 Solution

Use four request bits $r_0,r_1,r_2,r_3$ and four grant bits $g_0,g_1,g_2,g_3$. A high $r_i$ requests service for the coming allocation period, and a high $g_i$ identifies the requester granted the resource during the current period. At most one grant may be high. An all-zero grant vector means idle. The synchronous sequential circuit also has a clock and an initialization signal.

Requests are sampled at a clock edge; the resulting allocation appears during the following cycle. This fixes the Moore machine timing convention: current grants depend on the stored state, rather than combinationally on requests that can change within the cycle.