BTW, to reason a bit about this statement in a simpler fashion: "any natural number “K” can be obtained from sum of other natural numbers (less than K), where these natural numbers are powers of 2"<p>Think what you're doing mentally when converting a binary number to decimal. For example:
101001<p>Each one of those 1s represents 2^position, all added together, so:<p><pre><code> 41 = 32 (100000 = 2^5)
+ 8 ( 1000 = 2^3)
+ 1 ( 1 = 2^0)
</code></pre>
Since any natural number can be represented in decimal and binary, the rule applies that each binary 1 is the value of 2^that position, all summed up.