Base-16 representation: Difference between revisions
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#REDIRECT [[Base_16_numbers_needing_a_to_f]] |
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{{Draft task}} |
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;Task: |
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Show in decimal notation all positive integers (less than '''501''') which, when converted to hexadecimal notation, cannot be written without using at least one non-decimal digit ('a' to 'f'). |
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<br><br> |
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=={{header|C++}}== |
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<lang cpp>#include <iomanip> |
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#include <iostream> |
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// Returns true if the hexadecimal representation of n contains at least one |
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// non-decimal digit. |
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bool nondecimal(unsigned int n) { |
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for (; n > 0; n >>= 4) { |
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if ((n & 0xF) > 9) |
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return true; |
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} |
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return false; |
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} |
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int main() { |
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unsigned int count = 0; |
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for (unsigned int n = 0; n < 501; ++n) { |
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if (nondecimal(n)) { |
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++count; |
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std::cout << std::setw(3) << n << (count % 15 == 0 ? '\n' : ' '); |
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} |
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} |
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std::cout << "\n\n" << count << " such numbers found.\n"; |
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}</lang> |
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{{out}} |
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<pre> |
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10 11 12 13 14 15 26 27 28 29 30 31 42 43 44 |
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45 46 47 58 59 60 61 62 63 74 75 76 77 78 79 |
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90 91 92 93 94 95 106 107 108 109 110 111 122 123 124 |
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125 126 127 138 139 140 141 142 143 154 155 156 157 158 159 |
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160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 |
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175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 |
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190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 |
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205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 |
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220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 |
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235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 |
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250 251 252 253 254 255 266 267 268 269 270 271 282 283 284 |
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285 286 287 298 299 300 301 302 303 314 315 316 317 318 319 |
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330 331 332 333 334 335 346 347 348 349 350 351 362 363 364 |
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365 366 367 378 379 380 381 382 383 394 395 396 397 398 399 |
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410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 |
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425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 |
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440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 |
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455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 |
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470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 |
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485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 |
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500 |
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301 such numbers found. |
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</pre> |
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=={{header|Factor}}== |
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The <code>non-decimal?</code> word is a translation of C++'s <code>nondecimal</code> function. Having multiple exit points in a word is not very efficient (yet?) in Factor, so I've tweaked it to have one exit point at the end. |
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{{works with|Factor|0.99 2021-02-05}} |
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<lang factor>USING: combinators.short-circuit formatting grouping io kernel |
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lists lists.lazy math prettyprint sequences ; |
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! Returns t if the hexadecimal representation of n contains a |
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! non-decimal digit. |
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: non-decimal? ( n -- ? ) |
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[ dup { [ 0xF bitand 10 < ] [ 0 > ] } 1&& ] |
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[ -4 shift ] while zero? not ; |
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1 lfrom [ non-decimal? ] lfilter [ 501 < ] lwhile |
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list>array dup 15 group [ [ "%3d " printf ] each nl ] each nl |
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length pprint " such numbers found." print</lang> |
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{{out}} |
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<pre> |
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10 11 12 13 14 15 26 27 28 29 30 31 42 43 44 |
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45 46 47 58 59 60 61 62 63 74 75 76 77 78 79 |
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90 91 92 93 94 95 106 107 108 109 110 111 122 123 124 |
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125 126 127 138 139 140 141 142 143 154 155 156 157 158 159 |
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160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 |
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175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 |
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190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 |
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205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 |
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220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 |
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235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 |
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250 251 252 253 254 255 266 267 268 269 270 271 282 283 284 |
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285 286 287 298 299 300 301 302 303 314 315 316 317 318 319 |
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330 331 332 333 334 335 346 347 348 349 350 351 362 363 364 |
