Re: The difference between 16, 32, 64 bits.

Hey,

The Binary numeral system is a format for representing numbers in positional notation with a radix 2. That is, for each number from right to left in the number, the value it represents increases by a power of 2; in the same way that adding zeroes in normal (base-10) numbering increases in 10-fold. This is the common decimal system you know, which counts 1 to 9, then 10. In this system, "10" represents the value ten. In Binary, "10" represents the value 2, because the second position is worth one amount of 2's.

This system is representied electronically in binary computer busses by having 2 values for each line on a bus. So a 32-bit bus, has 32 lines, each representing a gradually increasin power of 2.

Now, as you know, 11 in decimal is the value eleven. However 1111 is not the value twenty-two. It is the value one thousand one hundred and eleven. The same goes for binary, and hexidecimal. Hexedecimal (the format you use when writing FFFF, is a positional notational, radix 16; so each position counts 1 to 9, and then A to F. The Value FFFF FFFF, is not simply two times FFFF, it is 65537 (10001) times larger.

Hexedecmial can easily be used to represent binary values because 16 is a power of 2. That means that there is a position in the binary notation (2^4, 2 to the power 4) that is equal to a position in hexedecimal (16^1). No such position appears in decimal, so it is difficult to convert between the two. This means that the any value stored in only 4 hexedecimal digits (FFFF) is equal to that which can be stored in 16 binary digits (1111111111111111).

So the maximum value that can be stored in 16-bits (16 binary digits) is 65535 (there are 65536 possible values including 0). That value is equal to 1 in al 16 positions or...

**Code:**

2^0+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10+2^11+2^12+2^13+2^14+2^15

Which is the same as simply

A 32-bit number continues the pattern, so it's maximum value is 4294967295 (2^32-1).

Thanks,

James