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.

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4 comments

  1. [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;

  2. @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:

    00419B4E  mov         dword ptr [po2],0  
    00419B55  mov         dword ptr [ebp-8],80000000h
    
  3. [quote] Your method assigns a power of two indirectly through knowledge of the underlying binary representation (two’s complement)[/quote]
    No, the << operator (as most things in the C standard) is defined with what it does to the numeric values of its operands, diregarding the actual implementation.

    Of course, as always with arithmetic in C, if you deal with unsigned integers the "overflow" is perfectly defined as modulo "TYPE_MAX", and if you deal with signed integers, you'll get an undefined behavior on overflow. The degree of undefinedness depends on the implementation, of course, but that's another story 🙂

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