Synthetic genetic devices can perform molecular computation in living bacteria, which may sense more than one environmental chemical signal, perform complex signal processing in a human-designed way, and respond in a logical manner. IMPLY is one of the four fundamental logic functions and unlike others, it is an "IF-THEN" constraint-based logic. By adopting physical hierarchy of electronics in the realm of in-cell systems chemistry, a full-spectrum transcriptional cascaded synthetic genetic IMPLY gate, which senses and integrates two environmental chemical signals, is designed, fabricated, and optimized in a single Escherichia coli cell. This IMPLY gate is successfully integrated into a 2-input-2-output integrated logic circuit and showed higher signal-decoding efficiency. Further, we showed simple application of those devices by integrating them with an inherent cellular process, where we controlled the cell morphology and color in a logical manner. To fabricate and optimize the genetic devices, a new process pipeline named NETWORK Brick is developed. This pipeline allows fast parallel kinetic optimization and reduction in the unwanted kinetic influence of one DNA module over another. A mathematical model is developed and it shows that response of the genetic devices are digital-like and are mathematically predictable. This single-cell IMPLY gate provides the fundamental constraint-based logic and completes the in-cell molecular logic processing toolbox. The work has significance in the smart biosensor, artificial in-cell molecular computation, synthetic biology, and microbiorobotics.