Unsigned Binary

The simplest representation assumes that all numbers are positive integers, with bit $b_0$ giving the coefficient of $2^0$, $b_1$ giving the coefficient of $2^1$, and so on, up to $b_k$ as the coefficient of $2^k$.

More formally, we have:

$$(b_k b_{k-1} b_{k-2}\ldots b_2 b_1 b_0)_2 = (\sum_{i=0}^{k} b_i 2^i)_{10}$$

For example, the binary version of 2087 is shown below:

$$(1000\;\;0010\;\; 0101)_2 = (1 \times 2^{11} + 1 \times 2^5 + 1 \times 2^2 + 1 \times 2^0)_{10}$$

Rule of Thumb: An n-bit string of all ones has the value of $2^{n} - 1$.