark; fourfold, double, single and half of both the florin and the drachm.
 However, the pennyweight stone of 812.347 mg is present twice to reach the mine.

To say, that the florin has a mass of two mean walnuts is a very good approximation.

On an average a European walnut weights about 13 grams*. 32 walnuts in a pound.

* Depending of course by its big- and dryness, but clearly confirmed by our multiples samples in 2006. 

 

Amount of substance, base unit: "hexa-i-mole"

Definition (since 2005, january 20) :

One hexa-i-mole equals  10 6 19. 109 257 3 16 -8  ≤  1. 624 693 872 746 5  mol.

Like the decimal mole refers to the decimal gram,
the hexadecimal mole refers to the hexa-i-gram, the drachm.
So, for values of the multiples and submultiples, please see above.

Further explications later.  Also see:  the decimal base unit: Mole.

 

Electric current, base unit: "hexa-i-Ampre"

Definition (since 2005, january 20) :

One hexa-i-Ampre equals  10 10 19. 109 257 4 16 -8 675 -2  ≤  0. 681 408 895  A.

Further explications later.  Also see:  the decimal base unit: Ampre.

 

Luminous intensity, base unit: "hexa-i-candela"

Definition (since 2005, january 20) :

One hexa-i-candela equals  683 10 3 19. 109 257 5 16 -3 675 -3  ≤  1. 382  cd.

Further explications later.  Also see:  the decimal base unit: Candela.


 

 

Some deduced units

From these seven base units all the other hexadecimal units can be deduced without any problem.

Regularly the new main unit is the hexa-i-unit. This even in the cases when the hexa-a-gram enters in the formula.
The only exception is the volume unit.
The hexa-a-litre is the hexadecimal pint. One cubic palm of pure water has the mass of one hexa-a-gram, one pound.

All the other unit names of the decimal SI like Volt, Watt, and Newton etc. are all overtaken.

Only one new unit name is added:  the speed unit, the hexa-i-Einstein.

 

The SMH velocity unit: "hexa-i-Einstein"

 
The global speed unit is named to honour Albert Einstein.

One hexa-i-Einstein equals one him per hit ;  the unit symbol :  hiEn.

 
  Colloquial term hexa-i-Einstein   m/s   km/h   Mi/h
  one equatorial speed
BQQ hiEn  
= 463. 831 +
= 1669. 792 +
= 1037. 561 -
  one cheetah speed
BQ hiEn  
= 28. 989 +
= 104. 362 +
= 64. 848 -
  one standard speed
B hiEn  
= 1. 812 -
= 6. 523 -
= 4. 053 -
  one turtle speed
.b hiEn  
= 0. 113 +
= 0. 408 -
= 0. 253 +
  one sloth speed
.qb hiEn  
= 0. 007 +
= 0. 025 +
= 0. 016 -

The speed of light in vacuum is about *  JY, KKVTX. v hexa-i-Einstein.  How read this number ? [4]

Thus speed of light is less than ten million cheetah-speeds. One cheetah-speed equals BQ hiEn.

Man in sprint drives a " third-cheetah ". Sprinters run quicker than Z.zzz hi En, i.e. about 9.663 m/s.

Earth at the equator turns by one hundred hexa-i-Einstein, i.e. one megane per hexadecimal hour.

 Note:  The superscript signs plus and minus after the values mean "a little more than" or "a little less than".
  * Speed of light in vacuum equals exactly  

 299, 792 458  

  x  

 675 

  hexa-i-Einstein. 

19. 109 257  

64

 

 

The SMH area unit: "square hexa-i-metre"

The square hexa-i-metre is the principal area unit.

One hundred hooves is a square league, nearly 24 km.

  Unit  Common term Square hexa-i-metre  Equivalence
 decimal
  B kimP  
one square mile
B QQQQQ himP  
= 1. 495 711 - km
  B hamP  
one hoof
BQQQQ himP  
= 93 482 -  m2
  B mumP  
one hexadecimal acre
BQQQ himP  
= 5 843 -  m2
  B hemP  
one clima
BQQ himP  
= 365 +  m2
  B momP  
one square perch
BQ himP  
= 23 -  m2
  B himP  
one square aune
B himP  
= 1. 426 421 -  m2
  B mamP  
one square foot
Q.b himP  
= 89 151 + mm2
  B umP  
one square palm
Q.qb himP  
= 5 572 - mm2
  B memP  
one square digit
Q.qqb himP  
= 348 + mm2
  B omP  
one square line
Q.qqqb himP  
= 22 - mm2
  B mimP  
one square stroke
Q.qqqqb himP  
= 1. 360 341 - mm2

 Note:  The superscript signs plus and minus after the values mean "a little more than" or "a little less than".

