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Electrical Engineering

Electrical Engineering

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Electrical Engineering

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  1. Engineering the Future Electrical Engineering Digital Circuits FundamentalsHands-on Full-Adder Simulation (afternoon)

  2. Engineering the Future Electrical Engineering: Digital Circuits Fundamentals Binary Numbers Binary Functions

  3. Decimal Numbers

  4. Binary Numbers

  5. Binary Numbers

  6. Binary Counting Exercise • Count up to ? Using 2 bits • Count up to ? Using 3 bits • Count up to ? Using 4 bits • Count up to ? Using 5 bits • Count up to ? Using 6 bits

  7. Binary Numbers

  8. Logic Gates

  9. Logic Gates

  10. Logic Gates

  11. Logic Gates http://www.williamson-labs.com/480_logic.htm#doors

  12. Logic Gates

  13. Binary Addition Networks (Half Adder) With two’s complement numbers, addition is sufficient SUM Half-adder Schematic CARRY

  14. Binary Addition Networks (Cascaded Multi-bit Adder) usually interested in adding more than two bits this motivates the need for the full adder

  15. Binary Addition Networks (Full Adder) S = A’B’CI+A’BCI+AB’CI’+ABCI = CI xor A xor B CO = B CI + A CI + A B = CI (A + B) + A B

  16. A S B Cout Cin A B Cin S Cout 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 One-bit adder • 1-bit binary adder • inputs: A, B, Carry-in • outputs: Sum, Carry-out

  17. Binary Addition Networks (Full Adder/ Half Adder) Standard Approach: 6 Gates Alternative Implementation: 5 Gates SUM CARRY OUT CARRY IN CO = A B + CI (A xor B) = A B + B CI + A CI