list the positions of the set bits in order of decreasing significance, 0-indexed so that bit position indices correspond to the exponents of powers of 2. stating the most significant bit first immediately gives the scale of the number, similar to place value words million, billion, etc. in decimal.
"decimal number two hundred one"76543210 "binary number with bits 7 or 6 or 3 or 0 set"
11001001
we need a separator word between exponents (indices), or else "20 1" is ambiguous with "21":
100000000000000000010 = 2^20 + 2^1
1000000000000000000000 = 2^21
we use the separator word "or" not "and" to avoid a problem in languages (e.g., Spanish) in which the word (say) 16 is pronounced "10 and 6". using the separator "or" is inspired by constructing binary bit masks with bitwise or.
note that "binary number with bits 0 set" is confusingly NOT 0; it is 1. "binary number with no bits set" is zero. "binary number with bits 1 set" is NOT 1 but 10 (base 2) or 2 (base 10).
always using "bits" even with only one bit set makes it slightly easier to programmatically decode the number from its words.
11001001.1100100100 "binary number with bits 7 or 6 or 3 or 0 or negative 1 or 2 or 5 or 8 set with significant zeros to negative 10"
fine structure constant: "scientific notation number with exponent base 2, exponent negative 7, mantissa binary number with bits negative 1 or 2 or 3 or 5 or 6 or 7 or 8 or 12 or 13 or 14 or 15 or 17 or 19 or 24 or 26 or 29 or 30 or 31 set with significant zeros to negative 33" = 2^-7 * (2^-1 + 2^-2 + 2^-3 + 2^-5 + 2^-6 + 2^-7 + 2^-8 + 2^-12 + 2^-13 + 2^-14 + 2^-15 + 2^-17 + 2^-19 + 2^-24 + 2^-26 + 2^-29 + 2^-30 + 2^-31). not sure if the exponent should be expressed as a binary number.
fine structure constant uncertainty (future post zdlugabl): "plus or minus scientific notation number with exponent base 2, exponent negative 7, mantissa binary number with bits negative 33 or 35 set"
previously numbers in scientific notation with exponent base 2.
0 = 0 = binary number with no bits set
1 = 1 = binary number with bits 0 set
2 = 10 = binary number with bits 1 set
3 = 11 = binary number with bits 1 or 0 set
4 = 100 = binary number with bits 2 set
5 = 101 = binary number with bits 2 or 0 set
6 = 110 = binary number with bits 2 or 1 set
7 = 111 = binary number with bits 2 or 1 or 0 set
8 = 1000 = binary number with bits 3 set
9 = 1001 = binary number with bits 3 or 0 set
10 = 1010 = binary number with bits 3 or 1 set
11 = 1011 = binary number with bits 3 or 1 or 0 set
12 = 1100 = binary number with bits 3 or 2 set
13 = 1101 = binary number with bits 3 or 2 or 0 set
14 = 1110 = binary number with bits 3 or 2 or 1 set
15 = 1111 = binary number with bits 3 or 2 or 1 or 0 set
16 = 10000 = binary number with bits 4 set
17 = 10001 = binary number with bits 4 or 0 set
18 = 10010 = binary number with bits 4 or 1 set
19 = 10011 = binary number with bits 4 or 1 or 0 set
20 = 10100 = binary number with bits 4 or 2 set
21 = 10101 = binary number with bits 4 or 2 or 0 set
22 = 10110 = binary number with bits 4 or 2 or 1 set
23 = 10111 = binary number with bits 4 or 2 or 1 or 0 set
