DNA computing has proven to possess strong parallel processing capabilities, offering notable advantages for multi-objective computation. Traditional, complex nonlinear DNA molecular logic circuits require the pre-construction of basic logic gates, followed by their cascading to achieve logic functions. However, as the number of cascade levels increases, more DNA strands are required to amplify and recover signals, causing the system's reaction time to grow exponentially. This paper introduces a novel approach for building complex nonlinear digital logic circuits using DNA winner-take-all neural networks. The logic circuit comprises four computational modules: weight multiplication, summation, competitive annihilation, and reporting. First, an annihilation strand is designed to control the reaction rate between two competing signals, resolving the interference between weight multiplication and competitive annihilation. Second, new grouping strategies—complementary annihilation, equal annihilation, and denoise annihilation—are introduced. These strategies exponentially reduce the number of competitive strands and significantly decrease system reaction time. The effect becomes more pronounced as the number of input patterns increases. Finally, 2-4, 3-8, and 4-16 decoder circuits are built using the winner-take-all neural networks, and an$\boldsymbol{n}\boldsymbol{-}\boldsymbol{2}^{\boldsymbol{n}}$universal decoder model is further developed. This study presents an effective method for implementing complex nonlinear logic circuits through DNA strand displacement reactions.