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365 366 367 378 379 380 381 382 383 394 395 396 397 398 399 |
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410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 |
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425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 |
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440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 |
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455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 |
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470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 |
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485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 |
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500 |
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301 such numbers found. |
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</pre> |
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=={{header|Raku}}== |
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Yet another poorly specced, poorly named, trivial task. |
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How many integers in base 16 cannot be written without using a hexadecimal digit? All of them. Or none of them. |
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Base 16 is not hexadecimal. Hexadecimal is ''an implementation'' of base 16. |
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<lang perl6>use Base::Any; |
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set-digits <⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕>; |
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say (7**35).&to-base(16); |
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# ⑭㉒⑱⑩⑰⑰⑳⑮⑱⑳⑩⑳⑱㉒㉑⑰㉒⑫⑭⑲⑯⑩㉔⑮⑰</lang> |
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How many of those glyphs are decimal digits? And yet it '''is''' in base 16, albeit with non-standard digit glyphs. So they '''all''' can be written without using a hexadecimal digit. |
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But wait a minute; is 2 a hexadecimal digit? Why yes, yes it is. So ''none'' of them can be written in hexadecimal without using a hexadecimal digit. |
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Bah. Show which when written in base 16, contain a digit glyph with a value greater than 9: |
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<lang perl6>say (0..500).grep( { any |.map: { .polymod(16 xx *) »>» 9 } } ).batch(20)».fmt('%3d').join: "\n";</lang> |
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{{out}} |
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<pre> 10 11 12 13 14 15 26 27 28 29 30 31 42 43 44 45 46 47 58 59 |
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60 61 62 63 74 75 76 77 78 79 90 91 92 93 94 95 106 107 108 109 |
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110 111 122 123 124 125 126 127 138 139 140 141 142 143 154 155 156 157 158 159 |
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160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 |
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180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 |
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200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 |
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220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 |
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240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 266 267 268 269 |
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270 271 282 283 284 285 286 287 298 299 300 301 302 303 314 315 316 317 318 319 |
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330 331 332 333 334 335 346 347 348 349 350 351 362 363 364 365 366 367 378 379 |
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380 381 382 383 394 395 396 397 398 399 410 411 412 413 414 415 416 417 418 419 |
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420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 |
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440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 |
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460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 |
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480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 |
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500</pre> |
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=={{header|REXX}}== |
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REXX automatically uses only uppercase when converting integers to hexadecimal, but the lowercase alphabetic letters where all included for boilerplate code. |
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<lang rexx>/*REXX pgm finds positive integers when shown in hexadecimal require an alphabetic glyph*/ |
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parse arg n cols . /*obtain optional argument from the CL.*/ |
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if n=='' | n=="," then n = 501 /*Not specified? Then use the default.*/ |
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if cols=='' | cols=="," then cols= 10 /* " " " " " " */ |
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w= 10 /*width of a number in any column. */ |
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@hHex= ' integers when displayed in hexadecimal that require an' , |
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"alphabetical glyph to be shown, where N < " n |
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say ' index │'center(@hHex, 1 + cols*(w+1) ) /*display the title for the output. */ |
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say '───────┼'center("" , 1 + cols*(w+1), '─') /* " a sep " " " */ |
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hHex= 0; y= 'abcdefABCDEF'; idx= 1 /*initialize # of high hexadecimal nums*/ |
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$= /*list of high hexadecimal #'s (so far)*/ |
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do j=1 for n-1 /*search for high hexadecimal numbers. */ |
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if verify(y, d2x(j), 'M')==0 then iterate /*No alphabetical characters? Then skip*/ |
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hHex= hHex + 1 /*bump number of high hexadecimal #'s. */ |
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$= $ right(j, w) /*add a high hexadecimal number──► list*/ |
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if hHex // cols \== 0 then iterate /*have we populated a line of output? */ |
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say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */ |
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idx= idx + cols /*bump the index count for the output*/ |
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end /*j*/ |
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if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ |
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say '───────┴'center("" , 1 + cols*(w+1), '─') /*display the foot sep for output. */ |
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say |
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say 'Found ' hHex @hHex |
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exit 0 /*stick a fork in it, we're all done. */</lang> |
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{{out|output|text= when using the default inputs:}} |
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<pre> |
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index │ integers when displayed in hexadecimal that require an alphabetical glyph to be shown, where N < 501 |
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───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
