1. Let $[x]$ denote the greatest integer not exceeding the real number $x$. Then the number of roots of the equation $2^{x}-2[x]-1=0$ is
A. 1
B. 2
C. 3
D. 4
Solve
$2^{x}=2[x]+1$, obviously $[x] \geqslant 0$, when $[x]=0$ then $x=0$; when $[x]=1$ then $x=\log _{2} 3$; when $[x]=2$ then $x=\log _{2} 5$; when $[x] \geqslant 3$ there is no solution. Therefore, the answer is $C$.