The ability to perform molecular-level computation in mammalian cells has the potential to enable a new wave of sophisticated cell-based therapies and diagnostics. To this end, we developed a Boolean logic framework utilizing artificial Cys(2)-His(2) zinc finger transcription factors (ZF-TFs) as computing elements. Artificial ZFs can be designed to specifically bind different DNA sequences and thus comprise a diverse set of components ideal for the construction of scalable networks. We generate ZF-TF activators and repressors and demonstrate a novel, general method to tune ZF-TF response by fusing ZF-TFs to leucine zipper homodimerization domains. We describe 15 transcriptional activators that display 2- to 463-fold induction and 15 transcriptional repressors that show 1.3- to 16-fold repression. Using these ZF-TFs, we compute OR, NOR, AND and NAND logic, employing hybrid promoters and split intein-mediated protein splicing to integrate signals. The split intein strategy is able to fully reconstitute the ZF-TFs, maintaining them as a uniform set of computing elements. Together, these components comprise a robust platform for building mammalian synthetic gene circuits capable of precisely modulating cellular behavior.