Based on the Grossberg mathematical model called the outstar, a modular neural net with on-chip learning and memory is designed and analyzed. The outstar is the minimal anatomy that can interpret the classical conditioning or associative memory. It can also be served as a general-purpose pattern learning device. To realize the outstar, CMOS (complimentary metal-oxide semiconductor) current-mode analog dividers are developed to implement the special memory called the ratio-type memory. Furthermore, a CMOS current-mode analog multiplier is used to implement the correlation. The implemented CMOS outstar can on-chip store the relative ratio values of the trained weights for a long time. It can also be modularized to construct general neural nets. HSPICE (a circuit simulator of Meta Software, Inc.) simulation results of the CMOS outstar circuits as associative memory and pattern learner have successfully verified their functions. The measured results of the fabricated CMOS outstar circuits have also successfully confirmed the ratio memory and on-chip learning capability of the circuits. Furthermore, it has been shown that the storage time of the ratio memory can be as long as five minutes without refreshment. Also the outstar can enhance the contrast of the stored pattern within a long period. This makes the outstar circuits quite feasible in many applications.