24 = 11000 = binary number with bits 4 or 3 set
25 = 11001 = binary number with bits 4 or 3 or 0 set
26 = 11010 = binary number with bits 4 or 3 or 1 set
27 = 11011 = binary number with bits 4 or 3 or 1 or 0 set
28 = 11100 = binary number with bits 4 or 3 or 2 set
29 = 11101 = binary number with bits 4 or 3 or 2 or 0 set
30 = 11110 = binary number with bits 4 or 3 or 2 or 1 set
31 = 11111 = binary number with bits 4 or 3 or 2 or 1 or 0 set
32 = 100000 = binary number with bits 5 set
33 = 100001 = binary number with bits 5 or 0 set
34 = 100010 = binary number with bits 5 or 1 set
35 = 100011 = binary number with bits 5 or 1 or 0 set
36 = 100100 = binary number with bits 5 or 2 set
37 = 100101 = binary number with bits 5 or 2 or 0 set
38 = 100110 = binary number with bits 5 or 2 or 1 set
39 = 100111 = binary number with bits 5 or 2 or 1 or 0 set
40 = 101000 = binary number with bits 5 or 3 set
41 = 101001 = binary number with bits 5 or 3 or 0 set
42 = 101010 = binary number with bits 5 or 3 or 1 set
43 = 101011 = binary number with bits 5 or 3 or 1 or 0 set
44 = 101100 = binary number with bits 5 or 3 or 2 set
45 = 101101 = binary number with bits 5 or 3 or 2 or 0 set
46 = 101110 = binary number with bits 5 or 3 or 2 or 1 set
47 = 101111 = binary number with bits 5 or 3 or 2 or 1 or 0 set
48 = 110000 = binary number with bits 5 or 4 set
49 = 110001 = binary number with bits 5 or 4 or 0 set
50 = 110010 = binary number with bits 5 or 4 or 1 set
51 = 110011 = binary number with bits 5 or 4 or 1 or 0 set
52 = 110100 = binary number with bits 5 or 4 or 2 set
53 = 110101 = binary number with bits 5 or 4 or 2 or 0 set
54 = 110110 = binary number with bits 5 or 4 or 2 or 1 set
55 = 110111 = binary number with bits 5 or 4 or 2 or 1 or 0 set
56 = 111000 = binary number with bits 5 or 4 or 3 set
57 = 111001 = binary number with bits 5 or 4 or 3 or 0 set
58 = 111010 = binary number with bits 5 or 4 or 3 or 1 set
59 = 111011 = binary number with bits 5 or 4 or 3 or 1 or 0 set
60 = 111100 = binary number with bits 5 or 4 or 3 or 2 set
61 = 111101 = binary number with bits 5 or 4 or 3 or 2 or 0 set
62 = 111110 = binary number with bits 5 or 4 or 3 or 2 or 1 set
63 = 111111 = binary number with bits 5 or 4 or 3 or 2 or 1 or 0 set
64 = 1000000 = binary number with bits 6 set
65 = 1000001 = binary number with bits 6 or 0 set
66 = 1000010 = binary number with bits 6 or 1 set
67 = 1000011 = binary number with bits 6 or 1 or 0 set
68 = 1000100 = binary number with bits 6 or 2 set
69 = 1000101 = binary number with bits 6 or 2 or 0 set
70 = 1000110 = binary number with bits 6 or 2 or 1 set
71 = 1000111 = binary number with bits 6 or 2 or 1 or 0 set
72 = 1001000 = binary number with bits 6 or 3 set
73 = 1001001 = binary number with bits 6 or 3 or 0 set
74 = 1001010 = binary number with bits 6 or 3 or 1 set
75 = 1001011 = binary number with bits 6 or 3 or 1 or 0 set
76 = 1001100 = binary number with bits 6 or 3 or 2 set
77 = 1001101 = binary number with bits 6 or 3 or 2 or 0 set
78 = 1001110 = binary number with bits 6 or 3 or 2 or 1 set
79 = 1001111 = binary number with bits 6 or 3 or 2 or 1 or 0 set
