Number bases

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Positive integers in decimal and in binary bases of the n-th power of two (2n).

  • decimal: base ten (10)
  • binary: base two (2 = 21, first power of two)
  • quaternary: base four (4 = 22, second power of two)
  • octal: base eight (8 = 23, third power of two)
  • hexadecimal: base sixteen (16 = 24, fourth power of two)
  • duotrigesimal: base thirty-two (32 = 25, fifth power of two)
  • tetrasexagesimal: base sixty-four (64 = 26, sixth power of two)
  • centoctovigesimal: base 128 = 27 (seventh power of two)
  • ducentohexaquinquagesimal: base 256 = 28 (eighth power of two)
  • quingentoduodecimal: base 512 = 29 (ninth power of two)
  • milletetravigesimal: base 1024 = 210 (tenth power of two)
  • dumilloctoquadragesimal: base 2048 = 211 (eleventh power of two)
  • quadramillehexanonagesimal: base 4096 = 212 (twelfth power of two)

Note that bases 63 and higher include arbitrary characters for numerals (since the number of Hindu-Arabic numerals, plus Roman uppercase and Roman lowercase letters, equals 62 characters). Base 64 is presented here using the additional two characters of "-" (hyphen) and "_" (underscore) from the "URL- and Filename-Safe Base-64 Alphabet" of Internet Engineering Task Force (IETF) RFC 4648.

