Number bases
Appearance
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 |