Binarized neural networks (BNNs) have shown exciting potential for utilising neural networks in embedded implementations where area, energy and latency constraints are paramount. With BNNs, multiply-accumulate (MAC) operations can be simplified to XnorPopcount operations, leading to massive reductions in both memory and computation resources. Furthermore, multiple efficient implementations of BNNs have been reported on field-programmable gate array (FPGA) implementations. This paper proposes a smaller, faster, more energy-efficient approximate replacement for the XnorPopcountoperation, called XNorMaj, inspired by state-of-the-art FPGAlook-up table schemes which benefit FPGA implementations. Weshow that XNorMaj is up to 2x more resource-efficient than the XnorPopcount operation. While the XNorMaj operation has a minor detrimental impact on accuracy, the resource savings enable us to use larger networks to recover the loss.