H2S87: A quick primer on base-mathematics:


Decimal<base-10>Octal<base-8>Hexadecimal<b-16>Binary<base-2>
0/0000x000 0 0 0 0 0 0 0
1/0010x010 0 0 0 0 0 0 1
2/0020x020 0 0 0 0 0 1 0
3/0030x030 0 0 0 0 0 1 1
4/0040x040 0 0 0 0 1 0 0
5/0050x050 0 0 0 0 1 0 1
6/0060x060 0 0 0 0 1 1 0
7/0070x070 0 0 0 0 1 1 1
8/0100x080 0 0 0 1 0 0 0
9/0110x090 0 0 0 1 0 0 1
10/0120x0A0 0 0 0 1 0 1 0
11/0130x0B0 0 0 0 1 0 1 1
12/0140x0C0 0 0 0 1 1 0 0
13/0150x0D0 0 0 0 1 1 0 1
14/0160x0E0 0 0 0 1 1 1 0
15/0170x0F0 0 0 0 1 1 1 1
16/0200x100 0 0 1 0 0 0 0
17/0210x110 0 0 1 0 0 0 1
18/0220x120 0 0 1 0 0 1 0
19/0230x130 0 0 1 0 0 1 1
20/0240x140 0 0 1 0 1 0 0
21/0250x150 0 0 1 0 1 0 1
22/0260x160 0 0 1 0 1 1 0
23/0270x170 0 0 1 0 1 1 1
24/0300x180 0 0 1 1 0 0 0
25/0310x190 0 0 1 1 0 0 1
26/0320x1A0 0 0 1 1 0 1 0
27/0330x1B0 0 0 1 1 0 1 1
28/0340x1C0 0 0 1 1 1 0 0
29/0350x1D0 0 0 1 1 1 0 1
30/0360x1E0 0 0 1 1 1 1 0
31/0370x1F0 0 0 1 1 1 1 1
32/0400x200 0 1 0 0 0 0 0
33/0410x210 0 1 0 0 0 0 1
34/0420x220 0 1 0 0 0 1 0
35/0430x230 0 1 0 0 0 1 1
36/0440x240 0 1 0 0 1 0 0
37/0450x250 0 1 0 0 1 0 1
38/0460x260 0 1 0 0 1 1 0
39/0470x270 0 1 0 0 1 1 1
40/0500x280 0 0 1 1 0 0 0
41/0510x290 0 0 1 1 0 0 1
42/0520x2A0 0 1 0 1 0 1 0
43/0530x2B0 0 1 0 1 0 1 1
44/0540x2C0 0 1 0 1 1 0 0
45/0550x2D0 0 1 0 1 1 0 1
46/0560x2E0 0 1 0 1 1 1 0
47/0570x2F0 0 1 0 1 1 1 1
48/0600x300 0 1 1 0 0 0 0
49/0610x310 0 1 1 0 0 0 1
50/0620x320 0 1 1 0 0 1 0
51/0630x330 0 1 1 0 0 1 1
52/0640x340 0 1 1 0 1 0 0
53/0650x350 0 1 1 0 1 0 1
54/0660x360 0 1 1 0 1 1 0
55/0670x370 0 1 1 0 1 1 1
56/0700x380 0 1 1 1 0 0 0
57/0710x390 0 1 1 1 0 0 1
58/0720x3A0 0 1 1 1 0 1 0
59/0730x3B0 0 1 1 1 0 1 1
60/0740x3C0 0 1 1 1 1 0 0
61/0750x3D0 0 1 1 1 1 0 1
62/0760x3E0 0 1 1 1 1 1 0
63/0770x3F0 0 1 1 1 1 1 1
64/1000x400 1 0 0 0 0 0 0
65/1010x410 1 0 0 0 0 0 1
66/1020x420 1 0 0 0 0 1 0
67/1030x430 1 0 0 0 0 1 1
68/1040x440 1 0 0 0 1 0 0
69/1050x450 1 0 0 0 1 0 1
70/1060x460 1 0 0 0 1 1 0
71/1070x470 1 0 0 0 1 1 1
72/1100x480 1 0 0 1 0 0 0
73/1110x490 1 0 0 1 0 0 1
74/1120x4A0 1 0 0 1 0 1 0
75/1130x4B0 1 0 0 1 0 1 1
76/1140x4C0 1 0 0 1 1 0 0
77/1150x4D0 1 0 0 1 1 0 1
78/1160x4E0 1 0 0 1 1 1 0
79/1170x4F0 1 0 0 1 1 1 1
80/1200x500 1 0 1 0 0 0 0
81/1210x510 1 0 1 0 0 0 1
82/1220x520 1 0 1 0 0 1 0
83/1230x530 1 0 1 0 0 1 1
84/1240x540 1 0 1 0 1 0 0
85/1250x550 1 0 1 0 1 0 1
86/1260x560 1 0 1 0 1 1 0
87/1270x570 1 0 1 0 1 1 1
88/1300x580 1 0 1 1 0 0 0
89/1310x590 1 0 1 1 0 0 1
90/1320x5A0 1 0 1 1 0 1 0
91/1330x5B0 1 0 1 1 0 1 1
92/1340x5C0 1 0 1 1 1 0 0
93/1350x5D0 1 0 1 1 1 0 1
94/1360x5E0 1 0 1 1 1 1 0
95/1370x5F0 1 0 1 1111
96/1400x600 1 1 0 0 0 0 0
97/1410x610 1 1 0 0 0 0 1
98/1420x620 1 1 0 0 0 1 0
99/1430x630 1 1 0 0 0 1 1
100/1440x640 1 1 0 0 1 0 0
101/1450x650 1 1 0 0 1 0 1
102/1460x660 1 1 0 0 1 1 0
103/1470x670 1 1 0 0 1 1 1
104/1500x680 1 1 0 1 0 0 0
105/1510x690 1 1 0 1 0 0 1
106/1520x6A0 1 1 0 1 0 1 0
107/1530x6B0 1 1 0 1 0 1 1
108/1540x6C0 1 1 0 1 1 0 0
109/1550x6D0 1 1 0 1 1 0 1
110/1560x6E0 1 1 0 1 1 1 0
111/1570x6F0 1 1 0 1 1 1 1
112/1600x700 1 1 1 0 0 0 0
113/1610x710 1 1 1 0 0 0 1
114/1620x720 1 1 1 0 0 1 0
115/1630x730 1 1 1 0 0 1 1
116/1640x740 1 1 1 0 1 0 0
117/1650x750 1 1 1 0 1 0 1
118/1660x760 1 1 1 0 1 1 0
119/1670x770 1 1 1 0 1 1 1
120/1700x780 1 1 1 1 0 0 0
121/1710x790 1 1 1 1 0 0 1
122/1720x7A0 1 1 1 1 0 1 0
123/1730x7B0 1 1 1 1 0 1 1
124/1740x7C0 1 1 1 1 1 0 0
125/1750x7D0 1 1 1 1 1 0 1
126/1760x7E0 1 1 1 1 1 1 0
127/1770x7F0 1 1 1 1 1 1 1
128/2000x801 0 0 0 0 0 0 0
129/2010x811 0 0 0 0 0 0 1
130/2020x821 0 0 0 0 0 1 0
131/2030x831 0 0 0 0 0 1 1
132/2040x841 0 0 0 0 1 0 0
133/2050x851 0 0 0 0 1 0 1
134/2060x861 0 0 0 0 1 1 0
135/2070x871 0 0 0 0 1 1 1
136/2100x881 0 0 0 1 0 0 0
137/2110x891 0 0 0 1 0 0 1
138/2120x8A1 0 0 0 1 0 1 0
139/2130x8B1 0 0 0 1 0 1 1
140/2140x8C1 0 0 0 1 1 0 0
141/2150x8D1 0 0 0 1 1 0 1
142/2160x8E1 0 0 0 1 1 1 0
143/2170x8F1 0 0 0 1 1 1 1
144/2200x901 0 0 1 0 0 0 0
145/2210x911 0 0 1 0 0 0 1
146/2220x921 0 0 1 0 0 1 0
147/2230x931 0 0 1 0 0 1 1
148/2240x941 0 0 1 0 1 0 0
149/2250x951 0 0 1 0 1 0 1
150/2260x961 0 0 1 0 1 1 0
151/2270x971 0 0 1 0 1 1 1
152/2300x981 0 0 1 1 0 0 0
153/2310x991 0 0 1 1 0 0 1
154/2320x9A1 0 0 1 1 0 1 0
155/2330x9B1 0 0 1 1 0 1 1
156/2340x9C1 0 0 1 1 1 0 0
157/2350x9D1 0 0 1 1 1 0 1
158/2360x9E1 0 0 1 1 1 1 0
159/2370x9F1 0 0 1 1 1 1 1
160/2400xA01 0 1 0 0 0 0 0
161/2410xA11 0 1 0 0 0 0 1
162/2420xA21 0 1 0 0 0 1 0
163/2430xA31 0 1 0 0 0 1 1
164/2440xA41 0 1 0 0 1 0 0
165/2450xA51 0 1 0 0 1 0 1
166/2460xA61 0 1 0 0 1 1 0
167/2470xA71 0 1 0 0 1 1 1
168/2500xA81 0 1 0 1 0 0 0
169/2510xA91 0 1 0 1 0 0 1
170/2520xAA1 0 1 0 1 0 1 0
