Post Number:#2 by Mallika Prova » Thu Apr 13, 2017 1:20 pm
$d_n$ the binary representation of a number that can't be expressed with a subtraction of two $n$ bit strings
having a total of $n$ $1's$ together.
we will prove that for a $d_n < 2^n $ there exists such $n$ bit strings
for a number $x < 2^n$ is a $n$ bit string with atmost $n$ $1's$
now for $a_0$ adjacent $0's$ we can find $\underbrace{10101010...1010}_{a_0}$ and $\underbrace{10101010...1010}_{a_0}$
and for $a_1$ adjacent $1's$ we can find $\underbrace{11111111...1111}_{a_1}$ and $\underbrace{00000000...0000}_{a_1}$
and we are done.. having $d_n=2^n$ a binary string with $1$ $1's$ and $n$ $0's$
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