What determines the value of $MaxNumber?

If you calculate Log[2,Log[2,$MaxNumber]], you'll get 29.999999828017338886225739 which is remarkably close to 30. Therefore I conclude that Mathematica calculates with a 31-bit exponent (1 bit for the exponent's sign). Which means that if Mathematica uses the same ordering as IEEE floats (i.e. first sign bit, then exponent, then mantissa), the first 32 bits (i.e. exactly 4 bytes) of a Mathematica floating point number contain the sign and the exponent.

As it seems to depend on more than machine bits I'm curious what $MaxNumber various Mathematica installs have.

If your setup is different please fill in system information and Log2 @ Log2 @ $MaxNumber // Round in the table below:

$$\begin{array}{r|c|c|l|c} \text{OS} & \text{Bits} & \text{Version} & \text{\\\$MaxNumber} & \log_2\log_2\\ \hline \\ % v7 \text{Windows} & 32 & 7.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Linux} & 64 & 7.0.1 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{Windows} & 64 & 7.0.1 & 1.233433712981650\times 10^{323228458} & 30 \\ % v8 \text{Windows} & 32 & 8.0.4 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Windows} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{OS X} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{Linux} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ % v9 \text{Windows} & 32 & 9.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Windows} & 64 & 9.0.1 & 2.174188391646043\times 10^{20686623745} & 36 \\ \text{OS X} & 64 & 9.0.1 & 8.768126706828697\times 10^{2711437152599256} & 53 \\ \text{Linux} & 64 & 9.0.1 & 8.768126706828697\times 10^{2711437152599256} & 53 \\ \text{Windows} & 64 & 10.1.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 10.2.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 10.3.1 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{OS X} & 64 & 10.4.1 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 11.0.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 11.3.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{OS X} & 64 & 12.1.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Linux ARM} & 32 & 12.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ % Your data here \end{array}$$