दो की घात
गणित में दो की घात का मतलब के रूप में लिखने योग्य संख्या से है जहाँ n एक पूर्णांक है, अर्थात 2 के आधार पर घातांक परिणाम जहाँ घातांक पूर्णांक n है।
उस प्रसंग में जहाँ केवल पूर्णांक काम में लिए जाते हैं n अपूर्णांक मान नहीं रख सकता।[1] अतः हमें 1, 2 और 2 अपने ही विभिन्न गुणज प्राप्त होंगे।[2] क्योंकि दो द्वयाधारी संख्या पद्धति का आधार है अतः दो की घात संगणक विज्ञान में सामान्य है। द्वयाधारी में लिखने पर दो की घात हमेसा 100…0 या 0.00…01 के रूप में प्राप्त होती हैं जो दशमलव में 10 की घात के तुल्य है।
व्यंजक और अंकन
मौखिक अभिव्यक्ति, गणितीय अंकन, संगणक प्रोग्रामन व्यंजक घात संकारक सहित अथवा फलन सहित:
- 2 की घात n
- 2 की n
- 2 power n
- power(2, n)
- pow(2, n)
- 2n
- 2 ^ n
- 2 ** n
कंप्यूटर विज्ञान
दो की प्रथम 96 घात
| 20 | = | 1 | 216 | = | 65,536 | 232 | = | 4,294,967,296 | 248 | = | 281,474,976,710,656 | 264 | = | 18,446,744,073,709,551,616 | 280 | = | 1,208,925,819,614,629,174,706,176 | 296 | = | 79,228,163,514,264,337,593,543,950,336 | |||||||
| 21 | = | 2 | 217 | = | 131,072 | 233 | = | 8,589,934,592 | 249 | = | 562,949,953,421,312 | 265 | = | 36,893,488,147,419,103,232 | 281 | = | 2,417,851,639,229,258,349,412,352 | ||||||||||
| 22 | = | 4 | 218 | = | 262,144 | 234 | = | 17,179,869,184 | 250 | = | 1,125,899,906,842,624 | 266 | = | 73,786,976,294,838,206,464 | 282 | = | 4,835,703,278,458,516,698,824,704 | ||||||||||
| 23 | = | 8 | 219 | = | 524,288 | 235 | = | 34,359,738,368 | 251 | = | 2,251,799,813,685,248 | 267 | = | 147,573,952,589,676,412,928 | 283 | = | 9,671,406,556,917,033,397,649,408 | ||||||||||
| 24 | = | 16 | 220 | = | 1,048,576 | 236 | = | 68,719,476,736 | 252 | = | 4,503,599,627,370,496 | 268 | = | 295,147,905,179,352,825,856 | 284 | = | 19,342,813,113,834,066,795,298,816 | ||||||||||
| 25 | = | 32 | 221 | = | 2,097,152 | 237 | = | 137,438,953,472 | 253 | = | 9,007,199,254,740,992 | 269 | = | 590,295,810,358,705,651,712 | 285 | = | 38,685,626,227,668,133,590,597,632 | ||||||||||
| 26 | = | 64 | 222 | = | 4,194,304 | 238 | = | 274,877,906,944 | 254 | = | 18,014,398,509,481,984 | 270 | = | 1,180,591,620,717,411,303,424 | 286 | = | 77,371,252,455,336,267,181,195,264 | ||||||||||
| 27 | = | 128 | 223 | = | 8,388,608 | 239 | = | 549,755,813,888 | 255 | = | 36,028,797,018,963,968 | 271 | = | 2,361,183,241,434,822,606,848 | 287 | = | 154,742,504,910,672,534,362,390,528 | ||||||||||
| 28 | = | 256 | 224 | = | 16,777,216 | 240 | = | 1,099,511,627,776 | 256 | = | 72,057,594,037,927,936 | 272 | = | 4,722,366,482,869,645,213,696 | 288 | = | 309,485,009,821,345,068,724,781,056 | ||||||||||