The area of Mongolia is nearly one square megane :  1, 564 116 km  ≤  Q.wwz MimP

Half-a-hexadecimal-acre is a yoke. Half-a-yoke is a hexadecimal rood, also called verge.
The quarter of one clima is the hexadecimal are. This is about 91.3% of one decimal are.
One square rod, one square pole and one square perch, the preferred term, are synonyms.

 

The SMH volume unit: "hexa-a-litre"

In the hexadecimal metric system (SMH), the main unit for the volumes is the hexa-a-litre, the pint :
The hexa-a-litre, with the symbol : hal, is the volume of one micro-a-metre cube. This is the palm cube.
The largest named volume unit is the hexadecimal tun, i. e. one hexa-i-meter cube or one mega-i-litre.
The micro-u-litre   the minim, the micro-o-metre cube, the line cube  is an onety millionth of the tun.

 

The main volumes

The hexadecimal tun is the volume of the cubic aune.

The amphora is one foot cube.      The pint is one palm cube.

The "shrek" is one digit cube.      The minim is one line cube.

4096

BQQQ hal

one tun

≥  17 hL

2048

TQQ hal

≤   852 L

1024

FQQ hal

one pipe

≤  426 L

512

PQQ hal

≤   213 L 

256

BQQ hal

one barrel

≤  106.5 L

128

TQ hal

one hemina

≥  53.2 L

64

FQ hal

one amphora

≥  26.6 L

32

PQ hal

one urna

≥  13.3 L

16

BQ hal

one velte

≥  6.65 L

8

T hal

one gallon

≤  3.33 L

4

F hal

one quart

≤  1664 mL

2

P hal

one pot

≤  832 mL

1

B hal

one pint

≤  416 mL

1 / 2

t hal

one chopin

≤  208 mL 

1 / 4

f hal

one gill

≤  104 mL

1 / 8

p hal

≤  52 mL

1 / 16

b hal

one roquille

≤  26 mL

1 / 32

qt hal

≤  13 mL

1 / 64

qf hal

one shrek

≤  6.5 mL

1 / 128

qp hal

≤  3.25 mL

1 / 256

qb hal

one muid

≤  1.625 mL

1 / 512

qqt hal

≥  0.8 mL

1 / 1024

qqf hal

≥  0.4 mL

1 / 2048

qqp hal

≥  0.2 mL 

1 / 4096

qqb hal

one minim

≥  0.1 mL

The hexa-i-litre is called muid, a French term deriving etymologically from the latin

modius, "the measure". However, the main volume measure is well the hexa-a-litre.

1 US wet pint
=
473. 176 473 000 0   mL
 ≥
B. pvvyt cqtzq f   hal
1    half-a-litre  
=
500. 000 000 000 0   mL
≤
B. vvkqb pjfwc q   hal
1 US dry pint
=
550. 610 471 357 5   mL
≤
B. zpxsc ggbxx v   hal
1 UK Imp. pint
=
568. 261 250 000 0   mL
≤
B. zykvy wqpgt y   hal

 

The "picot" serie

 Picot   Shrek   hex.   dec.
16 = 576 =
K. hal
≤ 5 L
 8 = 384 =
S. hal
≤ 2.5 L
 4 = 192 =
V. hal
≤ 1.25 L
 2 =  96 =
B. hal
≤ 624 mL
 1 =  48 =
Q. k  hal
≤ 312 mL
 1 / 2 =  24 =
Q. hal
≤ 156 mL
 1 / 4 =  12 =
Q. hal
≤ 78 mL
 1 / 8 =  6 =
Q. bt hal
≤ 39 mL
  1 / 16 =  3 =
Q. qk hal
≤ 19 mL

The picot is an auxiliary unit between the pint and the chopin.
Necessarily, it must be noted as twelve roquilles :  Q.k hal.
Beverages, for example, may also be sold in the "picot serie".

Sixteen picots equal twelve pints, i.e. about 4.991 litres.

1 / 64 picot:  One standard  teaspoon contains three muids:   V hil   4 78 mL.
3 / 64 picot:  One standard  tablespoon contains nine muids:   J hil   14 58 mL.

Evidently :  As long as oil is sold in capitalistic barrel petroleum (158.987 L),  it will be squandered !

The universal barrel petroleum (159.714 L equal six amphoras ) contains 726.6 (precious !) mL more .

