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KARNAUGH MAP Introduction Strategy for Minimization Minimization of Product-of-Sums Forms Minimization of More Complex Expressions Don't care Terms 1

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Introduction Why karnaugh map Example (With Boolean algebra) 2

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Introduction ( cont. ) Using Boolean algebra for minimization causes it’s own problem because of it mainly being a trial and error process, and we can almost never be sure that we have reached a minimal representation. If we can form a graphical notation for our Boolean algebra the insight need for the minimization will be less vital in solving the problems. We can come close to our aim by using a graphical notation named Karnaugh Map that will be defined in next slides 3

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Introduction ( cont. ) Comparing Karnaugh Map and Boolean Algebra ABW 000 011 101 111 Truth Table 0 1 1 1 B A 0 0 1 1 W Karnaugh Map 4 As it can be seen, each box of the Karnaugh map corresponds to a row of the truth table and has been numbered accordingly This form of representing w in the following example is called a Sum of Product (SOP) Which will be define in next slides

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Strategy for Minimization Terminology Minimization Procedure 5

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Terminology Implicant : Product term that implies function Prime Implicant : An Implicant that is not completely covered by any other Implicant but itself Essential prime Implicant : A prime Implicant that has a minter not covered by any other prime Implicant Product term : An and expression 6

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Terminology Minterm : We define a Minterm to be a product that contains all variables of that particular switching function in either complemented or non-complemented form Maxterm : We define a Maxterm to be a sum that contains all variables of that particular switching function in either complemented or non-complemented form Standard SOP(Sum Of Products) : In standard SOP, the products are obtained directly from the Karnaugh map or truth table, so the SOP contains all of the variables of the function Standard POS(Product Of Sums) : In standard POS, the products are obtained directly from the Karnaugh map or truth table, so the POS contains all of the variables of the function 7

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Terminology ( cont. ) A simpler shorthand form of representing a SOP is to use the number of the Minterms that appear in that representation. In the following example for instance we could have written 8 0001 1101 0 01 11 10 0 1 Karnaugh Map 13 2 4 5 7 6 0 AB C

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Terminology ( cont. ) Sometimes writing an expression in a POS form is easier as seen in the following example: 0110 1111 00 01 11 10 0 1 Karnaugh Map 1 3 2 5 7 6 4 0 AB C 9

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Strategy for Minimization Terminology Minimization Procedure 10

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