The  hexadecimal  metric  system

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

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

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): PQ°QQ'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	1024±0 × 16 4	B hut	= 43 200. 000 000 s
one hour	1024±0 × 16 3	B hot	= 2 700. 000 000 s
one maxim	1024±0 × 16 2	B hat	= 168. 750 000 s
one minute	1024±0 × 16 1	B het	= 10. 546 875 s
one second	1024±0 × 16 0	B hit	0. 659 180 s
one third	1024 -2 × 16 4	B µut	41 198. 730 489 µs

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) × 2^{1/ 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"

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° KC, exactly  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"

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.

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 µm  ·  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 µum	74 645. 535 156 µm
one line	1024 -2 × 16 3	B µom	4 665. 345 947 µm
one point	1024 -2 × 16 2	B µam	291. 584 122 µm
one link	1024 -2 × 16 1	B µem	18. 224 008 µm
one micron	1024 -2 × 16 0	B µim	1. 139 000 µm
(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.

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.

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

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

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	1024±2 × 16 0	B Mig	1. 703 615 Mg
one quintal *	1024±0 × 16 4	B hug	106 475. 937 644 g
one stone	1024±0 × 16 3	B hog	6 654. 746 103 g
one pound	1024±0 × 16 2	B hag	415. 921 631 g
one florin	1024±0 × 16 1	B heg	25. 995 102 g
one drachm	1024±0 × 16 0	B hig	1. 624 694 g
one ace	1024-2 × 16 4	B µug	101 543. 367 047 µg
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 µug 0.2 g
t hag 208 g one mark	t heg 13 g one peso	t hig 0.8 g one penny	t µug 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 écu 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

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

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-Ampère"

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

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

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.

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 km².
Unit	Common term	Square hexa-i-metre	Equivalence  decimal
B kimP	one square mile	B QQQQQ himP	= 1. 495 711 km2
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 µumP	one square palm	Q.qb himP	= 5 572 mm2
B memP	one square digit	Q.qqb himP	= 348 mm2
B µomP	one square line	Q.qqqb himP	= 22 mm2
B mimP	one square stroke	Q.qqqqb himP	= 1. 360 341 mm2

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

The main volumes

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. q  hal		5 L
8	=	384	=	S. q  hal		2.5 L
4	=	192	=	V. q  hal		1.25 L
2	=	96	=	B. t  hal		624 mL
1	=	48	=	Q. k  hal		312 mL
1 / 2	=	24	=	Q. s  hal		156 mL
1 / 4	=	12	=	Q. v  hal		78 mL
1 / 8	=	6	=	Q. bt hal		39 mL
1 / 16	=	3	=	Q. qk hal		19½ mL

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

  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 5½-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 %

The hexadecimal angle units

The hexadecimal arc degree

The circle comprises twonety arc degrees :   360° 00' 00".0   =   PQ°QQ'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  =  Z°ZZ'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 :

Hexadecimal multiplication table with omni-literal digits   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