Molecular logic gates are capable of performing various logic tasks for biomarker detection, disease diagnostics and therapy, and controlling biological progress. Herein, we integrated multiple components of a logic device into a single DNA 3D nano-assembly with a triangular prism structure. Compared with the separate construction of each component in previously reported DNA logic gate systems, such an integrated design strategy made the 3D DNA nanoprism universal for logic gates, it can be reconfigured to execute diverse logic operations. Binary basic logic gates (OR, AND, INHIBIT and XOR), combinatorial gates (INHIBIT-OR), and multi-valued logic gates (ternary INHIBIT gate) were readily achieved by taking this DNA nanoprism as a universal platform. Moreover, a logic gate system for identification of even numbers and odd numbers from natural numbers was established successfully by employing only this single DNA nanoprism and four short single-stranded DNA. The universality of this nanoprism greatly simplified the design of DNA logic gate system. Additionally, this nanoprism was able to perform logic operation steadily in a biological matrix, indicating that this box-like DNA nanostructure applies to logic gates in a complicated environment. This study provided a unique opportunity to design versatile 3D DNA nanostructure-based intelligent nanodevices, which show great potential in biocomputing, multi-parameter sensing, and intelligent disease diagnostics and therapy.