Binary, Octal and Hexadecimal Numbers
Decimal, binary, octal and hexadecimal numbers.
Denary (base 10) | Hexadecimal (base 16) | Octal (base 8) | Binary (base 2) |
---|---|---|---|
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
0 1 2 3 4 5 6 7 8 9 A B C D E F |
000 001 002 003 004 005 006 007 010 011 012 013 014 015 016 017 |
00000000 00000001 00000010 00000011 00000100 00000101 00000110 00000111 00001000 00001001 00001010 00001011 00001100 00001101 00001110 00001111 |
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 |
10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F |
020 021 022 023 024 025 026 027 030 031 032 033 034 035 036 037 |
00010000 00010001 00010010 00010011 00010100 00010101 00010110 00010111 00011000 00011001 00011010 00011011 00011100 00011101 00011110 00011111 |
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 |
20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F |
040 041 042 043 044 045 046 047 050 051 052 053 054 055 056 057 |
00100000 00100001 00100010 00100011 00100100 00100101 00100110 00100111 00101000 00101001 00101010 00101011 00101100 00101101 00101110 00101111 |
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 |
30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F |
060 061 062 063 064 065 066 067 070 071 072 073 074 075 076 077 |
00110000 00110001 00110010 00110011 00110100 00110101 00110110 00110111 00111000 00111001 00111010 00111011 00111100 00111101 00111110 00111111 |
64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 |
40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F |
100 101 102 103 104 105 106 107 110 111 112 113 114 115 116 117 |
01000000 01000001 01000010 01000011 01000100 01000101 01000110 01000111 01001000 01001001 01001010 01001011 01001100 01001101 01001110 01001111 |
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 |
50 51 52 53 54 55 56 57 58 59 5A 5B 5C 5D 5E 5F |
120 121 122 123 124 125 126 127 130 131 132 133 134 135 136 137 |
01010000 01010001 01010010 01010011 01010100 01010101 01010110 01010111 01011000 01011001 01011010 01011011 01011100 01011101 01011110 01011111 |
96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 |
60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F |
140 141 142 143 144 145 146 147 150 151 152 153 154 155 156 157 |
01100000 01100001 01100010 01100011 01100100 01100101 01100110 01100111 01101000 01101001 01101010 01101011 01101100 01101101 01101110 01101111 |
112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 |
70 71 72 73 74 75 76 77 78 79 7A 7B 7C 7D 7E 7F |
160 161 162 163 164 165 166 167 170 171 172 173 174 175 176 177 |
01110000 01110001 01110010 01110011 01110100 01110101 01110110 01110111 01111000 01111001 01111010 01111011 01111100 01111101 01111110 01111111 |
128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 |
80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F |
200 201 202 203 204 205 206 207 210 211 212 213 214 215 216 217 |
10000000 10000001 10000010 10000011 10000100 10000101 10000110 10000111 10001000 10001001 10001010 10001011 10001100 10001101 10001110 10001111 |
144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 |
90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F |
220 221 222 223 224 225 226 227 230 231 232 233 234 235 236 237 |
10010000 10010001 10010010 10010011 10010100 10010101 10010110 10010111 10011000 10011001 10011010 10011011 10011100 10011101 10011110 10011111 |
160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 |
A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 AA AB AC AD AE AF |
240 241 242 243 244 245 246 247 250 251 252 253 254 255 256 257 |
10100000 10100001 10100010 10100011 10100100 10100101 10100110 10100111 10101000 10101001 10101010 10101011 10101100 10101101 10101110 10101111 |
176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 |
B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 BA BB BC BD BE BF |
260 261 262 263 264 265 266 267 270 271 272 273 274 275 276 277 |
10110000 10110001 10110010 10110011 10110100 10110101 10110110 10110111 10111000 10111001 10111010 10111011 10111100 10111101 10111110 10111111 |
192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 |
C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 CA CB CC CD CE CF |
300 301 302 303 304 305 306 307 310 311 312 313 314 315 316 317 |
11000000 11000001 11000010 11000011 11000100 11000101 11000110 11000111 11001000 11001001 11001010 11001011 11001100 11001101 11001110 11001111 |
208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 |
D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 DA DB DC DD DE DF |
320 321 322 323 324 325 326 327 330 331 332 333 334 335 336 337 |
11010000 11010001 11010010 11010011 11010100 11010101 11010110 11010111 11011000 11011001 11011010 11011011 11011100 11011101 11011110 11011111 |
224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 |
E0 E1 E2 E3 E4 E5 E6 E7 E8 E9 EA EB EC ED EE EF |
340 341 342 343 344 345 346 347 350 351 352 353 354 355 356 357 |
11100000 11100001 11100010 11100011 11100100 11100101 11100110 11100111 11101000 11101001 11101010 11101011 11101100 11101101 11101110 11101111 |
240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 |
F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 FA FB FC FD FE FF |
360 361 362 363 364 365 366 367 370 371 372 373 374 375 376 377 |
11110000 11110001 11110010 11110011 11110100 11110101 11110110 11110111 11111000 11111001 11111010 11111011 11111100 11111101 11111110 11111111 |
- Denary - the Denary number system (decimal) is a base 10 number system used by people with 10 unique digits 0 to 9
- Octal - the Octal numeral system (Oct) is a base 8 number system that use the digits 0 to 7
- Hexadecimal - the Hexadecimal number system (Hex) is a base 16 number system using number 0 - 9 and letters A - F
- Binary - the Binary number system (Bin) is a base 2 number system using number 1 and 0
Binary to Decimal Conversion
The decimal numbering system has a radix of 10.
A denary (decimal) number can be expressed as
10.5
= 1 x 101 + 0 x 100 + 5 x 10-1
The binary numbering system has a radix of 2.
A binary number can be expressed as
1011.1
= 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20 + 1 x 2-1
= 8 + 0 + 1 + 1 + 1/2
= 10.5
The distinction binary vs. denary numbers can be indicated as
1011.12 = 10.510
Hexadecimal to Decimal Conversion
The hexadecimal numbering system has a radix of 16 and uses the following 16 distinct digits
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F
'A' corresponds to 10 in the denary system, B to 11, C to 12 ...
A hexadecimal number can be expressed as
1BC
= 1 x 162 + C x 161 + F x 160
= 1 x 162 + 12 x 161 + 15 x 160
= 256 + 192 + 15
= 463
Related Topics
-
Mathematics
Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.
Related Documents
-
ASCII Codes
ASCII codes and characters. -
Binary Adding, Subtraction, Multiplicaton and Division
Adding, subtracting, multiplying and dividing binary numbers. -
Binary to Decimal, Hexadecimal and ASCII Converter
Convert between binary, decimal and hexadecimal numbers. -
Binomial Theorem
Binomial theorem for positive integers. -
Boolean Algebra
Logic functions where the values of variables are true (1) or false (0). -
Data Types
Signed vs. unsigned datatypes. -
Decimal System Prefixes
Prefix names used for multiples and submultiples units. -
Designation of Large Numbers
Designation of large number in US vs. other countries. -
HTML Color Codes
Safe html color codes. -
Numbers - Square, Cube, Square Root and Cubic Root Calculator
Calculate square, cube, square root and cubic root. Values tabulated for numbers ranging 1 to 100. -
Prefixes for Binary Multiplies
IEC International Standard names and symbols -
Prime Numbers
Prime numbers up to 1000. -
Roman Numerals
Roman numerals are a combinations of seven letters.