week4 - NAND/NOR Implementations ■ NAND/NOR are universal...

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Unformatted text preview: NAND/NOR Implementations ■ NAND/NOR are universal gates ■ Use for different technologies ■ CMOS: Easy to implement NAND gates ■ Methodology ■ NAND Implementation ■ Use the K-map to develop a sum of products ■ Change AND/OR to NAND only Truth Tables to NANDs Truth Tables to NANDs X Y Z G 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 NOR Implementations ■ Methodology ■ NOR Implementation ■ Use the K-map to develop a product of sums ■ Focus on the zeros ■ Write F as a sum of products ■ Use DeMorgan’s Law to get F = F ■ Change OR/AND to NOR only Truth Tables to NORs Truth Tables to NORs X Y Z G 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Converting General Circuits to NAND/NOR form ■ Group gates into levels, insert double inversions on alternating levels (bubble matching) ■ Alternating AND/OR becomes all NAND or NOR A B C D E F A B C D E F Level 1 Level 2 Level 3 Level 4 Convert to NOR Circuit Convert to NAND Circuit Converting to NAND/NOR form ■ Some circuits may require internal inverters Level 1 Level 2 Level 3 A B C A B C Convert to NAND Circuit Convert to NOR Circuit Review: Circuit Implementation Techniques ■ Truth Tables - Case-by-case circuit description ■ Boolean Algebra - Math form for optimization ■ K-Maps - Simplification technique ■ Circuit Diagrams - TTL Implementations ■ AND/OR/INVERT for easy Sum of Products, Product of Sums ■ NAND/NOR/ to match underlying technology 10 Case Study: Seven Segment Display ■ Chip to drive digital display L1 L 6 L2 L3 L 7 L 4 L 5 11 Case Study (cont.) B3 B2 B1 B0 Val L1 L2 L3 L4 L5 L6 L7 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 4 1 1 1 1 1 1 5 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 7 1 1 1 1 8 1 1 1 1 1 1 1 1 1 9 1 1 1 1 1 1 L1 L 6 L2 L3 L 7 L 4 L 5 12 Case Study (cont.) ■ Implement L4: 13 Number Systems ■ Problem: Implement simple pocket calculator ■ Need: Display, adders & subtractors, inputs ■ Display: Seven segment displays ■ Inputs: Switches ■ Missing: Way to implement numbers in binary ■ Approach: From decimal to binary numbers (and back) 14...
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week4 - NAND/NOR Implementations ■ NAND/NOR are universal...

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