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ELEC1700 Computer Engineering 1 Week 5 Wednesday lecture Simplifying logic expressions

ELEC1700 Computer Engineering 1 Week 5 Wednesday lecture Simplifying logic expressions Semester 1, 2013. Simplification using Karnaugh maps. Simplifying logic expressions. A B C F 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1

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ELEC1700 Computer Engineering 1 Week 5 Wednesday lecture Simplifying logic expressions

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  1. ELEC1700Computer Engineering 1Week 5 Wednesday lectureSimplifying logic expressions Semester 1, 2013

  2. Simplification using Karnaugh maps Simplifying logic expressions

  3. A B C F 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 From truth table to Karnaugh map

  4. From truth table to Karnaugh map Draw the Karnaugh map for the expression defined by the following truth table A B C X minterms ------------------------------------ 0 0 0 0 0 0 1 1 A’B’C 0 1 0 1 A’BC’ 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 ABC’ 1 1 1 1 ABC

  5. 1 1 1 1 1 1 From expression to Karnaugh map Fill in the Karnaugh map for the expression: C 000 001 010 011 100 101 110 B 1 A Could also create truth table for expression, then use method on p7

  6. Simplification using Karnaugh maps After Karnaugh map has been filled in for a given expression, simplification is a 2-step process: Group the 1’s Groups to enclose adjacent cells Groups must be square or rectangular, and contain 1,2,4,8 or 16 cells Goal is to: Cover all 1’s at least once Maximise size of groups Minimise number of groups Determine simplified SOP expression

  7. Grouping the 1’s A B C X ------------------------------------ 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 Example: use a Karnaugh map to simplify the expression in the truth table below

  8. Determine simplified SOP expression Simplified expression:

  9. Some “wrap-around” adjacencies

  10. Grouping the 1’s

  11. Determining simplified SOP expression

  12. An example with wrap-around adjacency A B C X ------------------------------------ 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 Example: use a Karnaugh map to simplify the expression in the truth table below See Karnaugh map (b) on pp.10–11

  13. The alarm problem revisited Use a Karnaugh map to simplify the expression from the alarm problem in previous lecture, pp.14–19:

  14. C 1 1 B 1 1 A 1 1 The alarm problem revisited 1 1 1 1 1 1

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