Summary: Synchronized systems, has attracted much attention in [Theor. Comput. Sci. 44, 17–49 (1986; Zbl 0601.68056)] by F. Blanchard and G. Hansel, and extension of them has been of interest since that notion was introduced in [Contemp. Math. 135, 139–179 (1992; Zbl 0785.54036)] by D. Fiebig and U.-R. Fiebig. One was via half synchronized systems; that is, systems having half synchronizing blocks. In fact, if for a left transitive ray such as \(\cdots x_{-1}x_0m\) and \(mv\) any block in \(X\) one has again \(\cdots x_{-1}x_0mv\) a left ray in \(X\), then \(m\) is called half synchronizing. A block \(m\) is minimal (half-)synchronizing, whenever \(w \varsubsetneq m\), \(w\) is not (half-)synchronizing. Examples with \(\ell\) minimal (half-)synchronizing blocks has been given for \(0\leq \ell \leq \infty\). To do this we consider a \(\beta \)-shift and will replace 1 with some blocks \(u_i\) to have countable many new systems. Then, we will merge them.