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: This paper demonstrates that a designed Boolean logic circuit with feedback connections can transform completely random binary inputs into structured output sequences exhibiting lower Shannonentropy. We establish that the circuit output follows an ergodic Markov chain, which—by the law of large numbers—converges to a non-uniform probability distribution over sequences. This convergence reduces Shannon entropy from its maximum value of 4.7004 bits (for perfectly random sequences) to lower values. We formalize the circuit architecture using combinational logic gates with controlled probabilities and demonstrate through both mathematical derivation and computational experiments that random inputs, when processed through appropriate logic arrangements, can produce increasingly deterministic patterns. This work establishes a fundamental connection between Boolean circuit topology and information-theoretic properties, suggesting that determinism can emerge from randomness through structural design.