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1 │ 10 11 12 13 14 15 26 27 28 29 |
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11 │ 30 31 42 43 44 45 46 47 58 59 |
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21 │ 60 61 62 63 74 75 76 77 78 79 |
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31 │ 90 91 92 93 94 95 106 107 108 109 |
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41 │ 110 111 122 123 124 125 126 127 138 139 |
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51 │ 140 141 142 143 154 155 156 157 158 159 |
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61 │ 160 161 162 163 164 165 166 167 168 169 |
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71 │ 170 171 172 173 174 175 176 177 178 179 |
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81 │ 180 181 182 183 184 185 186 187 188 189 |
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91 │ 190 191 192 193 194 195 196 197 198 199 |
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101 │ 200 201 202 203 204 205 206 207 208 209 |
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111 │ 210 211 212 213 214 215 216 217 218 219 |
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121 │ 220 221 222 223 224 225 226 227 228 229 |
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131 │ 230 231 232 233 234 235 236 237 238 239 |
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141 │ 240 241 242 243 244 245 246 247 248 249 |
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151 │ 250 251 252 253 254 255 266 267 268 269 |
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161 │ 270 271 282 283 284 285 286 287 298 299 |
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171 │ 300 301 302 303 314 315 316 317 318 319 |
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181 │ 330 331 332 333 334 335 346 347 348 349 |
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191 │ 350 351 362 363 364 365 366 367 378 379 |
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201 │ 380 381 382 383 394 395 396 397 398 399 |
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211 │ 410 411 412 413 414 415 416 417 418 419 |
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221 │ 420 421 422 423 424 425 426 427 428 429 |
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231 │ 430 431 432 433 434 435 436 437 438 439 |
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241 │ 440 441 442 443 444 445 446 447 448 449 |
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251 │ 450 451 452 453 454 455 456 457 458 459 |
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261 │ 460 461 462 463 464 465 466 467 468 469 |
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271 │ 470 471 472 473 474 475 476 477 478 479 |
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281 │ 480 481 482 483 484 485 486 487 488 489 |
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291 │ 490 491 492 493 494 495 496 497 498 499 |
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301 │ 500 |
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───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
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Found 301 integers when displayed in hexadecimal that require an alphabetical glyph to be shown, where N < 501 |
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</pre> |
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=={{header|Ring}}== |
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<lang ring> |
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see "working..." + nl |
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baseList = ["a","b","c","d","e","f"] |
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row = 1 |
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limit = 500 |
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for n = 1 to limit |
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num = 0 |
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flag = 1 |
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hex = hex(n) |
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lenHex = len(hex) |
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for m = 1 to lenHex |
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ind = find(baseList,hex[m]) |
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if ind < 1 |
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num = num + 1 |
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ok |
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next |
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if num != lenHex |
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row = row + 1 |
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see "" + n + " " |
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if row%10 = 0 |
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see nl |
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ok |
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ok |
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next |
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see nl + "done..." + nl |
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</lang> |
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{{out}} |
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<pre> |
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working... |
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10 11 12 13 14 15 26 27 28 |
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29 30 31 42 43 44 45 46 47 58 |
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59 60 61 62 63 74 75 76 77 78 |
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79 90 91 92 93 94 95 106 107 108 |
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109 110 111 122 123 124 125 126 127 138 |
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139 140 141 142 143 154 155 156 157 158 |
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159 160 161 162 163 164 165 166 167 168 |
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169 170 171 172 173 174 175 176 177 178 |
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179 180 181 182 183 184 185 186 187 188 |
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189 190 191 192 193 194 195 196 197 198 |
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199 200 201 202 203 204 205 206 207 208 |
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209 210 211 212 213 214 215 216 217 218 |
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219 220 221 222 223 224 225 226 227 228 |
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229 230 231 232 233 234 235 236 237 238 |
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239 240 241 242 243 244 245 246 247 248 |
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249 250 251 252 253 254 255 266 267 268 |
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269 270 271 282 283 284 285 286 287 298 |
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299 300 301 302 303 314 315 316 317 318 |
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319 330 331 332 333 334 335 346 347 348 |
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349 350 351 362 363 364 365 366 367 378 |
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379 380 381 382 383 394 395 396 397 398 |
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399 410 411 412 413 414 415 416 417 418 |
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419 420 421 422 423 424 425 426 427 428 |
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429 430 431 432 433 434 435 436 437 438 |
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439 440 441 442 443 444 445 446 447 448 |
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449 450 451 452 453 454 455 456 457 458 |
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459 460 461 462 463 464 465 466 467 468 |
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469 470 471 472 473 474 475 476 477 478 |
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479 480 481 482 483 484 485 486 487 488 |
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489 490 491 492 493 494 495 496 497 498 |
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499 500 |
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done... |
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</pre> |
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=={{header|Wren}}== |
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{{libheader|Wren-fmt}} |
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<lang ecmascript>import "/fmt" for Conv, Fmt |
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var nondecimal = "abcdef" |
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var c = 0 |
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for (i in 0..500) { |
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var hex = Conv.hex(i) |
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if (hex.any { |c| nondecimal.contains(c) }) { |
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Fmt.write("$3s ", i) |
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c = c + 1 |
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if (c % 15 == 0) System.print() |
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} |
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} |
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System.print("\n\n%(c) such numbers found.")</lang> |
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{{out}} |
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<pre> |
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10 11 12 13 14 15 26 27 28 29 30 31 42 43 44 |
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45 46 47 58 59 60 61 62 63 74 75 76 77 78 79 |
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90 91 92 93 94 95 106 107 108 109 110 111 122 123 124 |
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125 126 127 138 139 140 141 142 143 154 155 156 157 158 159 |
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160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 |
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175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 |
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190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 |
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205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 |
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220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 |
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235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 |
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250 251 252 253 254 255 266 267 268 269 270 271 282 283 284 |
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285 286 287 298 299 300 301 302 303 314 315 316 317 318 319 |
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330 331 332 333 334 335 346 347 348 349 350 351 362 363 364 |
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365 366 367 378 379 380 381 382 383 394 395 396 397 398 399 |
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410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 |
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425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 |
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440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 |
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455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 |
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470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 |
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485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 |
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500 |
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301 such numbers found. |
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</pre> |
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=={{header|XPL0}}== |
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Borrowed masking concept from C++, which was much more elegant than my first solution. |
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<lang XPL0>func HasHex(N); |
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int N; |
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[while N do |
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[if (N&$F) > 9 then return true; N:= N>>4]; |
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return false; |
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]; |
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int N, Cnt; |
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[Cnt:= 0; |
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for N:= 1 to 500 do |
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[if HasHex(N) then |
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[if N<100 then ChOut(0, ^ ); |
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IntOut(0, N); |
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Cnt:= Cnt+1; |
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if rem(Cnt/20) = 0 then CrLf(0) else ChOut(0, ^ ); |
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]; |
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]; |
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CrLf(0); |
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IntOut(0, Cnt); Text(0, " such numbers found."); CrLf(0); |
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]</lang> |
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{{out}} |
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<pre> |
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10 11 12 13 14 15 26 27 28 29 30 31 42 43 44 45 46 47 58 59 |
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60 61 62 63 74 75 76 77 78 79 90 91 92 93 94 95 106 107 108 109 |
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110 111 122 123 124 125 126 127 138 139 140 141 142 143 154 155 156 157 158 159 |
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160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 |
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180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 |
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200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 |
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220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 |
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240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 266 267 268 269 |
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270 271 282 283 284 285 286 287 298 299 300 301 302 303 314 315 316 317 318 319 |
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330 331 332 333 334 335 346 347 348 349 350 351 362 363 364 365 366 367 378 379 |
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380 381 382 383 394 395 396 397 398 399 410 411 412 413 414 415 416 417 418 419 |
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420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 |
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440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 |
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460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 |
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480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 |
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500 |
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301 such numbers found. |
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</pre> |
Latest revision as of 14:20, 6 August 2021
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