# Numbers immediately to the right and left of $2^k$

What are machine numbers immediately to the right and left of $2^k$ ? How far is each from $2^k$?

When you say machine numbers, you mean binary representation of integers ? If so, what is the representation of $2^k$...? What is the meaning of your second question ? How far for which metric ? Hamming's metric ? –  user37238 Sep 17 '13 at 9:19
By machine numbers I mean $IEEE_{754}$ –  John Lennon Sep 17 '13 at 10:04