Design automation in general, and in particular logic synthesis, can play a key role in enabling the design of application-specific Binarized Neural Networks (BNN). This paper presents the hardware design and synthesis of a purely combinational BNN for ultra-low power near-sensor processing. We leverage the major opportunities raised by BNN models, which consist mostly of logical bit-wise operations and integer counting and comparisons, for pushing ultra-low power deep learning circuits close to the sensor and coupling it with binarized mixed-signal image sensor data. We analyze area, power and energy metrics of BNNs synthesized as combinational networks. Our synthesis results in GlobalFoundries 22nm SOI technology shows a silicon area of 2.61mm2 for implementing a combinational BNN with 32x32 binary input sensor receptive field and weight parameters fixed at design time. This is 2.2x smaller than a synthesized network with re-configurable parameters. With respect to other comparable techniques for deep learning near-sensor processing, our approach features a 10x higher energy efficiency.