Re: Binary number digits <- > Decimal number digits

On Dec 9, 4:21 pm, Adam <n...@xxxxxxxx> wrote:
On Sun, 09 Dec 2007 16:44:00 -0500, Adam wrote:
On Sun, 9 Dec 2007 07:39:24 -0800 (PST), fc wrote:
And: how to generalize for any decimal number of any length?

Consider the following two 5-digit decimal numbers:

expression decimal number bits required
2^16 - 1 65,535 16
2^16 + 2^14 81,920 17

5 * log(10) / log(2) = 16.6

Round up or down comes into play again.

It's even messier than that:

expression decimal number bits required

none 10,000 14
2^14 16,384 15
2^15 32,768 16
2^16 + 2^14 81,920 17

Not messy at all:

x = 99999
gmpy.numdigits(x,2)
17



Adam

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