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Fundamental of Digital Logic (1)

Fundamental of Digital Logic (1). Outline. Boolean Algebra: Boolean Functions/ Logic Functions and Gates Theorems and Properties of Boolean Al gebra Practices: Introduction of Solderless Breadboard Lab practices. Boolean Algebra. Boolean Functions and Gates (1/ 6 ).

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Fundamental of Digital Logic (1)

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  1. Fundamental of Digital Logic (1)

  2. Outline • Boolean Algebra: Boolean Functions/ Logic Functions and Gates Theorems and Properties of Boolean Algebra • Practices: Introduction of Solderless Breadboard Lab practices

  3. Boolean Algebra

  4. Boolean Functions and Gates (1/6)

  5. Boolean Functions and Gates (2/6) AND F = A‧B = AB

  6. Boolean Functions and Gates (3/6) OR F = A + B

  7. Boolean Functions and Gates (4/6)

  8. Boolean Functions and Gates (5/6)

  9. Boolean Functions and Gates (6/6) Exclusive-OR (XOR) F = AB’ + A’B = A ⊕ B

  10. Example The Boolean Function of F1 = x + y’z

  11. Theorems and Properties of Boolean Algebra Single Variable Theorems Two- and Three- Variable Properties

  12. Examples (1/3) • F1(x, y, z) = x’y’z + x’yz + xy’ = x’z(y’ + y) + xy’ = x’z + xy’

  13. Examples (2/3) • F2(x, y) = x(x’ + y) = xx’ + xy = 0 + xy = xy

  14. Examples (3/3) • F3(x, y) = (x’ + y’) ’ = xy (DeMorgan) • F4(x, y) = (x’y’)’ = x + y (DeMorgan)

  15. Practices

  16. Introduction of Solderless Breadboard • Solderless Bredboard is a convenient kit for lay outing circuits without any soldering work. It is very useful for circuit test and modification during practical training. • Components in lab can be reused with breadboard. • Normally, component’s pins are inserted into holes on breadboard. Every five holes are connected together by a brass strip under plastic cover. One of holes is connected to component’s pin and the other holes are for circuit connection with jumpers.

  17. Top View of Solderless Breadboard • Different types of Breadboards

  18. Example: Connection with 74LS00 Chip • Example • VCC & GND must be connected!!

  19. Lab I (1/2) • Equipment:

  20. Lab I (2/2) 1. Please utilize AND and OR gates to demonstrate the Boolean Function of: • X = A ‧ B • X = A + B 2. Pleasefinish the following circuit with Truth Table.

  21. Lab II • Please use Boolean Theorems and Properties to simplify the following functions, and finish circuits with breadboard and Truth Tables. • F1(A, B) = (A + B)’(A’ + B’) • F2(A, B) = A’+ AB • Equipment:

  22. 74LS00

  23. 74LS04

  24. 74LS08

  25. 74LS32

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