Understanding the neural code for vision remains a major challenge for neuroscience, with recent efforts influenced by the success of convolutional neural networks. However, spiking neurons make biological vision fundamentally different from the firing rate model implicit in these artificial neural networks. In region V1 of the primate visual cortex, a flashed image is processed in tens of milliseconds, allowing time for only a few action potentials, typically across a small subset of neurons. Moreover, persistent eye motion (ocular drift) changes the location of retinal responses, and thus cortical input, as an image is encoded. Here, we develop a discrete computational model, to explore how these characteristics of the visual system can generate cortical representations that match experimental observations and encode images unambiguously. Our model explicitly represents retinal cone cells, lateral geniculate nucleus (LGN) neurons, and V1 layer 4 (V1L4) neurons, in a feedforward circuit with binary (0 or 1) neural activity and binary connection weights. We incorporate random eye motion, to present each image as a sequence of retinal activity patterns. Hebbian learning, from natural images, determines LGN-V1L4 connectivity. Despite its relative simplicity, our model successfully reproduces phenomena observed in V1L4 simple cells, including: separate on/off receptive fields, orientation tuning, end-inhibition and contrast invariance. Quantitative comparisons with experimental data, for receptive field shapes and tuning curve bandwidths, show good agreement. To investigate ambiguity in the cortical encoding of sensory input, we probe the system with an adversarial attack that finds an alternative image creating exactly the same V1L4 activity pattern as the original image. We discover that microscopic eye movements substantially reduce ambiguity, compared to a static retina. This demonstrates a beneficial role for ocular drift, removing ambiguity from cortical representations.