A fundamental property of many organisms is an ability to sense, evaluate, and respond to environmental signals. In some situations, generation of an appropriate response requires long-term information storage. A classic example is vernalization, where plants quantitatively sense long-term cold and epigenetically store this cold-exposure information to regulate flowering time. In Arabidopsis thaliana, stable epigenetic memory of cold is digital: following long-term cold exposure, cells respond autonomously in an all-or-nothing fashion, with the fraction of cells that stably silence the floral repressor FLOWERING LOCUS C (FLC) increasing with the cold exposure duration. However, during cold exposure itself it is unknown whether vernalizing cold is registered at FLC in individual cells in an all-or-nothing (digital) manner or is continuously varying (analog). Using mathematical modeling, we found that analog registration of cold temperature is problematic due to impaired analog-to-digital conversion into stable memory. This disadvantage is particularly acute when responding to short cold periods, but is absent when cold temperatures are registered digitally at FLC. We tested this prediction experimentally, exposing plants to short periods of cold interrupted with even shorter warm breaks. For FLC expression, we found that the system responds similarly to both interrupted and uninterrupted cold, arguing for a digital mechanism integrating long-term temperature exposure.