| 29 | = | 512 | 225 | = | 33,554,432 | 241 | = | 2,199,023,255,552 | 257 | = | 144,115,188,075,855,872 | 273 | = | 9,444,732,965,739,290,427,392 | 289 | = | 618,970,019,642,690,137,449,562,112 | ||||||||||
| 210 | = | 1,024 | 226 | = | 67,108,864 | 242 | = | 4,398,046,511,104 | 258 | = | 288,230,376,151,711,744 | 274 | = | 18,889,465,931,478,580,854,784 | 290 | = | 1,237,940,039,285,380,274,899,124,224 | ||||||||||
| 211 | = | 2,048 | 227 | = | 134,217,728 | 243 | = | 8,796,093,022,208 | 259 | = | 576,460,752,303,423,488 | 275 | = | 37,778,931,862,957,161,709,568 | 291 | = | 2,475,880,078,570,760,549,798,248,448 | ||||||||||
| 212 | = | 4,096 | 228 | = | 268,435,456 | 244 | = | 17,592,186,044,416 | 260 | = | 1,152,921,504,606,846,976 | 276 | = | 75,557,863,725,914,323,419,136 | 292 | = | 4,951,760,157,141,521,099,596,496,896 | ||||||||||
| 213 | = | 8,192 | 229 | = | 536,870,912 | 245 | = | 35,184,372,088,832 | 261 | = | 2,305,843,009,213,693,952 | 277 | = | 151,115,727,451,828,646,838,272 | 293 | = | 9,903,520,314,283,042,199,192,993,792 | ||||||||||
| 214 | = | 16,384 | 230 | = | 1,073,741,824 | 246 | = | 70,368,744,177,664 | 262 | = | 4,611,686,018,427,387,904 | 278 | = | 302,231,454,903,657,293,676,544 | 294 | = | 19,807,040,628,566,084,398,385,987,584 | ||||||||||
| 215 | = | 32,768 | 231 | = | 2,147,483,648 | 247 | = | 140,737,488,355,328 | 263 | = | 9,223,372,036,854,775,808 | 279 | = | 604,462,909,807,314,587,353,088 | 295 | = | 39,614,081,257,132,168,796,771,975,168 |
यहाँ यह देखा जा सकता है कि प्रथम व्यंजक का अन्तिम अंक 2 से आरम्भ होता है और उसके पश्चात आवर्त रूप से 4 और उसके बाद चक्रीय क्रम में 2–4–8–6–,
1024 की घात
210 की कुछ घात जो 1000 से थोड़ी अधिक हैं:
| 210 | = | 1 024 | ≈ 10001 | (2.3% विचलन) |
| 220 | = | 1 048 576 | ≈ 10002 | (4.6% विचलन) |
| 230 | = | 1 073 741 824 | ≈ 10003 | (6.9% विचलन) |
| 240 | = | 1 099 511 627 776 | ≈ 10004 | (9.1% विचलन) |
| 250 | = | 1 125 899 906 842 624 | ≈ 10005 | (11.2% विचलन) |
| 260 | = | 1 152 921 504 606 846 976 | ≈ 10006 | (13.3% विचलन) |
| 270 | = | 1 180 591 620 717 411 303 424 | ≈ 10007 | (15.3% विचलन) |
ये भी देखें IEEE 1541-2002.
दो की कुछ चयनित घात
अन्य गुणधर्म
ये भी देखें
सन्दर्भ
- ↑ Lipschutz, Seymour (1982). Schaum's Outline of Theory and Problems of Essential Computer Mathematics. New York: McGraw-Hill. पृ॰ 3. आई॰ऍस॰बी॰ऍन॰ 0-07-037990-4.
- ↑ Sewell, Michael J. (1997). Mathematics Masterclasses. Oxford: Oxford University Press. पृ॰ 78. आई॰ऍस॰बी॰ऍन॰ 0-19-851494-8.
