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Universal fractions

The « Bi lo bi la bi »

Hexadecimal zillions

  The universal number names in SHOL* numeration

16 × 5  =  80  different syllabes suffice to count up to the hexadecimal million ( 1024 × 1024 = )  1, 048 576 . 

			- [ i ]	- [ e ]	- [ a ]	- [ o ]	- [ u ]			[ IPA ]
	×		16 0	16 1	16 2	16 3	16 4
hex.	dec.								IBM hex.
Q	0		Q qi 0 × 1	QQ qe 0 × 16	QQQ qa 0 × 256	QQQQ qo 0 × 4 096	QQQQQ qu 0 × 65 536		0x 0	[ ʔ ]
B	1		B bi 1	BQ be 16	BQQ ba 256	BQQQ bo 4 096	BQQQQ bu 65 536		0x 1	[ b ]
P	2		P pi 2	PQ pe 32	PQQ pa 512	PQQQ po 8 192	PQQQQ pu 131 072		0x 2	[ p ]
V	3		V vi 3	VQ ve 48	VQQ va 768	VQQQ vo 12 288	VQQQQ vu 196 608		0x 3	[ v ]
F	4		F fi 4	FQ fe 64	FQQ fa 1 024	FQQQ fo 16 384	FQQQQ fu 262 144		0x 4	[ f ]
Z	5		Z zi 5	ZQ ze 80	ZQQ za 1 280	ZQQQ zo 20 480	ZQQQQ zu 327 680		0x 5	[ z ]
S	6		S si 6	SQ se 96	SQQ sa 1 536	SQQQ so 24 576	SQQQQ su 393 216		0x 6	[ s ]
D	7		D di 7	DQ de 112	DQQ da 1 792	DQQQ do 28 672	DQQQQ du 458 752		0x 7	[ d ]
T	8		T ti 8	TQ te 128	TQQ ta 2 048	TQQQ to 32 768	TQQQQ tu 524 288		0x 8	[ t ]
J	9		J ji 9	JQ je 144	JQQ ja 2 304	JQQQ jo 36 864	JQQQQ ju 589 824		0x 9	[ ʒ ]
C	10		C ci 10	CQ ce 160	CQQ ca 2 560	CQQQ co 40 960	CQQQQ cu 655 360		0x A	[ ʃ ]
G	11		G gi 11	GQ ge 176	GQQ ga 2 816	GQQQ go 45 056	GQQQQ gu 720 896		0x B	[ g ]
K	12		K ki 12	KQ ke 192	KQQ ka 3 072	KQQQ ko 49 152	KQQQQ ku 786 432		0x C	[ k ]
Y	13		Y yi 13	YQ ye 208	YQQ ya 3 328	YQQQ yo 53 248	YQQQQ yu 851 968		0x D	[ j ]
X	14		X xi 14	XQ xe 224	XQQ xa 3 584	XQQQ xo 57 344	XQQQQ xu 917 504		0x E	[ x ]
W	15		W wi 15	WQ we 240	WQQ wa 3 840	WQQQ wo 61 440	WQQQQ wu 983 040		0x F	[ w ]
H	16		H hi 16	HQ he 256	HQQ ha 4 096	HQQQ ho 65 536	HQQQQ hu 1, 048 576		0x10	[ h ]

Remark :  The hexadecimal numbers 0x E and 0x E0 (= 14 and 224), in SHOL :  X and XQ are pronounced  [ çi ]  and  [ çe ]  and not  [ xi ]  and  [ xe ] .

In SHOL, the voiceless palatal fricative [ ç ]  (before the vowels e and i)  and the voiceless velar fricative  [ x ]  (before a, o and u)  are allophones.

H   &   M Next to the 16 hexadecimal digits :  B  to  W  and  Q ,  the SHOL posesses two auxiliary digits. The base number as one-digit may be used e.g. in a listing as sixteenth and definitively last element. Both, H and M are used in exponentiation expressions. Example:  B,QQQQQ  =  B × H Z  =  B × M B. Orally, the syllables : mi, me, ma, mo and mu express universally the five first hexadecimal zillions. 1
One-digit-base: H  =  sixteen	hi H 1	he H 2	ha H 3	ho H 4	hu H 5	16 256 4 096 65 536 1, 048 576
Superbase: M  =  million	mi M 1	me M 2	ma M 3	mo M 4	mu M 5	1, 048 576 1, 099 511, 627 776 1, 152 921, 504 606, 846 976 1, 208 925, 819 614, 629 174, 706 176 1, 267 650, 600 228, 229 401, 496 703, 205 376

Example :  The highly composite number 10080  is of course also highly composite in base-16 :  P ^Z × V ^P × Z ^B × D ^B.

10080 ₁₀ = P DSQ _H   –   Enunciated as :  Hexadecimal,  two thousand seven hundred sixty  or :  podase(qi) .

 The perimeter constant   π  ≈ V. pfvws  is proposed to be called henceforth Euler-pi or greek-pi to avoid all confusions.

Similarly, the Golden ratio number φ  ≈ B . jxvdt is  – orally –  the "Phidias number", in short "Phidias" or also greek-phi.

Don't ever confound SMH unit symboles and SHOL number names.  Therefor see this caution.

  * SHOL :  système hexadécimal omni-littéral.  The English translation of this French term is "omni-literal hexadecimal system".  

 

This page is online since 2006, September 17 ;