43. BCD to Gray Converter

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  • 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.

Boolean Equations:

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