4. The equation $|2 x-1|-a=0$ has exactly two positive solutions. Then the range of values for $a$ is ( ).
(A) $-1<a<0$
(B) $-1<a<1$
(C) $0<a<1$
(D) $\frac{1}{2}<a<1$
4. C.

Since the equation $|2 x-1|-a=0$ has exactly two positive solutions, we have
$$
\left\{\begin{array}{l}
a>0, \\
x=\frac{a+1}{2}>0, \\
x=\frac{1-a}{2}>0 .
\end{array}\right.
$$

Solving this, we get $0<a<1$.