 

The SMH frequency unit: "hexa-i-Hertz"

One hexa-i-Hertz equals one hexa-i-timple - B,  i.e. exactly 1024 / 675 Hz.

One billion referring of course to long scale hexa-i-Hertz is one tera-i-Hertz.  

  Hexadecimal Hertz   Equivalence
  decimal
B QQQQQ QQQQQ hiHz   = B TiHz  
= 1. 667 999 86 + THz  
BQQQQ QQQQQ hiHz   = B MuHz  
= 104 249. 99 + MHz  
BQQQ QQQQQ hiHz   = B MoHz  
= 6 156. 24 + MHz  
BQQ QQQQQ hiHz   = B MaHz  
= 407. 23 - MHz  
BQ QQQQQ hiHz   = B MeHz  
= 25. 45 + MHz  
B QQQQQ hiHz   = B MiHz  
= 1. 590 728 63 - MHz  
BQQQQ hiHz   = B huHz  
= 99 420. 54 - Hz  
BQQQ hiHz   = B hoHz  
= 6 213. 78 + Hz  
BQQ hiHz   = B haHz  
= 388. 36 + Hz  
BQ hiHz   = B heHz  
= 24. 27 + Hz  
B hiHz   = B hiHz  
= 1. 517 037 04 - Hz  
Note:  Plus and minus after the values means respectively "a little more than" and "a little less than".

The adapted unit for the frequency of microprocessors is well the mega-a-Hertz.
The 80386-chip reached Q.b MaHz, then Pentium II more than one mega-a-Hertz.
At present (2006) microprocessors exceed J MaHz, but not yet attain BQ MaHz.

If in theory a subsystem of odd magnitudes in frequencies also exists,
in practice however, it is neither necessary nor useful to employ it.

 

Frequency of typical visible light

Visible light

from red to violet

Hexadecimal

Frequency

Decimal

Frequency

Decimal

length of wave

Transition :

Nearest infra-red

to visible red.

XQ TiHz

373.6 THz

802.4 nm

WQ TiHz

400.3 THz

748.9 nm

Typical visible light

is situated between

BQQ to BKQ TiHz

ca. 700 to 400 nm.

BQQ TiHz

427.0 THz

702.1 nm

BKQ TiHz

747.3 THz

401.2 nm

Transition :

 Visible violet to

nearest ultra-violet.

BXQ TiHz

800.6 THz

387.4 nm

PQQ TiHz

854.0 THz

351.0 nm

 

The frequency of the musical note  Sol at G-clef  is defined  BQQ hexa-i-Hertz.

The old standard pitch, so-called A 440 didn't have any rational base. After long discords, it was defined completly arbitary.

In BI-SMH standard, the musical note G 4 of the  G clef is defined one hundred hexa-i-Hertz as  a binary multiple of Earth-day.

Thus, the new standard pitch La is now :  ( 224 / 43200 ) 21/ 6  ≥   435.921 decimal Hertz, but at  onety degrees Kelvin-Celsius .

 

 

  Three new SMH units  :   added in  February  2007.

The information units:

1. Name of bit-lengths

2. Information quantity: hexa-i-byte vs. hexa-i-fit

3. Symbol rate: hexa-i-Baud

1. Name of bit-lengths  ( in computing registers, information busses etc. )

Bits

English

name

Universal

name

hexa-i-Byte

Encoding possibilities

1

bit

bit

bit

.p hiB

=

2

1

=

2

 

 

2

bits

crumb

pit

.f hiB

=

2

2

=

4

 

 

4

bits

nibble

fit

.t hiB

=

2

4

=

16

 

 

8

bits

byte

tit

 B hiB

=

2

8

=

256

 

 

16

bits

word

bet

 P hiB

=

2

16

=

64k

 

 

32

bits

double-word

pet

 F hiB

=

2

32

=

4

G

 

64

bits

" sissa "

fet

 T hiB

=

2

64

=

16

E

 

128

bits

" double-sissa "

tet

BQ hiB

=

2

128

=

256

E

2

256

bits

" quadri-sissa "

bat

PQ hiB

=

2

256

=

64k

E

4

txt - information is encoded on  a tit , i.e. one byte, since this defines 256 characters.

The 65 536  Unicode-characters are encoded on a bet . The CPU-bus is now a sissa.

One filled SHOL double- sissa is W,WWWW,WWWW,WWWWW : W,WWWW,WWWW,WWWWW.

