Output Select Analysis: By treating the unused binary combinations (1010 through 1111) as don't-care states, Karnaugh maps simplify the logic equations significantly. The highest bit G3 matches the input D3 perfectly within the valid BCD range.
Hardware Optimization: The circuit routes the BCD inputs into a minimized gate network. G2 relies on a single OR gate, G1 uses an XOR structure, and G0 is constructed from a small network of AND, OR, and NOT gates to handle the non-linear jump at the edge of the BCD range with minimal components.