171/2530xAB1 0 1 0 1 0 1 1
172/2540xAC1 0 1 0 1 1 0 0
173/2550xAD1 0 1 0 1 1 0 1
174/2560xAE1 0 1 0 1 1 1 0
175/2570xAF1 0 1 0 1 1 1 1
176/2600xB01 0 1 1 0 0 0 0
177/2610xB11 0 1 1 0 0 0 1
178/2620xB21 0 1 1 0 0 1 0
179/2630xB31 0 1 1 0 0 1 1
180/2640xB41 0 1 1 0 1 0 0
181/2650xB51 0 1 1 0 1 0 1
182/2660xB61 0 1 1 0 1 1 0
183/2670xB71 0 1 1 0 1 1 1
184/2700xB81 0 1 1 1 0 0 0
185/2710xB91 0 1 1 1 0 0 1
186/2720xBA1 0 1 1 1 0 1 0
187/2730xBB1 0 1 1 1 0 1 1
188/2740xBC1 0 1 1 1 1 0 0
189/2750xBD1 0 1 1 1 1 0 1
190/2760xBE1 0 1 1 1 1 1 0
191/2770xBF1 0 1 1 1 1 1 1
192/3000xC01 1 0 0 0 0 0 0
193/3010xC11 1 0 0 0 0 0 1
194/3020xC21 1 0 0 0 0 1 0
195/3030xC31 1 0 0 0 0 1 1
196/3040xC41 1 0 0 0 1 0 0
197/3050xC51 1 0 0 0 1 0 1
198/3060xC61 1 0 0 0 1 1 0
199/3070xC71 1 0 0 0 1 1 1
200/3100xC81 1 0 0 1 0 0 0
201/3110xC91 1 0 0 1 0 0 1
202/3120xCA1 1 0 0 1 0 1 0
203/3130xCB1 1 0 0 1 0 1 1
204/3140xCC1 1 0 0 1 1 0 0
205/3150xCD1 1 0 0 1 1 0 1
206/3160xCE1 1 0 0 1 1 1 0
207/3170xCF1 1 0 0 1 1 1 1
208/3200xD01 1 0 1 0 0 0 0
209/3210xD11 1 0 1 0 0 0 1
210/3220xD21 1 0 1 0 0 1 0
211/3230xD31 1 0 1 0 0 1 1
212/3240xD41 1 0 1 0 1 0 0
213/3250xD51 1 0 1 0 1 0 1
214/3260xD61 1 0 1 0 1 1 0
215/3270xD71 1 0 1 0 1 1 1
216/3300xD81 1 0 1 1 0 0 0
217/3310xD91 1 0 1 1 0 0 1
218/3320xDA1 1 0 1 1 0 1 0
219/3330xDB1 1 0 1 1 0 1 1
220/3340xDC1 1 0 1 1 1 0 0
221/3350xDD1 1 0 1 1 1 0 1
222/3360xDE1 1 0 1 1 1 1 0
223/3370xDF1 1 0 1 1 1 1 1
224/3400xE01 1 1 0 0 0 0 0
225/3410xE11 1 1 0 0 0 0 1
226/3420xE21 1 1 0 0 0 1 0
227/3430xE31 1 1 0 0 0 1 1
228/3440xE41 1 1 0 0 1 0 0
229/3450xE51 1 1 0 0 1 0 1
230/3460xE61 1 1 0 0 1 1 0
231/3470xE71 1 1 0 0 1 1 1
232/3500xE81 1 1 0 1 0 0 0
233/3510xE91 1 1 0 1 0 0 1
234/3520xEA1 1 1 0 1 0 1 0
235/3530xEB1 1 1 0 1 0 1 1
236/3540xEC1 1 1 0 1 1 0 0
237/3550xED1 1 1 0 1 1 0 1
238/3560xEE1 1 1 0 1 1 1 0
239/3570xEF1 1 1 0 1 1 1 1
240/3600xF01 1 1 1 0 0 0 0
241/3610xF11 1 1 1 0 0 0 1
242/3620xF21 1 1 1 0 0 1 0
243/3630xF31 1 1 1 0 0 1 1
244/3640xF41 1 1 1 0 1 0 0
245/3650xF51 1 1 1 0 1 0 1
246/3660xF61 1 1 1 0 1 1 0
247/3670xF71 1 1 1 0 1 1 1
248/3700xF81 1 1 1 1 0 0 0
249/3710xF91 1 1 1 1 0 0 1
250/3720xFA1 1 1 1 1 0 1 0
251/3730xFB1 1 1 1 1 0 1 1
252/3740xFC1 1 1 1 1 1 0 0
253/3750xFD1 1 1 1 1 1 0 1
254/3760xFE1 1 1 1 1 1 1 0
255/3770xFF1 1 1 1 1 1 1 1