 

2. Information quantity ,   with the base unit :  hexa-i-byte   [ hiB ] 

The hexadecimal multiples

of the base unit hexa-i-byte

Expressed in the mass-

storage unit tera-i-bytes

Decimal

Equivalence

B   hiB
one   hexa -i-byte
Q.qqqqq qqqqb   TiB
= 1.000=

 B

B   kiB
one   kilo -i-byte
Q.qqqqq qqf   TiB
= 1.024=

kB

B   MiB
one   mega -i-byte
Q.qqqqb   TiB
= 1.049-

MB

B   GiB
one   giga -i-byte
Q.qqf   TiB
= 1.074-

GB

B   TiB

one

 

tera

-i-byte

B   TiB
= 1.100-

TB

B   PiB
one   peta -i-byte
FQQ   TiB
= 1.126-

PB

B   EiB
one   exa -i-byte
B,QQQQQ   TiB
= 1.153-

EB

B   ZiB
one   zetta -i-byte
FQQ,QQQQQ   TiB
= 1.181-

ZB

B   YiB
one   yotta -i-byte
B,QQQQQ,QQQQQ   TiB
= 1.209-

YB

The multiple of base unit  tera-i-byte  was the adapted unit for mass storage media.

 

Tera-i-byte [ TiB ]  versus  tera-i-fit [ Tifit ] .

The TiB-unit, just defined, already depreciated.    Why ?

The therefor answer in four sentences :

   2 1 :  The binary system is in.

   2 3 :  The vinary system is vile.

   2 4 :  The finary system is fine.

   2 8 :  The tinary system is out !

The more explicit answer is :

When during the second half of last century BigBlue - Wintel established their standards

at first, in 5-floppy times, letters were really encoded on a byte. Digital photos, music,

films etc. didn't exist. So, it seemed justified to count information in byte, kilobyte, etc.

An IBM-tinary system with 256 digits exists except as txt it is however unhuman !

Which human being could learn it by heart ?   Byte-digits are cryptic, therefore unhelpful.

Thus BI-SMH depreciates the byte-unit in profit of the unit : hexa-i-fit. That's the nibble.

The conversion: tera-i-byte  tera-i-fit is as easy as a multiplication or a division per two.

  

 B TiB = P Tifit (say: tera-i-fit),   and  B Tifit = t TiB.

Resolution:  Since 2007, February 20, the existing hexadecimal unit hexa-i-Byte

is officially depreciated by BI-SMH, replaced by the commended unit :  hexa-i-fit .

 

3. The symbol rate unit :   hexa-i-baud, with the unit symbol  [ hiBd ] .

Definition :  One hexa-i-baud is one fit   i.e. four bits   per hexa-i-timple.

This means that  B hiBd  ==  4096 675 -1  ==  6.06814 bps.

BQQQ   MiBd
one thousand   mega

-i-baud

26 062.5-

Mbps

BQQ   MiBd
one hundred   mega

-i-baud

1 628.9-

Mbps

BQ   MiBd
onety   mega

-i-baud

101.8+

Mbps

B

 

MiBd

one

 

mega

-i-baud

6.4-

Mbps

Q.b   MiBd
one onetieth   mega

-i-baud

0.40-

Mbps

Q.qb   MiBd
one hundredth   mega

-i-baud

0.025-

Mbps

Q.qqb   MiBd
one thousandth   mega

-i-baud

0.0016-

Mbps

The symbol rate unit baud, since 1927 means transmitted  symbols per second .

One hexa-i-baud means transmitted  symbols per hexadecimal second , per hit.

But it is useful to underline, that the meant symbol is the hexadecimal digit.

Traditional 56k-modem transmission is J kiBd, two hundredths mega-i-baud.

ADSL - transmissions are generally still inside several onetieths mega-i-baud.

Net working at 100 Mbps, allows transmissions close to onety mega-i-baud.

The Gigabit Network corresponds to more than ninety-thirteen mega-i-baud.

 

 

In four examples :  Conversion of all the other decimal SI units .

The SMH units of force, pressure, energy and power

 Derived quantity   Name of unit Symbol Expressed in SMH base units Conversion factors for the exact value 

Approximation

  Force   hexa-i-Newton    hiN  him   hag hit-P
2 -29 3 - 6 5 -25 19, 109 257  4  
  =  1. 143 214 +   N
  Pressure, stress   hexa-i-Pascal  hiPa him-B hag hit-P
2 -  9 3 - 6 5 -13 19, 109 257  2  
  =  0. 801 457 -   Pa
  Energy, work   hexa-i-Joule  hiJ  him P hag hit-P
2 -39 3 - 6 5 -31 19, 109 257  5  
  =  1. 365 374 -    J
  Power, radiant flux   hexa-i-Watt  hiW  him P hag hit-V
2 -29 3 - 9 5 -33 19, 109 257  5  
  =  2. 071 322 +   W

  Also see :  SI derived units.