base 10 base 2 base 4 base 8 base 16 base 32 base 64
0 0 0 0 0 0 0
1 1 1 1 1 1 1
2 10 2 2 2 2 2
3 11 3 3 3 3 3
4 100 10 4 4 4 4
5 101 11 5 5 5 5
6 110 12 6 6 6 6
7 111 13 7 7 7 7
8 1000 20 10 8 8 8
9 1001 21 11 9 9 9
10 1010 22 12 A A A
11 1011 23 13 B B B
12 1100 30 14 C C C
13 1101 31 15 D D D
14 1110 32 16 E E E
15 1111 33 17 F F F
16 10000 100 20 10 G G
17 10001 101 21 11 H H
18 10010 102 22 12 I I
19 10011 103 23 13 J J
20 10100 110 24 14 K K
21 10101 111 25 15 L L
22 10110 112 26 16 M M
23 10111 113 27 17 N N
24 11000 120 30 18 O O
25 11001 121 31 19 P P
26 11010 122 32 1A Q Q
27 11011 123 33 1B R R
28 11100 130 34 1C S S
29 11101 131 35 1D T T
30 11110 132 36 1E U U
31 11111 133 37 1F V V
32 100000 200 40 20 10 W
33 100001 201 41 21 11 X
34 100010 202 42 22 12 Y
35 100011 203 43 23 13 Z
36 100100 210 44 24 14 a
37 100101 211 45 25 15 b
38 100110 212 46 26 16 c
39 100111 213 47 27 17 d
40 101000 220 50 28 18 e
41 101001 221 51 29 19 f
42 101010 222 52 2A 1A g
43 101011 223 53 2B 1B h
44 101100 230 54 2C 1C i
45 101101 231 55 2D 1D j
46 101110 232 56 2E 1E k
47 101111 233 57 2F 1F l
48 110000 300 60 30 1G m
49 110001 301 61 31 1H n
50 110010 302 62 32 1I o
51 110011 303 63 33 1J p
52 110100 310 64 34 1K q
53 110101 311 65 35 1L r
54 110110 312 66 36 1M s
55 110111 313 67 37 1N t
56 111000 320 70 38 1O u
57 111001 321 71 39 1P v
58 111010 322 72 3A 1Q w
59 111011 323 73 3B 1R x
60 111100 330 74 3C 1S y
61 111101 331 75 3D 1T z
62 111110 332 76 3E 1U -
63 111111 333 77 3F 1V _
64 1000000 1000 100 40 20 10
65 1000001 1001 101 41 21 11
66 1000010 1002 102 42 22 12
67 1000011 1003 103 43 23 13
68 1000100 1010 104 44 24 14
69 1000101 1011 105 45 25 15
70 1000110 1012 106 46 26 16
71 1000111 1013 107 47 27 17
72 1001000 1020 110 48 28 18
73 1001001 1021 111 49 29 19
74 1001010 1022 112 4A 2A 1A
75 1001011 1023 113 4B 2B 1B
76 1001100 1030 114 4C 2C 1C
77 1001101 1031 115 4D 2D 1D
78 1001110 1032 116 4E 2E 1E
79 1001111 1033 117 4F 2F 1F
80 1010000 1100 120 50 2G 1G
81 1010001 1101 121 51 2H 1H
82 1010010 1102 122 52 2I 1I
83 1010011 1103 123 53 2J 1J
84 1010100 1110 124 54 2K 1K
85 1010101 1111 125 55 2L 1L
86 1010110 1112 126 56 2M 1M
87 1010111 1113 127 57 2N 1N
88 1011000 1120 130 58 2O 1O
89 1011001 1121 131 59 2P 1P
90 1011010 1122 132 5A 2Q 1Q
91 1011011 1123 133 5B 2R 1R
92 1011100 1130 134 5C 2S 1S
93 1011101 1131 135 5D 2T 1T
94 1011110 1132 136 5E 2U 1U
95 1011111 1133 137 5F 2V 1V
96 1100000 1200 140 60 30 1W
97 1100001 1201 141 61 31 1X
98 1100010 1202 142 62 32 1Y
99 1100011 1203 143 63 33 1Z
100 1100100 1210 144 64 34 1a
101 1100101 1211 145 65 35 1b
102 1100110 1212 146 66 36 1c
103 1100111 1213 147 67 37 1d
104 1101000 1220 150 68 38 1e
105 1101001 1221 151 69 39 1f
106 1101010 1222 152 6A 3A 1g
107 1101011 1223 153 6B 3B 1h
108 1101100 1230 154 6C 3C 1i
109 1101101 1231 155 6D 3D 1j
110 1101110 1232 156 6E 3E 1k
111 1101111 1233 157 6F 3F 1l
112 1110000 1300 160 70 3G 1m
113 1110001 1301 161 71 3H 1n
114 1110010 1302 162 72 3I 1o
115 1110011 1303 163 73 3J 1p
116 1110100 1310 164 74 3K 1q
117 1110101 1311 165 75 3L 1r
118 1110110 1312 166 76 3M 1s
119 1110111 1313 167 77 3N 1t
120 1111000 1320 170 78 3O 1u
121 1111001 1321 171 79 3P 1v
122 1111010 1322 172 7A 3Q 1w
123 1111011 1323 173 7B 3R 1x
124 1111100 1330 174 7C 3S 1y
125 1111101 1331 175 7D 3T 1z
126 1111110 1332 176 7E 3U 1-
127 1111111 1333 177 7F 3V 1_
128 10000000 2000 200 80 40 20
129 10000001 2001 201 81 41 21
130 10000010 2002 202 82 42 22
131 10000011 2003 203 83 43 23
132 10000100 2010 204 84 44 24
133 10000101 2011 205 85 45 25
134 10000110 2012 206 86 46 26
135 10000111 2013 207 87 47 27
136 10001000 2020 210 88 48 28
137 10001001 2021 211 89 49 29
