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Boolean Function Analysis and Optimization

Solve problems related to Boolean functions, identify primary implicants, and optimize using SOP form. Understand cost and efficient circuit design.

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Boolean Function Analysis and Optimization

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  1. Problem 4.5 SOP form Primary implicants: , x2 x1x2 x x x x 1 2 1 2 x x x x 3 4 3 4 00 01 11 10 00 01 11 10 00 0 0 1 0 00 1 1 1 1 01 1 1 1 1 01 1 1 1 1 11 0 0 0 0 11 0 1 1 0 10 1 1 1 0 10 0 0 0 0 (b) =0 (b) =1 F= +

  2. POS form x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 0 0 1 0 00 1 1 1 1 01 1 1 1 1 01 1 1 1 1 11 0 0 0 0 11 0 1 1 0 10 1 1 1 0 10 0 0 0 0 (a) (a) F= () () () ()()

  3. Problem 4.6 x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 1 1 1 d 00 1 1 1 1 01 1 1 0 1 01 0 0 0 0 11 d d 0 d 11 1 1 0 1 10 d 1 0 1 1 10 d 0 1 (b) (a) + +++

  4. x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 1 1 1 d 00 1 1 1 1 01 1 1 0 1 01 0 0 0 0 11 d d 0 d 11 1 1 0 1 10 d 1 0 1 1 10 d 0 1 (b) (a) + + +

  5. Problem 4.7 x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 1 1 1 1 00 0 d 0 d 01 0 0 1 1 01 0 1 1 0 11 1 1 1 1 11 1` 0 1 d 10 0 0 0 d 10 1 1 1 1 (b) (a)

  6. x x 1 2 x x x x 1 2 3 4 x x 00 01 11 10 3 4 00 01 11 10 00 1 0 0 1 00 1 0 0 1 01 d 0 0 1 01 d 0 0 1 11 d d 1 0 11 d d 1 0 10 1 d 0 1 10 1 d 0 1 (a) f (a) f f= + f=

  7. Problem 4.12 x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 d 1 0 0 00 1 1 0 0 01 0 0 d 1 01 0 0 0 1 11 0 0 1 0 11 0 1 0 d 10 1 0 d 1 10 1 1 0 d (a) g (a) f f= g= f= g= f= + g= + f= + g= +

  8. Problem 4.12 x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 d 1 0 0 00 1 1 0 0 01 0 0 d 1 01 0 0 0 1 11 0 0 1 0 11 0 1 0 d 10 1 0 d 1 10 1 1 0 d (a) g (a) f f= + g= +

  9. Problem 4.12 x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 d 1 0 0 00 1 1 0 0 01 0 0 d 1 01 0 0 0 1 11 0 0 1 0 11 0 1 0 d 10 1 0 d 1 10 1 1 0 d (a) g (a) f f= + g= + Cost = 5AND+2OR+16ins-AND+8ins-or = 31 < (15+21)=36

  10. Problem 4.12 x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 d 1 0 0 00 1 1 0 0 01 0 0 d 1 01 0 0 0 1 11 0 0 1 0 11 0 1 0 d 10 1 0 d 1 10 1 1 0 d (a) g (a) f f= Cost = 3AND+1OR+8ins-AND+3ins-or =15 g= + Cost = 4AND+1OR+12ins-AND+4ins-or =21

  11. Problem 1 and 3 x x 1 2 x x x 1 2 3 x x 00 01 11 10 3 4 00 01 11 10 0 0 0 d d 00 0 1 1 1 01 0 1 1 0 1 1 0 1 1 11 0 0 0 0 g= F = ()() 10 0 1 0 0 (a) f

  12. Problem 5 wx wx yz yz 00 01 11 10 00 01 11 10 00 0 0 1 1 00 0 0 1 1 01 0 1 1 0 01 0 1 1 0 11 1 1 d d 11 1 1 d d 10 0 0 d d 10 0 0 d d (a) f f= + f = ()()

  13. Problem 5 AB AB CD 00 01 11 10 CD 00 01 11 10 00 0 1 1 0 00 0 1 1 0 01 1 0 0 1 01 1 0 0 1 11 0 0 0 0 11 0 0 0 0 10 0 1 1 0 10 0 1 1 0 g g= D g= () ()(B)

  14. x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 0 0 0 0 00 0 1 d 0 01 1 0 0 1 01 0 d 1 0 11 1 0 0 1 11 0 d d 0 10 1 1 1 1 d 10 1 1 d (b) (a) f= +

  15. x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 0 0 0 0 00 0 1 d 0 01 1 0 0 1 01 0 d 1 0 0 11 1 0 1 11 0 d d 0 10 1 1 1 1 d 10 1 1 d (b) (a) f = ()() ()

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