In this paper we address the problem of unsupervised learning of discrete subword units. Our approach is based on Deep Autoencoders (AEs), whose encoding node values are thresholded to subsequently generate a symbolic, i.e., 1-of-K (with K = No. of subwords), representation of each speech frame. We experiment with two variants of the standard AE which we have named Binarized Autoencoder and Hidden-Markov-Model Encoder. The first forces the binary encoding nodes to have a U-shaped distribution (with peaks at 0 and 1) while minimizing the reconstruction error. The latter jointly learns the symbolic encoding representation (i.e., subwords) and the prior and transition distribution probabilities of the learned subwords. The ABX evaluation of the Zero Resource Challenge - Track 1 shows that a deep AE with only 6 encoding nodes, which assigns to each frame a 1-of-K binary vector with K = 2^6, can outperform real-valued MFCC representations in the across-speaker setting. Binarized AEs can outperform standard AEs when using a larger number of encoding nodes, while HMM Encoders may allow more compact subword transcriptions without worsening the ABX performance.