For quick conversions, feel free to use the conversion table.

Published: February 19, 2024.

## Hex to Decimal and Decimal to Hex Conversion

Note: Conversions are possible only for integer numbers since converting "fractional parts" may be very challenging due to the nature of floating-point arithmetic and representation; there might be precision issues, especially with very long fractional parts, so to avoid such issues, these two converters are limited only to integer numbers.

## Binary, Octal, Decimal, and Hexadecimal Numbers Conversion Table

The following conversion table contains binary, octal, decimal, and hexadecimal numbers for fast and easy conversion.

 Binary Numbers Octal Numbers Decimal Numbers Hexadecimal Numbers 00000000 0 0 0 00000001 1 1 1 00000010 2 2 2 00000011 3 3 3 00000100 4 4 4 00000101 5 5 5 00000110 6 6 6 00000111 7 7 7 00001000 10 8 8 00001001 11 9 9 00001010 12 10 A 00001011 13 11 B 00001100 14 12 C 00001101 15 13 D 00001110 16 14 E 00001111 17 15 F 00010000 20 16 10 00010001 21 17 11 00010010 22 18 12 00010011 23 19 13 00010100 24 20 14 00010101 25 21 15 00010110 26 22 16 00010111 27 23 17 00011000 30 24 18 00011001 31 25 19 00011010 32 26 1A 00011011 33 27 1B 00011100 34 28 1C 00011101 35 29 1D 00011110 36 30 1E 00011111 37 31 1F 00100000 40 32 20 00100001 41 33 21 00100010 42 34 22 00100011 43 35 23 00100100 44 36 24 00100101 45 37 25 00100110 46 38 26 00100111 47 39 27 00101000 50 40 28 00101001 51 41 29 00101010 52 42 2A 00101011 53 43 2B 00101100 54 44 2C 00101101 55 45 2D 00101110 56 46 2E 00101111 57 47 2F 00110000 60 48 30 00110001 61 49 31 00110010 62 50 32 00110011 63 51 33 00110100 64 52 34 00110101 65 53 35 00110110 66 54 36 00110111 67 55 37 00111000 70 56 38 00111001 71 57 39 00111010 72 58 3A 00111011 73 59 3B 00111100 74 60 3C 00111101 75 61 3D 00111110 76 62 3E 00111111 77 63 3F 01000000 100 64 40 01000001 101 65 41 01000010 102 66 42 01000011 103 67 43 01000100 104 68 44 01000101 105 69 45 01000110 106 70 46 01000111 107 71 47 01001000 110 72 48 01001001 111 73 49 01001010 112 74 4A 01001011 113 75 4B 01001100 114 76 4C 01001101 115 77 4D 01001110 116 78 4E 01001111 117 79 4F 01010000 120 80 50 01010001 121 81 51 01010010 122 82 52 01010011 123 83 53 01010100 124 84 54 01010101 125 85 55 01010110 126 86 56 01010111 127 87 57 01011000 130 88 58 01011001 131 89 59 01011010 132 90 5A 01011011 133 91 5B 01011100 134 92 5C 01011101 135 93 5D 01011110 136 94 5E 01011111 137 95 5F 01100000 140 96 60 01100001 141 97 61 01100010 142 98 62 01100011 143 99 63 01100100 144 100 64 01100101 145 101 65 01100110 146 102 66 01100111 147 103 67 01101000 150 104 68 01101001 151 105 69 01101010 152 106 6A 01101011 153 107 6B 01101100 154 108 6C 01101101 155 109 6D 01101110 156 110 6E 01101111 157 111 6F 01110000 160 112 70 01110001 161 113 71 01110010 162 114 72 01110011 163 115 73 01110100 164 116 74 01110101 165 117 75 01110110 166 118 76 01110111 167 119 77 01111000 170 120 78 01111001 171 121 79 01111010 172 122 7A 01111011 173 123 7B 01111100 174 124 7C 01111101 175 125 7D 01111110 176 126 7E 01111111 177 127 7F 10000000 200 128 80 10000001 201 129 81 10000010 202 130 82 10000011 203 131 83 10000100 204 132 84 10000101 205 133 85 10000110 206 134 86 10000111 207 135 87 10001000 210 136 88 10001001 211 137 89 10001010 212 138 8A 10001011 213 139 8B 10001100 214 140 8C 10001101 215 141 8D 10001110 216 142 8E 10001111 217 143 8F 10010000 220 144 90 10010001 221 145 91 10010010 222 146 92 10010011 223 147 93 10010100 224 148 94 10010101 225 149 95 10010110 226 150 96 10010111 227 151 97 10011000 230 152 98 10011001 231 153 99 10011010 232 154 9A 10011011 233 155 9B 10011100 234 156 9C 10011101 235 157 9D 10011110 236 158 9E 10011111 237 159 9F 10100000 240 160 A0 10100001 241 161 A1 10100010 242 162 A2 10100011 243 163 A3 10100100 244 164 A4 10100101 245 165 A5 10100110 246 166 A6 10100111 247 167 A7 10101000 250 168 A8 10101001 251 169 A9 10101010 252 170 AA 10101011 253 171 AB 10101100 254 172 AC 10101101 255 173 AD 10101110 256 174 AE 10101111 257 175 AF 10110000 260 176 B0 10110001 261 177 B1 10110010 262 178 B2 10110011 263 179 B3 10110100 264 180 B4 10110101 265 181 B5 10110110 266 182 B6 10110111 267 183 B7 10111000 270 184 B8 10111001 271 185 B9 10111010 272 186 BA 10111011 273 187 BB 10111100 274 188 BC 10111101 275 189 BD 10111110 276 190 BE 10111111 277 191 BF 11000000 300 192 C0 11000001 301 193 C1 11000010 302 194 C2 11000011 303 195 C3 11000100 304 196 C4 11000101 305 197 C5 11000110 306 198 C6 11000111 307 199 C7 11001000 310 200 C8 11001001 311 201 C9 11001010 312 202 CA 11001011 313 203 CB 11001100 314 204 CC 11001101 315 205 CD 11001110 316 206 CE 11001111 317 207 CF 11010000 320 208 D0 11010001 321 209 D1 11010010 322 210 D2 11010011 323 211 D3 11010100 324 212 D4 11010101 325 213 D5 11010110 326 214 D6 11010111 327 215 D7 11011000 330 216 D8 11011001 331 217 D9 11011010 332 218 DA 11011011 333 219 DB 11011100 334 220 DC 11011101 335 221 DD 11011110 336 222 DE 11011111 337 223 DF 11100000 340 224 E0 11100001 341 225 E1 11100010 342 226 E2 11100011 343 227 E3 11100100 344 228 E4 11100101 345 229 E5 11100110 346 230 E6 11100111 347 231 E7 11101000 350 232 E8 11101001 351 233 E9 11101010 352 234 EA 11101011 353 235 EB 11101100 354 236 EC 11101101 355 237 ED 11101110 356 238 EE 11101111 357 239 EF 11110000 360 240 F0 11110001 361 241 F1 11110010 362 242 F2 11110011 363 243 F3 11110100 364 244 F4 11110101 365 245 F5 11110110 366 246 F6 11110111 367 247 F7 11111000 370 248 F8 11111001 371 249 F9 11111010 372 250 FA 11111011 373 251 FB 11111100 374 252 FC 11111101 375 253 FD 11111110 376 254 FE 11111111 377 255 FF

