Decimal/Binary Conversion Table
(Published June 30th, 2009) Here is a table you can use to convert small integers — integers between 0 and 255 — directly between decimal and binary (as an alternative to using a decimal/binary converter):
Articles from June, 2009
Nines in Binary
I discovered a cool property of positive integers of the form 10n-1, that is, integers made up of n digits of 9s: they have binary representations that have exactly n digits of trailing 1s. For example, 9,999,999 in decimal is 100110001001011001111111 in binary.
The property is interesting in and of itself, but what is more interesting is the process I went through to discover it. It’s a small-scale example of experimental mathematics: I observed something interesting, experimented to collect more data, developed a hypothesis, and constructed a proof.