 

Some mathematical units

 

The hexadecimal percentage

  Hexadecimal
  percentage

Notation

    Decimal
 Equivalence

  one hundred percents
BQQ . qqq %
= 100 . 000 000 = %
  onety percents
BQ . qqq %
= 6 . 250 000 = %
  one percent
B . qqq %
= 0 . 390 625 = %
  one onetieth percent
Q . bqq %
= 0 . 024 414 + %
  one hundredth percent
Q . qbq %
= 0 . 001 526 - %
  one thousandth percent
Q . qqb %
= 0 . 000 095 + %

  Example:  10.0 %   =   BJ.j % .

    Ten decimal percents are onety-nine percents three fifth ;

    since Q.j is nine fifteenth. This can be shortened :  three fifth.

Other example :   BT.q %   =   9.375 %.

 Onety-eight percents are nine decimal percents, three eighths.

 

The hexadecimal angle units

 

The hexadecimal arc degree

The circle comprises twonety arc degrees :  

360 00' 00".0   =   PQQQ'qqq 

 

  Hexadecimal
degrees and minutes
Notation  Equivalence
 sexagesimal
  onety arc degrees
BQ
= 180 . 00000 =
  one arc degree
B
= 11 . 25000 =
  onety arc minutes
BQ '
= 42 ' . 18750 =
  one arc minute
B '
= 2 ' . 63672 -
  one onetieth arc minute
' b
= 9 ' . 88770 -
  one hundredth arc minute
' qb
= 0 " . 61798 +
  one thousandth arc minute
' qqb
= 0 " . 03862 +

 

Example:  60 00' 00".0  =  ZZZ'zzz 

Five hexadecimal arc degrees and fifty-five minutes a third.

One thousandth hexadecimal arc minute at the equator

corresponds per definition exactly to one hexa-i-metre

A practical application of the hexadecimal arc degrees

can now be studied at http://www.hexadecimal.free.fr.

The hexadecimal radian

 Certainly, the hexadecimal radian also exists.

One radian :

 B rad 

=   BQ / π

=   Z BD' kkp -

Five hexadecimal arc degrees, onety-seven minutes and

a little less than twelve hundred twelfty-two thousandth.

  Remark that the hexadecimal value of π is V.pfvws scttt s-.

 


 

Additional explications

 

 

Digits and letters

 

The omni-literal hexadecimal digits of  SHOL :

All the odd digits are represented by voiced consonants,

digit zero and the even digits by voiceless consonants.

The omni-literal system makes the following equation:

0x10x20x30x4
0x50x60x70x8
0x90xA0xB0xC
0xD0xE0xF0x0
=

B

P

V

F

Z

S

D

T

J

C

G

K

Y

X

W

Q

Beside, the five vowels of the western alphabet give the ranks inside

magnitudes (see just below).  However, vowels are never used as digits.

Item the following three special, single letters :

The nasal consonant N, the lateral L, also R,

latter-one is normally an alveolar or uvular trill.

In particular uses H can mean sixteen, but it is never called onety.

Be careful, because there we are leaving the positional arithmetic.

H is the base as one digit  and  M expresses the superbase million.

Some important fractions, easy to retain 

  1/ 2 = Q.t 1/ 3 = Q.z 1/ 5 = Q.v  
  1/ 4 = Q.f 1/ 6 = Q.pc 1/ 10 = Q.bj  
  1/ 8 = Q.p 1/ 12 = Q.bz 1/ 20 = Q.qk  

An other important hexadecimal fraction is :   1/ 15  =  Q.b

 

 

Hexadecimal multiplication table with omni-literal digits

 Click to enlarge.

Click to enlarge.

Three available .doc documents :

 This multiplication table with SHOL numerals,  just like above.

 The multiplication table with universal number names  ( UNN ).

 The Bo lo bi la bi  , a mathematical poem.

Therefore please also see our dynamical multiplication table.

 

 

The rank inside magnitudes  (cf.  System of units, chapter: Ranks)

10242 equals 165.   Thus the SMH always groups five digits: millions, billions etc. respectively
millionth, billionth etc. The place of each one of these hexadecimal digits gives the hexadecimal
rank inside the magnitude. The role played by these five ranks is comparable to the four decimal
prefixes: centi-, deci-, deca- and hecto-. Latter ones are never used in the hexadecimal system.

