44. Gray Code to BCD Converter

• Output Select Analysis: By treating the invalid decimal values (10 through 15) as don't-care states, Karnaugh maps simplify the logic equations down to a streamlined structure. The highest bit D3 turns on only when both G3 and G2 are active.
• Hardware Optimization: The circuit routes the Gray code inputs into a cascading network of gates. D2, D1, and D0 leverage shared XOR structures to decode the non-linear Gray transitions back into sequential binary values using the fewest possible parts.

Boolean Equations:

• D3 = G3 . G2
• D2 = G3 ^ G2
• D1 = (G3 ^ G2) ^ G1
• D0 = (G3 ^ G2) ^ (G1 ^ G0)