The control of gene expression is an important tool for metabolic engineering, the design of synthetic gene networks, and protein manufacturing. The most successful approaches to date are based on modulating mRNA synthesis via an inducible coupling to transcriptional effectors. Here we present a biological programming structure that leverages a system of engineered transcription factors and complementary genetic architectures. We use a modular design strategy to create 27 non-natural and non-synonymous transcription factors using the lactose repressor topology as a guide. To direct systems of engineered transcription factors we employ parallel and series genetic (DNA) architectures and confer fundamental and combinatorial logical control over gene expression. Here we achieve AND, OR, NOT, and NOR logical controls in addition to two non-canonical half-AND operations. The basic logical operations and corresponding parallel and series genetic architectures represent the building blocks for subsequent combinatorial programs, which display both digital and analog performance.