This is currently (2016) the exit area. The last building one passes to the left of the exit is the Timing Room (Muvakkithane). In the Ottoman period there were rooms where prayer time was calculated, there used to be 38 i9n town, of which 29 survived. This is the one for Hagia Sophia. The structure had been built by Fossatti Brothers in 1853 who managed the repair of Hagia Sophia in the period of Sultan Abdülmecid (1839 - 1861). It is a pareticularly fine one. The building has a square layout and meshed walls made of face stone. The entrance is on the north façade. There is a round table made of monolithic marble with marble legs in the middle of the timing room. The windows are managed to large in order have the clock placed over the table for pendulum adjustment and the other clocks inside visible for everybody outside. Some of the legged big clocks located in the timing room during mosque period are preserved in the storage of the museum. The building is currently used as a Museum Office.
(Text from the official site used).