Power of Two - Powers of Two Whose Exponents Are Powers of Two

Powers of Two Whose Exponents Are Powers of Two

Because data (specifically integers) and the addresses of data are stored using the same hardware, and the data is stored in one or more octets (23), double exponentials of two are common. For example,

21 = 2

22 = 4

24 = 16

28 = 256

216 = 65,536

232 = 4,294,967,296

264 = 18,446,744,073,709,551,616

2128 = 340,282,366,920,938,463,463,374,607,431,768,211,456

2256 =115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936.

2512 = 13,407,807,929,942,597,099,574,024,998,205,846,127,479,365,820,592,393,377,723,561,443,721,764,030,073,546,976,801,874,298,166,903,427,690,031,858,186,486,050,853,753,882,811,946,569,946,433,649,006,084,096

Several of these numbers represent the number of values representable using common computer data types. For example, a 32-bit word consisting of 4 bytes can represent 232 distinct values, which can either be regarded as mere bit-patterns, or are more commonly interpreted as the unsigned numbers from 0 to 232 − 1, or as the range of signed numbers between −231 and 231 − 1. Also see tetration and lower hyperoperations. For more about representing signed numbers see two's complement.

In a connection with nimbers these numbers are often called Fermat 2-powers.