So, the hierarchy of the five vowels signifying the five ranks is established by linguistic criterions
(cf. the trapezium of vowels). So their meanings are "i" = 1x, "e" = 16x, "a" = 256x, "o" = 4096x
and finally "u" = 65536 times the magnitude of the concerned unit.

By comparing to the decimal SI, the significant difference of the conception of rank in magnitude:
These multiples of magnitude, the ranks, are used in any magnitude. Example: mega-a-unit.
However in practice each scientific application field will choice their adequate main multiples
and submultiples by preferring generally the basic "i -" and the central "a-units".

Because these ranks are used in the very same manner as well as for the positive magnitudes,
just as in the same way with the negative magnitudes, the micro-u-unit, for example, signifies:
One micro-u-unit is rightly the binary millionth of the basic unit multiplied by binary 64k.

 

The hexadecimal alphabet, in its lexicographical order

Q B P V F Z S D T J C G K
[ʔ] [b] [p] [v] [f] [z] [s] [d] [t] [ʒ] [ʃ] [g] [k]
Y X W H I E A O U M N L R
[j] [x] [w] [h] [i] [e] [a] [o] [u] [m] [n] [l] [r]
Remark :  The phonetical main meaning of the four consonants formatted in red font colour differs from IPA.

So, the first entry in a modern English dictionary might be the word "quibbling",

the last one "ruralize".   Who knows all the words from quibbling to ruralize ?

 

  The onety-ten letters of the hexadecimal alphabet:

"Q" is the first letter, defined zero, with the modern phonetical main meaning glottal stop,

 then, the letters from "B" to "K", the main consonants, alternating voiced and voiceless.

 Thirteen letters, id est the first half of the alphabet.

The first approximant "Y" is followed by "X", i.e. []-[x]-[χ], and the other approximant "W".

 So far: The onety hexadecimal omni-literal digits.

Then the "H" and the five vowels: "I", "E", "A", "O", "U" :  [i] [e]-[ɛ] [a]-[ɑ] [ɔ]-[o] [u];

followed by two nasal consonants "M" and "N", finally the lateral "L" and the trill "R" [r]-[ʀ].

 

Even if now a modern, universal main meaning of each letter is well defined,

nevertheless, all precipitant orthography reforms are categorically to reject. 

 

The hexadecimal number names

The names of the hexadecimal  "oneties"  in several languages
Oneties
 
Universal
names

[ IPA ]
English
names

 
French
names

(in France)
French
names

Francophonie
German
names

 
Decimal
value

 
(QQ)
(qe   [ʔe])  
(zero oneties) (zro unantaine) <= (Null Einziger)

0

BQ
be [be]  
onety unant <= einzig 16
PQ
pe [pe]  
twonety vingt <= zwanzig 32
VQ
ve [ve]  
thirty trente <= dreiig 48
FQ
fe [fe]  
forty quarante <= vierzig 64
ZQ
ze [ze]  
fifty cinquante <= fnfzig 80
SQ
se [se]  
sixty soixante <= sechzig 96
DQ
de [de]  
seventy soixante-unant septante siebzig 112
TQ
te [te]  
eighty quatre-vingt octante achtzig 128
JQ
je [ʒe]  
ninety quatre-mi-vingt nonante neunzig 144
CQ
ce [ ʃe]  
tenty cinq-vingt dixante zehnzig 160
GQ
ge [ge]  
eleventy cinq-mi-vingt onzeante elfzig 176
KQ
ke [ke]  
twelfty six-vingt douzeante zwlfzig 192
YQ
ye [ je ]  
thirteenty six-mi-vingt treizeante dreizehnzig 208
XQ
xe [xe]  
fourteenty sept-vingt quatorzeante vierzehnzig 224
WQ
we [we]  
fifteenty sept-mi-vingt quinzeante fnfzehnzig 240
(HQ)
BQQ
(he  [he])  
ba[ba]  
(sixteenty)
one hundred
(huit-vingt)
cent
(seizeante)
<=
(sechzehnzig)
einhundert
256

   Example :

   2, 000 000  =  0x 1, E8480  =  B, XTFTQ

Two million decimal units in hexadecimal numbering equal :

one million fourteenty-eight thousand four hundred eighty units.

Internationally, this number can also be read :   Bi mi, xu to fa te (qi).

Note : The universal number names recall Āryabhaa, the creator of the Sanskrit numerals.

Remarks:

Many francophone countries or provinces while using "septante" and "nonante" instead of the 'hexagonal' terms "soixante-dix" and "quatre-vingt-dix" however

employ "quatre-vingt" for "octante" or (rare) "huitante". They can, of course, continue to use quatre-vingt, even for the hexadecimal number (= 128, Base -10).

The hexadecimal number "soixante-et-onze" does not exist. This is artless "soixante-onze". One says "unant-et-un", "unant-deux", "unant-trois" etc.

But "cinq-vingt-un" like "quatre-vingt-un". The hexadecimal numbers such as "six-mi-vingt-quinze" endue six and a half times twonety plus fifteen, i.e.

"six-(et-de)mi-(fois-)vingt-(plus-)quinze" (= 223). For not francophones, by the way, dixante is rightly pronounced [di:ztə] like some other french xs.

German hexadecimal onety-numbers are invariably enunciated in the modern, logical order: First the onties, then the ones.

Example :  the decimal number 336 (= BZQ) in german: "drei hundert sechsunddreiig " ;  but the hexadecimal number VVS (= 822) is always said

"drei hundert dreiig-sechs". 17 is "einzig-eins", 18 "einzig-zwei " etc. The german term "der Einzigste" ( formerly   at the most   very incorrect for

"der Einzige", the only one, the unique one)  now exists :  That is this one who arrives after the fifteenth.

In all languages the oneties and the ones are joined with hyphens. The other number-parts are unhyphenated.

English example:  Three hundred tenty- fourteen :  VCX  equal  94210.

Universal number names:  It is easy to understand that 16 5 = 80  different syllables suffice to enunciate all natural numbers including zero, as far as 1, 048 575.

Therefor see this detailed page. The negative numbers are expressed with the prefix n-.  Exemple : " ndabi "  =  -DQB  =  -1793. With ten additional zillion names the

interval 2 16 ^5 1, 048 576 ^5 - 1 is covered by simple number names, i.e. from  minus  2.66 10 ^36  to  plus  2.66 10 ^36 and in the fractions :  0.79 10 ^-30.

However, an exponentiation expression, like million to the power of seventeen, precisely :  mir-bebi, extends the field of pronounceable numbers potentially to infinity.

Actually, with the exponentiation expression: mur-hu, only up to ( (16 5 ) 5 ) 1, 048 576.  So, in a small font-size: Digits for about 80 km or 50 miles. Serious scientists generally settle for using up to 1, 048 576 16.

 

 

The hexadecimal point, the millions separator, etc.

The hexadecimal point is an obligation due to the good standard. It is the matter of a point not a comma worldwide.

Some meddlesome jackanapes could argue the hexadecimal point is not necessary, because upper case and lower case letters already distinguish the units and the hexadecimal fractions.

They receive this answer: In the opposite, lower cases are not obligatory, however normal. The hexadecimal point is essential by following hexadecimal fractions. Just a question of good style.

The millions separator (groups of five digits) is also obligatory. The comma is commended, the non-breaking space is admitted.

The millionths separator (groups of five digits in the fractional part) is not obligatory, but recommended. The comma is commended, non-breaking space admitted.

 

Excursus to the old, out-dated and now ruled long scale versus short scale controversy:

The great colleague Nicolas Chuquet once made, now makes and will continue to make authority on this topic, worldwide and forevermore.

This Chuquet billion is the universal billion, which is engaging for everybody.

His own example number was 745324' 804300' 700023' 654321 to read as: " 745324 tryllions 804300 byllions 700023 millions 654321 ".

Later on, the original six digit groups were split again, into two groups of three digits, with the argument of better legibility.

Now, an ignorant and nameless minority imagined in the course of this passage from the older six-digit-groups to the modern three-digit-groups,

by itself a good idea to change the good old meaning of the great numbers. Never !

That was not a sufficient reason, to break with the ingenious and really progressive logarithmic definition of the million names.

This minority was influent in Italy and particularly in France till the beginning of the 20th century. Thus in older French encyclopaedia the reformed short scale

was always mentioned, presented as standard. There, the original long scale is often hushed up or if this is not the case noted as "now obsolete meaning".

(So, we can see: A "said dead" lives longer ! )  Then even in France   sanity won, and France since there are no hopeless cases reconverted to Chuquet.

Now, neither in France nor anywhere else at continental Europe like virtually everywhere worldwide: None will ever disavow the only consistent Chuquet billion.

The current preposterous U.S. billion-use is for say it in short nothing other than a puerile daftness of a former Crown Colony (cf. the case of Brazil)

introduced in error by incompetent French pseudo-savants, which were certainly neither mathematicians nor philologists.

Then, the U.S.A. persevered "to make it different from their old repudiated mother". But an error remains an error. It can't be helped.