80 = 1010000 = binary number with bits 6 or 4 set
81 = 1010001 = binary number with bits 6 or 4 or 0 set
82 = 1010010 = binary number with bits 6 or 4 or 1 set
83 = 1010011 = binary number with bits 6 or 4 or 1 or 0 set
84 = 1010100 = binary number with bits 6 or 4 or 2 set
85 = 1010101 = binary number with bits 6 or 4 or 2 or 0 set
86 = 1010110 = binary number with bits 6 or 4 or 2 or 1 set
87 = 1010111 = binary number with bits 6 or 4 or 2 or 1 or 0 set
88 = 1011000 = binary number with bits 6 or 4 or 3 set
89 = 1011001 = binary number with bits 6 or 4 or 3 or 0 set
90 = 1011010 = binary number with bits 6 or 4 or 3 or 1 set
91 = 1011011 = binary number with bits 6 or 4 or 3 or 1 or 0 set
92 = 1011100 = binary number with bits 6 or 4 or 3 or 2 set
93 = 1011101 = binary number with bits 6 or 4 or 3 or 2 or 0 set
94 = 1011110 = binary number with bits 6 or 4 or 3 or 2 or 1 set
95 = 1011111 = binary number with bits 6 or 4 or 3 or 2 or 1 or 0 set
96 = 1100000 = binary number with bits 6 or 5 set
97 = 1100001 = binary number with bits 6 or 5 or 0 set
98 = 1100010 = binary number with bits 6 or 5 or 1 set
99 = 1100011 = binary number with bits 6 or 5 or 1 or 0 set
100 = 1100100 = binary number with bits 6 or 5 or 2 set
101 = 1100101 = binary number with bits 6 or 5 or 2 or 0 set
102 = 1100110 = binary number with bits 6 or 5 or 2 or 1 set
103 = 1100111 = binary number with bits 6 or 5 or 2 or 1 or 0 set
104 = 1101000 = binary number with bits 6 or 5 or 3 set
105 = 1101001 = binary number with bits 6 or 5 or 3 or 0 set
106 = 1101010 = binary number with bits 6 or 5 or 3 or 1 set
107 = 1101011 = binary number with bits 6 or 5 or 3 or 1 or 0 set
108 = 1101100 = binary number with bits 6 or 5 or 3 or 2 set
109 = 1101101 = binary number with bits 6 or 5 or 3 or 2 or 0 set
110 = 1101110 = binary number with bits 6 or 5 or 3 or 2 or 1 set
111 = 1101111 = binary number with bits 6 or 5 or 3 or 2 or 1 or 0 set
112 = 1110000 = binary number with bits 6 or 5 or 4 set
113 = 1110001 = binary number with bits 6 or 5 or 4 or 0 set
114 = 1110010 = binary number with bits 6 or 5 or 4 or 1 set
115 = 1110011 = binary number with bits 6 or 5 or 4 or 1 or 0 set
116 = 1110100 = binary number with bits 6 or 5 or 4 or 2 set
117 = 1110101 = binary number with bits 6 or 5 or 4 or 2 or 0 set
118 = 1110110 = binary number with bits 6 or 5 or 4 or 2 or 1 set
119 = 1110111 = binary number with bits 6 or 5 or 4 or 2 or 1 or 0 set
120 = 1111000 = binary number with bits 6 or 5 or 4 or 3 set
121 = 1111001 = binary number with bits 6 or 5 or 4 or 3 or 0 set
122 = 1111010 = binary number with bits 6 or 5 or 4 or 3 or 1 set
123 = 1111011 = binary number with bits 6 or 5 or 4 or 3 or 1 or 0 set
124 = 1111100 = binary number with bits 6 or 5 or 4 or 3 or 2 set
125 = 1111101 = binary number with bits 6 or 5 or 4 or 3 or 2 or 0 set
126 = 1111110 = binary number with bits 6 or 5 or 4 or 3 or 2 or 1 set
127 = 1111111 = binary number with bits 6 or 5 or 4 or 3 or 2 or 1 or 0 set
128 = 10000000 = binary number with bits 7 set
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