138 10001010 2022 212 8A 4A 2A
139 10001011 2023 213 8B 4B 2B
140 10001100 2030 214 8C 4C 2C
141 10001101 2031 215 8D 4D 2D
142 10001110 2032 216 8E 4E 2E
143 10001111 2033 217 8F 4F 2F
144 10010000 2100 220 90 4G 2G
145 10010001 2101 221 91 4H 2H
146 10010010 2102 222 92 4I 2I
147 10010011 2103 223 93 4J 2J
148 10010100 2110 224 94 4K 2K
149 10010101 2111 225 95 4L 2L
150 10010110 2112 226 96 4M 2M
151 10010111 2113 227 97 4N 2N
152 10011000 2120 230 98 4O 2O
153 10011001 2121 231 99 4P 2P
154 10011010 2122 232 9A 4Q 2Q
155 10011011 2123 233 9B 4R 2R
156 10011100 2130 234 9C 4S 2S
157 10011101 2131 235 9D 4T 2T
158 10011110 2132 236 9E 4U 2U
159 10011111 2133 237 9F 4V 2V
160 10100000 2200 240 A0 50 2W
161 10100001 2201 241 A1 51 2X
162 10100010 2202 242 A2 52 2Y
163 10100011 2203 243 A3 53 2Z
164 10100100 2210 244 A4 54 2a
165 10100101 2211 245 A5 55 2b
166 10100110 2212 246 A6 56 2c
167 10100111 2213 247 A7 57 2d
168 10101000 2220 250 A8 58 2e
169 10101001 2221 251 A9 59 2f
170 10101010 2222 252 AA 5A 2g
171 10101011 2223 253 AB 5B 2h
172 10101100 2230 254 AC 5C 2i
173 10101101 2231 255 AD 5D 2j
174 10101110 2232 256 AE 5E 2k
175 10101111 2233 257 AF 5F 2l
176 10110000 2300 260 B0 5G 2m
177 10110001 2301 261 B1 5H 2n
178 10110010 2302 262 B2 5I 2o
179 10110011 2303 263 B3 5J 2p
180 10110100 2310 264 B4 5K 2q
181 10110101 2311 265 B5 5L 2r
182 10110110 2312 266 B6 5M 2s
183 10110111 2313 267 B7 5N 2t
184 10111000 2320 270 B8 5O 2u
185 10111001 2321 271 B9 5P 2v
186 10111010 2322 272 BA 5Q 2w
187 10111011 2323 273 BB 5R 2x
188 10111100 2330 274 BC 5S 2y
189 10111101 2331 275 BD 5T 2z
190 10111110 2332 276 BE 5U 2-
191 10111111 2333 277 BF 5V 2_
192 11000000 3000 300 C0 60 30
193 11000001 3001 301 C1 61 31
194 11000010 3002 302 C2 62 32
195 11000011 3003 303 C3 63 33
196 11000100 3010 304 C4 64 34
197 11000101 3011 305 C5 65 35
198 11000110 3012 306 C6 66 36
199 11000111 3013 307 C7 67 37
200 11001000 3020 310 C8 68 38
201 11001001 3021 311 C9 69 39
202 11001010 3022 312 CA 6A 3A
203 11001011 3023 313 CB 6B 3B
204 11001100 3030 314 CC 6C 3C
205 11001101 3031 315 CD 6D 3D
206 11001110 3032 316 CE 6E 3E
207 11001111 3033 317 CF 6F 3F
208 11010000 3100 320 D0 6G 3G
209 11010001 3101 321 D1 6H 3H
210 11010010 3102 322 D2 6I 3I
211 11010011 3103 323 D3 6J 3J
212 11010100 3110 324 D4 6K 3K
213 11010101 3111 325 D5 6L 3L
214 11010110 3112 326 D6 6M 3M
215 11010111 3113 327 D7 6N 3N
216 11011000 3120 330 D8 6O 3O
217 11011001 3121 331 D9 6P 3P
218 11011010 3122 332 DA 6Q 3Q
219 11011011 3123 333 DB 6R 3R
220 11011100 3130 334 DC 6S 3S
221 11011101 3131 335 DD 6T 3T
222 11011110 3132 336 DE 6U 3U
223 11011111 3133 337 DF 6V 3V
224 11100000 3200 340 E0 70 3W
225 11100001 3201 341 E1 71 3X
226 11100010 3202 342 E2 72 3Y
227 11100011 3203 343 E3 73 3Z
228 11100100 3210 344 E4 74 3a
229 11100101 3211 345 E5 75 3b
230 11100110 3212 346 E6 76 3c
231 11100111 3213 347 E7 77 3d
232 11101000 3220 350 E8 78 3e
233 11101001 3221 351 E9 79 3f
234 11101010 3222 352 EA 7A 3g
235 11101011 3223 353 EB 7B 3h
236 11101100 3230 354 EC 7C 3i
237 11101101 3231 355 ED 7D 3j
238 11101110 3232 356 EE 7E 3k
239 11101111 3233 357 EF 7F 3l
240 11110000 3300 360 F0 7G 3m
241 11110001 3301 361 F1 7H 3n
242 11110010 3302 362 F2 7I 3o
243 11110011 3303 363 F3 7J 3p
244 11110100 3310 364 F4 7K 3q
245 11110101 3311 365 F5 7L 3r
246 11110110 3312 366 F6 7M 3s
247 11110111 3313 367 F7 7N 3t
248 11111000 3320 370 F8 7O 3u
249 11111001 3321 371 F9 7P 3v
250 11111010 3322 372 FA 7Q 3w
251 11111011 3323 373 FB 7R 3x
252 11111100 3330 374 FC 7S 3y
253 11111101 3331 375 FD 7T 3z
254 11111110 3332 376 FE 7U 3-
255 11111111 3333 377 FF 7V 3_
256 100000000 10000 400 100 80 40

Additional Resources[edit]