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Combinational Logic Circuits

Combinational Logic Circuits. Chapter 2. Logic gates. Boolean algebra. Example. Example. 1. 2. 3. 4. 5. 6. Example. Standard form: M interms and maxterms. Example. Maxterms. Some properties. 1. 若有 n 個變數，則有 2 n 個項 (0~2 n -1) 2.

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Combinational Logic Circuits

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  1. Combinational Logic Circuits Chapter 2

  2. Logic gates

  3. Boolean algebra

  4. Example

  5. Example 1. 2. 3. 4. 5. 6.

  6. Example

  7. Standard form: Minterms and maxterms

  8. Example

  9. Maxterms

  10. Some properties 1. 若有n個變數，則有2n個項(0~2n-1) 2. 3. G(x,y)=m(0,1,2,3)=1; G(x,y,z)=m(0,1,2,3,4,5,6,7)=1

  11. Sum-of-products (S.O.P)

  12. (三級) (二級)

  13. Product-of-sums

  14. Example F(x,y,z)=m(1,4,5,6,7)

  15. Map simplification Two variables

  16. Example

  17. Three variables

  18. F(x,y,z)=m(2,3,4,5)

  19. (a) F(x,y,z)=m(0,2,4,6)(b) F(x,y,z)=m(0,1,2,3,6,7)

  20. Examples

  21. F(x,y,z)=m(1,3,4,5,6)

  22. F(x,y,z)=m(1,2,3,5,7)

  23. Four-variable map

  24. F(w,x,y,z)=m(0,1,2,4,5,6,8,9,12,13,14)

  25. F(A,B,C,D)=m(0,1,2,6,8,9,10)

  26. Prime implicants

  27. Essential prime implicants

  28. F(A,B,C,D)=m(0,1,2,4,5,10,11,13,15)

  29. F(A,B,C,D)=m(0,1,2,5,8,9,10) SOP: POS:

  30. POSSOP

  31. Don’t-care conditions F(A,B,C,D)=m(1,3,7,11,15) d(A,B,C,D)=m(0,2,5)

  32. NAND gate – a universal gate

  33. Example: NAND

  34. NOR

  35. Exclusive-OR gate

  36. Some properties

  37. Gates

  38. Odd function

  39. Even parity generator Parity generator XYZ XYZP C Communication channel Parity checker If no bits error If an error occurs

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