Number bases

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

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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 | edit source]

* Number bases/Introduction
* Wikipedia's List of Numeral Systems
* Wiktionary Appendex on Names for Number Bases
* Names of Bases on The Math Forum
* Names of Number Bases by a "Radicologist"
* Conversion List for Binary, Octal, and Hexadecimal Numbers
* Table of Bases on Wikipedia