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Codiode/Problems/Combinational Logic

Four-Variable K-Map: Basic Grouping with a Group of 8

EasyLogic CircuitAnalyze

Logic synthesis tools rely on Boolean minimization to reduce transistor counts and optimize propagation delay. The Karnaugh map below represents a four-variable Boolean function F(A, B, C, D).

| AB \ CD | 00 | 01 | 11 | 10 | |---|---|---|---|---| | 00 | 1 | 1 | 1 | 1 | | 01 | 1 | 1 | 1 | 1 | | 11 | 0 | 0 | 0 | 0 | | 10 | 1 | 1 | 0 | 0 |

The top two rows correspond to A = 0 and are completely filled with 1s. The bottom row contains two additional 1s in the first two columns.

Determine the optimal groupings to produce the minimal sum-of-products expression for F.

Constraints

  • Groupings must follow standard Karnaugh map rules for adjacency and power-of-two sizing.
  • The final expression must be in minimal sum-of-products (SOP) form.
  • Literals should be written in alphabetical order.

Topics

boolean-algebracombinational-logicsimplificationk-map

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