| Logic Simplification |
| Logic Expression Simplification |
| Simplification Example |
| Notice Certain ÒAdjacenciesÓ |
| Any other Adjacencies? (ok to use a row more than once) |
| Adjacencies can Overlap |
| Any More Adjacencies? |
| Any More Adjacencies? |
| unsimplified majority |
| simplified majority |
| Simplified/Unsimplified Comparison for Majority |
| Implications for Simplified Functions |
| Visualizing Adjacencies |
| Hypercubes (connected vertices = adjacent) |
| Hypercubes |
| Sub-cubes |
| Sub-cubes |
| Which sets are subcubes? |
| Plotting Functions on Hypercubes |
| Simplified Functions on Hypercubes |
| Sub-Cube Dimensions |
| SOP Circuits |
| Simplified Covers |
| Maximality |
| Maximality |
| More-is-Less Principle |
| EinsteinÕs Principle: |
| Non-Uniqueness of Simplest Cover |
| Non-Uniqueness of Simplest Cover |
| 4-D Hypercube |
| Alternate 4-D hypercube
representation (= ÒshadowÓ of a Tesseract) |
| Plotting Function on 4-D Hypercube |
| Plotting Function on 4-D Hypercube |
| Plotting Function on 4-D Hypercube |
| Plotting Function on 4-D Hypercube |
| Plotting Function on 4-D Hypercube |
| Plotting Function on 4-D Hypercube |
| Plotting Function on 4-D Hypercube |
| Plotting Function on 4-D Hypercube |
| Plotting Function on 4-D Hypercube |
| Hypercube Function-Plotting Applet |
| Gray Code on a Hypercube |
| Other CS uses of Hypercubes |
| Non-CS uses of Hypercubes |
| Hypercubes occur wherever independent attributes are found: e.g. genetics, ÒcomplexityÓ |
| More Hypercube Projections |
| Non-CS uses of Hypercubes: chemistry |
| Hypercube Game |
| RubickÕs Hypercube |
| Karnaugh Maps |
| Ò3-DÓ Karnaugh Map |
| Covering on a Karnaugh Map |
| Covering on a Karnaugh Map |
| Try this one |
| Answer |
| Using a Karnaugh Map to Prove Equalities |
| Using a Karnaugh Map to Prove Equalities |
| 4-D Karnaugh Map |
| Implied connections on
4-D Karnaugh Map |
| Minterm Numbering on 4-D Karnaugh Map |
| Assorted Sub-Cubes on 4-D Karnaugh Maps |
| Try this one |
| Exercises, etc. |
| Simplification with ÒDonÕt CareÓ Combinations |
| Example: mod 3 adder |
| Plot Function on a K-Map |
| Plot Function on a K-Map |
| Do the other half. |
| The other half. |
| The other half. |
| Implementation using NAND gates |
| Sufficiency |
| Sufficiency |
| nand alone is sufficient |
| Exercises |
| Bubble Logic |
| SOP form using nandÕs only |
| Logic Rebuses |
| Common Logic Packages |
| mod-2 adder with carry-out |
| mod-2 adder with carry-in/out |
| 4-bit ripple-carry adder |
| 4-bit decoder |
| 4-bit encoder |
| multiplexor |
| demultiplexor |
| Exercises |