A Table of Nonnegative Powers of Two
(Published November 14th, 2008) Copyright © 2008-2012 Exploring Binary
http://www.exploringbinary.com/a-table-of-nonnegative-powers-of-two/
Here is a table of the first 65 nonnegative powers of two (from 20 to 264):
| n | 2n |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
| 6 | 64 |
| 7 | 128 |
| 8 | 256 |
| 9 | 512 |
| 10 | 1,024 |
| 11 | 2,048 |
| 12 | 4,096 |
| 13 | 8,192 |
| 14 | 16,384 |
| 15 | 32,768 |
| 16 | 65,536 |
| 17 | 131,072 |
| 18 | 262,144 |
| 19 | 524,288 |
| 20 | 1,048,576 |
| 21 | 2,097,152 |
| 22 | 4,194,304 |
| 23 | 8,388,608 |
| 24 | 16,777,216 |
| 25 | 33,554,432 |
| 26 | 67,108,864 |
| 27 | 134,217,728 |
| 28 | 268,435,456 |
| 29 | 536,870,912 |
| 30 | 1,073,741,824 |
| 31 | 2,147,483,648 |
| 32 | 4,294,967,296 |
| 33 | 8,589,934,592 |
| 34 | 17,179,869,184 |
| 35 | 34,359,738,368 |
| 36 | 68,719,476,736 |
| 37 | 137,438,953,472 |
| 38 | 274,877,906,944 |
| 39 | 549,755,813,888 |
| 40 | 1,099,511,627,776 |
| 41 | 2,199,023,255,552 |
| 42 | 4,398,046,511,104 |
| 43 | 8,796,093,022,208 |
| 44 | 17,592,186,044,416 |
| 45 | 35,184,372,088,832 |
| 46 | 70,368,744,177,664 |
| 47 | 140,737,488,355,328 |
| 48 | 281,474,976,710,656 |
| 49 | 562,949,953,421,312 |
| 50 | 1,125,899,906,842,624 |
| 51 | 2,251,799,813,685,248 |
| 52 | 4,503,599,627,370,496 |
| 53 | 9,007,199,254,740,992 |
| 54 | 18,014,398,509,481,984 |
| 55 | 36,028,797,018,963,968 |
| 56 | 72,057,594,037,927,936 |
| 57 | 144,115,188,075,855,872 |
| 58 | 288,230,376,151,711,744 |
| 59 | 576,460,752,303,423,488 |
| 60 | 1,152,921,504,606,846,976 |
| 61 | 2,305,843,009,213,693,952 |
| 62 | 4,611,686,018,427,387,904 |
| 63 | 9,223,372,036,854,775,808 |
| 64 | 18,446,744,073,709,551,616 |
With enough exposure to computers and binary numbers you will likely memorize 20 through 216.
Here’s the same table without commas in the numbers, to make it more convenient to copy and paste one into your code:
| n | 2n |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
| 6 | 64 |
| 7 | 128 |
| 8 | 256 |
| 9 | 512 |
| 10 | 1024 |
| 11 | 2048 |
| 12 | 4096 |
| 13 | 8192 |
| 14 | 16384 |
| 15 | 32768 |
| 16 | 65536 |
| 17 | 131072 |
| 18 | 262144 |
| 19 | 524288 |
| 20 | 1048576 |
| 21 | 2097152 |
| 22 | 4194304 |
| 23 | 8388608 |
| 24 | 16777216 |
| 25 | 33554432 |
| 26 | 67108864 |
| 27 | 134217728 |
| 28 | 268435456 |
| 29 | 536870912 |
| 30 | 1073741824 |
| 31 | 2147483648 |
| 32 | 4294967296 |
| 33 | 8589934592 |
| 34 | 17179869184 |
| 35 | 34359738368 |
| 36 | 68719476736 |
| 37 | 137438953472 |
| 38 | 274877906944 |
| 39 | 549755813888 |
| 40 | 1099511627776 |
| 41 | 2199023255552 |
| 42 | 4398046511104 |
| 43 | 8796093022208 |
| 44 | 17592186044416 |
| 45 | 35184372088832 |
| 46 | 70368744177664 |
| 47 | 140737488355328 |
| 48 | 281474976710656 |
| 49 | 562949953421312 |
| 50 | 1125899906842624 |
| 51 | 2251799813685248 |
| 52 | 4503599627370496 |
| 53 | 9007199254740992 |
| 54 | 18014398509481984 |
| 55 | 36028797018963968 |
| 56 | 72057594037927936 |
| 57 | 144115188075855872 |
| 58 | 288230376151711744 |
| 59 | 576460752303423488 |
| 60 | 1152921504606846976 |
| 61 | 2305843009213693952 |
| 62 | 4611686018427387904 |
| 63 | 9223372036854775808 |
| 64 | 18446744073709551616 |
The constants 232 through 263 require 64-bit integers (264 won’t fit in a 64-bit integer). Here’s an example of how to use these large constants in a C program:
unsigned long long po2 = 9223372036854775808ULL; //2^63
The ‘long long’ declaration means 64-bit integer, and the ‘ULL’ suffix means an ‘unsigned long long’ constant.
(5 votes, average: 4.40 out of 5)
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February 7th, 2011 at 9:30 am
[quote]
unsigned long long po2 = 9223372036854775808ULL; //2^63
[/quote]
Please don’t ever do that.
Use the left shift operator (<<) instead, like
unsigned long long po2 = 1ULL<<63;
February 7th, 2011 at 10:01 am
@lallehat,
My method assigns a decimal power of two from the table directly to a variable. Your method assigns a power of two indirectly through knowledge of the underlying binary representation (two’s complement) and bit shifting operations. Both methods work: mine uses the “2n” column, and yours uses the “n” column. I would think it’s just a matter of personal preference as to which method you choose.
As for performance, there’s no difference. Both should be resolved at compile time. For example, under Visual C++, both resolve to these two assembler statements: