Another Way to Look at Powers of 2
The sometimes huge numbers we get when we put exponents on a small number like 2 can be off putting. So here are some calculations that, while I don't think they bring the larger numbers into the realm of human sensibility, might show a bit how they relate to the smaller powers of 2.
Here I'm representing the power of 2 by the height of a stack of paper.
Generally the thickness of a single sheet of 20 pound bond paper, the common copy paper most Americans are used to, is 0.0038 inches thick. The table below shows how high a stack you get with the powers of 2 shown.
| Height of Stack |
|---|
|
Sheets |
Inches |
Feet |
Miles |
Light years |
| 28 |
256 |
0.973 |
|
|
|
| 216 |
65,536 |
249.037 |
20.753 |
|
|
| 232 |
4,294,967,296
|
16,320,875 |
1,360,072.977 |
257.59 |
|
| 264 |
|
|
|
1,106,338,817,552 |
0.188 |
| 2128 |
|
|
|
|
3,471,626,652,501,820,000 |
Some Comments On These Numbers
- 28
- This is the memory address space for 8-bit computers such as the Apple ][™ series, the Atari™ 8-bit, and the Commodore™ lines. This was the size of the external address space of the original IBM™ PC's. The stack of this number of standard papers would be 256 sheets and would be a little less than one inch in height.
- 216
- This is the memory address space for computers such as the Hewlett-Packard BPC™, IBM AT™ and other systems using CPUs such as the Intel 8086 and 80286 microprocessors and the Motorola 68000 microprocessor. The paper stack is now the height of a two storey building.
- 232
- This is the memory address space for 32-bit computers. It is also the address space for IPv4, which is why that 4,294,967,296 number may look familiar to many folks. The paper stack is now about 10 miles taller than the maximum height that the International Space Station gets to.
- 264
- This is the memory address space for 64-bit computers. Our stack of papers now reaches well into the midst of the Oort Cloud, and is a noticeable fraction of a light year in height.
- 2128
- This is the address space for IPv6. Our stack of papers now exceeds by an enormous amount the length of any straight line that can be contained in the universe. So IPv6 is unlikely to run out of address spaces any time soon.
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