Powers of Two
Every power of two up to 2⁶⁴, with the largest unsigned value that many bits can hold in the last column. The exponent is also the number of bits.
65 rows
| Exponent | 2ⁿ | 2ⁿ − 1 |
|---|---|---|
| 0 | 1 | 0 |
| 1 | 2 | 1 |
| 2 | 4 | 3 |
| 3 | 8 | 7 |
| 4 | 16 | 15 |
| 5 | 32 | 31 |
| 6 | 64 | 63 |
| 7 | 128 | 127 |
| 8 | 256 | 255 |
| 9 | 512 | 511 |
| 10 | 1 024 | 1 023 |
| 11 | 2 048 | 2 047 |
| 12 | 4 096 | 4 095 |
| 13 | 8 192 | 8 191 |
| 14 | 16 384 | 16 383 |
| 15 | 32 768 | 32 767 |
| 16 | 65 536 | 65 535 |
| 17 | 131 072 | 131 071 |
| 18 | 262 144 | 262 143 |
| 19 | 524 288 | 524 287 |
| 20 | 1 048 576 | 1 048 575 |
| 21 | 2 097 152 | 2 097 151 |
| 22 | 4 194 304 | 4 194 303 |
| 23 | 8 388 608 | 8 388 607 |
| 24 | 16 777 216 | 16 777 215 |
| 25 | 33 554 432 | 33 554 431 |
| 26 | 67 108 864 | 67 108 863 |
| 27 | 134 217 728 | 134 217 727 |
| 28 | 268 435 456 | 268 435 455 |
| 29 | 536 870 912 | 536 870 911 |
| 30 | 1 073 741 824 | 1 073 741 823 |
| 31 | 2 147 483 648 | 2 147 483 647 |
| 32 | 4 294 967 296 | 4 294 967 295 |
| 33 | 8 589 934 592 | 8 589 934 591 |
| 34 | 17 179 869 184 | 17 179 869 183 |
| 35 | 34 359 738 368 | 34 359 738 367 |
| 36 | 68 719 476 736 | 68 719 476 735 |
| 37 | 137 438 953 472 | 137 438 953 471 |
| 38 | 274 877 906 944 | 274 877 906 943 |
| 39 | 549 755 813 888 | 549 755 813 887 |
| 40 | 1 099 511 627 776 | 1 099 511 627 775 |
| 41 | 2 199 023 255 552 | 2 199 023 255 551 |
| 42 | 4 398 046 511 104 | 4 398 046 511 103 |
| 43 | 8 796 093 022 208 | 8 796 093 022 207 |
| 44 | 17 592 186 044 416 | 17 592 186 044 415 |
| 45 | 35 184 372 088 832 | 35 184 372 088 831 |
| 46 | 70 368 744 177 664 | 70 368 744 177 663 |
| 47 | 140 737 488 355 328 | 140 737 488 355 327 |
| 48 | 281 474 976 710 656 | 281 474 976 710 655 |
| 49 | 562 949 953 421 312 | 562 949 953 421 311 |
| 50 | 1 125 899 906 842 624 | 1 125 899 906 842 623 |
| 51 | 2 251 799 813 685 248 | 2 251 799 813 685 247 |
| 52 | 4 503 599 627 370 496 | 4 503 599 627 370 495 |
| 53 | 9 007 199 254 740 992 | 9 007 199 254 740 991 |
| 54 | 18 014 398 509 481 984 | 18 014 398 509 481 983 |
| 55 | 36 028 797 018 963 968 | 36 028 797 018 963 967 |
| 56 | 72 057 594 037 927 936 | 72 057 594 037 927 935 |
| 57 | 144 115 188 075 855 872 | 144 115 188 075 855 871 |
| 58 | 288 230 376 151 711 744 | 288 230 376 151 711 743 |
| 59 | 576 460 752 303 423 488 | 576 460 752 303 423 487 |
| 60 | 1 152 921 504 606 846 976 | 1 152 921 504 606 846 975 |
| 61 | 2 305 843 009 213 693 952 | 2 305 843 009 213 693 951 |
| 62 | 4 611 686 018 427 387 904 | 4 611 686 018 427 387 903 |
| 63 | 9 223 372 036 854 775 808 | 9 223 372 036 854 775 807 |
| 64 | 18 446 744 073 709 551 616 | 18 446 744 073 709 551 615 |
Exact past 2⁵³
A JavaScript number stops being exact above 2⁵³, so this table is computed with arbitrary-precision integers. Every digit shown is the digit, not a rounding.
Questions
Why does the third column matter?
2ⁿ − 1 is the largest unsigned value n bits can hold, because n bits count from zero. Eight bits reach 255, sixteen reach 65 535, thirty-two reach 4 294 967 295.
Where does 2 147 483 647 come from?
It is 2³¹ − 1, the largest value of a signed 32-bit integer. One of the thirty-two bits carries the sign, leaving thirty-one for the magnitude.
Is a kilobyte 1000 or 1024 bytes?
Both are in use. The SI prefix kilo means 1000, while the binary prefix kibi (KiB) means 1024 — this table lists the powers of two, so 2¹⁰ is 1024.
Sources and last check
Information, not professional advice.