## Brief History of Decimal and Hexadecimal Number Systems

The decimal and hexadecimal number systems play crucial roles in the fields of mathematics, computing, and digital electronics. Their origins and development underscore humanity's evolving relationship with numbers and technology. Here's a concise exploration of their histories.

### The Decimal System: A Universal Standard

The decimal number system, also known as base-10, has been the cornerstone of most human numerical systems due to the ten fingers on human hands, which naturally influenced counting and numerical representation.

Its origins trace back to ancient civilizations, with evidence of its use in ancient Egypt, Mesopotamia, and among the Mayans.

• Early Records: The earliest known usage of a decimal system dates back to around 3100 BCE in Egypt. The system was hieroglyphic, with separate symbols for 1, 10, 100, and so on, which were combined to represent any number.
• Adoption and Evolution: The concept of zero as a number, crucial for the decimal system's development, was first recorded in the 7th century by Indian mathematicians. The full decimal positional system, which uses zero and place values, was developed in India by the 9th century, spreading to the Islamic world and eventually to Europe through translations of Arabic texts.
• Global Standardization: By the 17th century, the decimal system was widely used in Europe, thanks in part to its promotion by mathematicians like Simon Stevin, who wrote "De Thiende" ("The Tenth"), advocating for its use in daily life. The system's simplicity and efficiency facilitated its adoption as the international standard for trade, science, and mathematics.

### The Hexadecimal System: From Ancient to Modern Computing

The hexadecimal system, or base-16, uses sixteen symbols to represent values (0-9 and A-F). While not as intuitive as the decimal system for everyday human use, its efficiency in digital computing has made it indispensable.

• Ancient Uses: Evidence of base-16 systems dates back to the 3rd millennium BCE with the Elamites of ancient Iran, who used a semi-hexadecimal system for their weights and measures. However, the system was not fully developed or widely adopted beyond these specific applications.
• Rise in Computing: The hexadecimal system gained prominence with the advent of modern computing. In the mid-20th century, as engineers worked on digital circuits and early computers, they found that hexadecimal provided a more straightforward method than decimal for representing binary numbers (the base-2 system directly underlying computing processes). A single hexadecimal digit can represent four binary digits (bits), making it efficient for programming, debugging, and understanding machine-level data.
• Current Applications: Today, the hexadecimal system is ubiquitous in computing and digital electronics. It's used in programming to denote memory addresses, color codes in web design (e.g., #FFFFFF for white), and much more, due to its direct correlation with binary data and ease of conversion.

The decimal system's roots in ancient counting practices and its development over millennia highlight humanity's innate drive to quantify and understand the world.

In contrast, the hexadecimal system's evolution reflects the pragmatic needs of modern technology, offering a bridge between the binary language of computers and the more familiar decimal system used by humans.

Together, these systems exemplify the diverse ways in which cultures and technology shape our approaches to numbers and mathematics.