Self-assembly-the autonomous organization of components into patterns and structures-is a promising technology for the mass production of organic electronics. Making integrated circuits using a bottom-up approach involving self-assembling molecules was proposed in the 1970s. The basic building block of such an integrated circuit is the self-assembled-monolayer field-effect transistor (SAMFET), where the semiconductor is a monolayer spontaneously formed on the gate dielectric. In the SAMFETs fabricated so far, current modulation has only been observed in submicrometre channels, the lack of efficient charge transport in longer channels being due to defects and the limited intermolecular pi-pi coupling between the molecules in the self-assembled monolayers. Low field-effect carrier mobility, low yield and poor reproducibility have prohibited the realization of bottom-up integrated circuits. Here we demonstrate SAMFETs with long-range intermolecular pi-pi coupling in the monolayer. We achieve dense packing by using liquid-crystalline molecules consisting of a pi-conjugated mesogenic core separated by a long aliphatic chain from a monofunctionalized anchor group. The resulting SAMFETs exhibit a bulk-like carrier mobility, large current modulation and high reproducibility. As a first step towards functional circuits, we combine the SAMFETs into logic gates as inverters; the small parameter spread then allows us to combine the inverters into ring oscillators. We demonstrate real logic functionality by constructing a 15-bit code generator in which hundreds of SAMFETs are addressed simultaneously. Bridging the gap between discrete monolayer transistors and functional self-assembled integrated circuits puts bottom-up electronics in a new perspective.