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Logic Gates

Logic Gates. Transistors as Switches. EB voltage controls whether the transistor conducts in a common base configuraiton. Logic circuits can be built. AND. In order for current to flow, both switches must be closed Logic notation A B = C. OR. Current flows if either switch is closed

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Logic Gates

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  1. Logic Gates

  2. Transistors as Switches • EB voltage controls whether the transistor conducts in a common base configuraiton. • Logic circuits can be built

  3. AND • In order for current to flow, both switches must be closed • Logic notation AB = C

  4. OR • Current flows if either switch is closed • Logic notation A + B = C

  5. Properties of AND and OR • Commutation • A + B = B + A • A  B = B  A Same as Same as

  6. Properties of AND and OR • Associative Property • A + (B + C) = (A + B) + C • A  (B  C) = (A  B)  C =

  7. Properties of AND and OR • Distributive Property • A + B  C = (A + B)  (A + C) • A + B  C

  8. Distributive Property • (A + B)  (A + C)

  9. Binary Addition Notice that the carry results are the same as AND C = A  B

  10. Inversion (NOT) Logic:

  11. Exclusive OR (XOR) Either A or B, but not both This is sometimes called the inequality detector, because the result will be 0 when the inputs are the same and 1 when they are different. The truth table is the same as for S on Binary Addition. S = A  B

  12. Getting the XOR Two ways of getting S = 1

  13. Circuit for XOR Accumulating our results: Binary addition is the result of XOR plus AND

  14. Half Adder Called a half adder because we haven’t allowed for any carry bit on input. In elementary addition of numbers, we always need to allow for a carry from one column to the next. 18 25 3 (plus a carry) 4

  15. Full Adder

  16. Full Adder Circuit

  17. Chaining the Full Adder Possible to use the same scheme for subtraction by noting that A – B = A + (-B)

  18. Binary Counting Use 1 for ON Use 0 for OFF = 00101011 So our example has 25 + 23 + 21 + 20 = 32 + 8 + 2 + 1 = 43 Binary Counter

  19. NAND (NOT AND)

  20. NOR (NOT OR)

  21. Exclusive NOR Equality Detector

  22. Summary

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