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Our proposed solution enables the training of binary multi-layer perceptrons by using exclusively XNOR, Popcount, and increment\/decrement operations. Experimental results on multi-class classification benchmarks show test accuracy improvements of up to +35.47% over the only existing fully binary single-layer state-of-the-art solution. Compared to full-precision SGD, our solution improves test accuracy by up to +35.30% under the same total memory demand, while also reducing computational cost by two to three orders of magnitude in terms of the total number of Boolean gates. 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