SPADnet is a sensor platform for the detection and processing of gamma photons generated in a PET system. SPADnet uses the novel technique of deferred coincidence detection, whereas timestamps associated with gamma events and their energy are routed at high speed (up to 3.3 million events per second) over a 2Gbps network, along with synchronization information. In this work, we describe SPADnet's key building block, a tile of SPADnet-I chips. SPADnet-I is a 50 mm2, 8x16 pixel digital SiPM where each pixel includes an array of 720 SPADs and the logic to count photons and record their arrival time. A fill factor of 42.9% is achieved. A distributed adder provides the number of photons detected throughout the whole array every 10 ns. On-chip triggering logic monitors this value in real time to discriminate gamma events from dark counts. The chip features a 10.8% energy resolution and a CRT of 288ps when coupled to a 3x3x10 mm3 LYSO crystal. High spatial resolution is obtained by combining the data generated by each pixel to efficiently locate the gamma absorption in the 2D space even when coupled to large arrays of crystal needles as small as 1.12x1.12mm2. The tile is built on a 5x5 array of SPADnet-I sensors. A Xilinx Spartan6 FPGA controls the whole module and monitors the gamma activity across the 25 sensors. Here, the large amount of data generated for each detected gamma is processed in real time to extract energy, position and time-of-arrival. Pile-up detection and energy windowing are applied to the events, which are then fed to a network of tiles for coincidence detection. A centralized snooper recognizes coincidence pairs while thermal, Compton, and single events are discarded. The system is inherently scalable, as it enables single- or multi-rings of photonic modules for potentially large PET systems.