If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then the range of $f$ is:

• A
  $\{x \in R: 0 \leq x \leq 1\}$
• B
  $\{0, 1\}$
• C
  $\{x \in R: x > 0\}$
• D
  $\{x \in R: x \leq 0\}$