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CPE 169 Digital Design Laboratory

Experiment #3: Introduction to Function Reduction, Implementation, and Function Forms. CPE 169 Digital Design Laboratory. Function Reduction. General approach: make function smaller Underlying purpose: make it cheaper to implement the function.

william-garza
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CPE 169 Digital Design Laboratory

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  1. Experiment #3:Introduction to Function Reduction, Implementation, and Function Forms CPE 169 Digital Design Laboratory

  2. Function Reduction • General approach: make function smaller • Underlying purpose: make it cheaperto implement the function. • True definition dependent upon how “cheaper” is defined • General correlation between a “reduced function” and an inexpensive implementation

  3. Minimum Cost Implementation • Based on definition of “cost” • Cost has no absolute definition: • Could include: • Cost of components (digital IC’s, circuit board,…) • Cost of development (engineering labor, tools,…) • Cost of manufacturing (tooling, test fixtures,…) • Component Costs change with: • current part availability and/or pricing • quantity discounts • changes in technology • Our metrics: • # of IC’s • # of Gates (including NOT gates) • # of Gate Inputs • # of Literals • Experiment 3: minimum cost defined by the number of gates required to implement function.

  4. Reducing Functions • Computer-based methods • fast, concise but cookbook approach • Boolean algebra • instructive but slow, error prone • Karnaugh Maps • fun and exciting but limited to functions of 4 - 5 variables

  5. Function Forms • Boolean functions can be used to describe complex operations such as adders, multipliers, etc. • Infinite number of different circuits can be used to implement any given function • Standard function forms: • SOP (AND/OR) • POS (OR/AND) • Several common forms are derived from SOP and POS using DeMorgan’s theorem

  6. DeMorgan’s Theorems • Can be used to generate different function forms:

  7. Experiment 3 Procedure Overview • Download circuit from CPE 169 website • .bit file (Nexys) • Analyze the implemented function • Create a Truth Table (include in report!!) • Reduce the function to minimized SOP & POS forms • K-Maps (include in report!!) • Implement the function on the Nexys and breadboard using discrete logic IC’s: (Don’t forget detailed schematics in report!!) • NAND / NAND form (SOP) • NOR / NOR form (POS) • Compare results • Get Instructor Sign-off Sheet & signature (include in report!)

  8. Note for Next Week BEFORE LAB: • Be sure to run through the B2 Spice A/D Tutorial (on the CPE-169 website) Brief overview of the logic circuit simulation tool you will be using in next week’s lab

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