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Codiode/Problems/Combinational Logic

4-Variable Function via 8:1 MUX

HardLogic CircuitBuild

Area-constrained standard cell designs frequently map complex logic functions directly into multiplexer trees. Shannon expansion allows a hardware designer to fold an N-variable Boolean function into an (N-1)-variable multiplexer to save significant silicon area.

Implement the 4-variable logic function Y defined by the following truth table.

| A | B | C | D | Y | |-----|-----|-----|-----|-----| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 0 | 0 | 1 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 0 | | 1 | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 1 | | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | 1 |

Constraints

  • Use exactly one 8:1 MUX.
  • Use at most one NOT gate.
  • Do not use any other logic gates.
  • Connect B, C, and D to the MUX select lines, with B as the most significant bit.

Topics

shannon-expansionmultiplexersboolean-logic

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