Hu: Value can be conceived of as a quantity #, and every numbering system having the inherent function of counting. The base#, #, refers to the amount of value that can be held by each decimal | point in that base-system, before the next decimal | place is introduced. For example, in base-10, the default | numbering system globally in ’22<smashing!><fbno> the next decimal point is added after the 10th count, from 0 #defd, ie <first>0, 1, 2, 3, 4, 5, 6, 7, 8, <tenth>9, followed by 10, a numeral that now contains 2 decimal places. In a binary, or base-2 system, the next decimal point is added after the 2nd count, ie <first>0, <second>1, followed by 01. In hexadecimal, the next decimal point is added after the 16th digit, and in compsci, values 10-15, inclusive, are represented by the first 6 alphabet-chars, since Arabic | numerals peak at ‘9’. [D] via cactus.io<a-r>

H2-H4S1: Converting FF to decimal:

FF is the a count to 16, performed 16 times, or 16*16=256 counts; if the count started at 0, then the resulting value # will be equal to 255, in the decimal | system.

H2-H4S2: Converting FF to binary:

FF is the a count to 16, performed 16 times, or 16*16=256 counts; in binary, a new decimal | point is added after the 2nd, then the 4th, then the 8th counts, and the total number of decimal points can be determined by log2(total-counts)<Turing!>. Therefore, if we have 256 total counts, then log2(256)=8, and there will be 8 decimal points. Moreover, since 256 is the last total-count before the total decimal points exceeds 8, all 8 rows will be filled, by 1s<Turing!>

H3S1: Base intervals as q.tum-note,intervals:

<WP.MIC-H2S135,H3S5.H4S1-H5S1><MIC.clarinet-gallery>

References:

http://cactus.io/resources/toolbox/decimal-binary-octal-hexadecimal-conversion

https://www.omnicalculator.com/math/log-2

https://en.wikipedia.org/wiki/Names_of_large_numbers


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