The Efficient Binary Arithmetic Model (EBAM) introduces a novel approach to digital logic circuit design aimed at minimizing transistor usage in binary arithmetic operations such as addition and subtraction. By employing the Transformer Logic Section (TLS) for one-to-one mapping of arithmetic pairs and separating operations into standardized and carry states, EBAM reduces computational complexity while optimizing circuit space. This unique design, which relies solely on AND gates for operation, demonstrates the ability to handle both neutral and carry states efficiently. Results show that EBAM is versatile, with potential expansion for other arithmetic operations such as multiplication, making it an ideal candidate for light-based or quantum processing environments where efficient circuit design is crucial.