If the grown-up, prospered ex-son now try to impose his kept boorishness to his ex-ma (here guised as this, on the topo, pseudo-modernist Wilson) :

This doesn't change absolutely nothing on the fact that the short scale is not consistent, now happily unmasked by the hexadecimal billion.

The best way to write today the Chuquet example number should be:

745 324, 804 300, 700 023,  654 321  to read as: 745 324 trillion, 804 300 billion, 700 023 million, 654 321 units. Trilliardbilliard and milliard are also admitted.

Surely, the decimal comma practised in France, Romania, the Netherlands, Germany, Switzerland, Italy a.s.o.m. may be antiquated and abolishing worthy.

Just like this extravagant German all-thousand-point could probably be a folly...

But since the BI-SMH is not concerned by decimal notation rules, it forbears itself to stipulate any mandatory regulation on this topic.

One should never transgress his responsibilities !  Just this doesn't apply to this objectively false ten -power -nine -pseudo -billion :

Neither the United States of America, nor Brazil will ever have the possibility to delegate scientists with voting rights

to the International Bureau without a previous and effective official renouncement to this nonsense short scale billion.

Certainly, the future "Hexadecimal Metre Convention" will have a very explicit article on this topic.

After all it's easy to replace in all official uses the word billion either by thousand million or by milliard, the error is corrected.

During the 20th century, notably two nations, Italy and France, clearly proofed by switching back  :  It's possible. No problem.

Merely, some too-proud US-Dollar billionaires, one morning will awake as blemished and ridiculous milliardaires. C'est la vie.

 

 

User royalties?

  • Yes.  All the governments of all the states wishing to adhere to the future "Hexadecimal Metre Convention" have to pay both :

    A substantial, one-time sum (cf. Sissa who once demanded an entire 64-bit-bus filled with grains of wheat. This equals onety trillion grains of wheat minus one.)

    in the very personal pocket of the initiator of the SMH for the accomplished labor. Then clearly separated with an objective controlling an annual sum for the

    good working conditions of the International Bureau for the hexadecimal metric system (BI-SMH).

  • No.  None has to pay, neither private persons nor incorporated enterprises. All use is free and gratis.    No proprietary standards !

 

 

Also see

The new civil, historical and astronomical chronology and its Civil Calendar

The latter page is edited under responsability of the " Virtual observatory of Florence situated in Paris (OvFsP) ".

This chronology is in plenary concordance with the tropical year by its only correct 128-year-exceptional-common-year-rule. *

This chronology defines the civil year zero for the 365 first days of  1792, worldwide, the year of the beginning of history of Modern Times.

  Universal event of the year 1792 :  the effective abolishing of Ancient Regime by the bloody, revolutionary, French bourgoisie on AD 1792-09-21.

   The local event of the year 1792 :  the foundation of the US-capital Washington by a well-known, poor ' workmen-association ' on AD 1792-10-13.

Likewise, for US citizens, the Common Era (CE) may denote "since United States Mint" on AD 1792-04-02.

This chronology is civil one, since it is not a religious Era. All citizens live in 3rd century, including e.g. the Windsors. Everybody is born in this chronology.

Additionally, all Christians   but only by their baptism   enter in the Christian Era, a religious chronicle, but without a year zero, surely not a real chronology.

The astronomical  "Cassini Era"  is a chronology. However with its defined leap year zero, astronomically false for about 6000 years, additional uncontinious from 1582-10-04 to 1582-10-15.

*  First proposed in late 19th c. by the German astronomer von Mdler, director of the Dorpat (Tartu) Observatory in Estonia. Stange to say, he proposed this rule for 1900 (= 14 128 +108).

 

 

 

References

Official precis of the decimal SI in English language.  BIPM:  SI-brochure.pdf.
French compendium of the hexadecimal base units.  BI-SMH:  Les units du SMH.doc.

Many other references, either at the end of the concerned page, example, references for the ancient measures at the Viennese yard page, or within the text by

a hyperlink, example :  the reference for the formula of the tropical year, Bretagnon, 2000 at the page Civil Calendar by this link to Observatory Paris-Meudon.

 

 

 

External links

Intuitor.com's Hexclock

http://www.intuitor.com promotes  since 1997   an exactly half slow-going hexadecimal time format.

Dr Beat.li's Time Page

http://www.drbeat.li displays several time formats in JavaScript :  SwatchTime, Hexclock, Florencetime...

Hexadecimal Earthgrid

http://www.hexadecimal.free.fr shows the hexadecimal Earthgrid conform to M. Florencetime's proposal.

 

 


 

This page is online since 2006, June 29 

 

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