LOGIC6_r2

# LOGIC6_r2 - Chapter 6 Quine-McCluskey Method Microwave...

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Chapter 6 Quine-McCluskey Method

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(1) Express a function to a minterm expansion. EX : f(A,B,C,D)= Σ m(0,1,2,5,6,7,8,9,10,14) (2) Write each minterm in its binary form, then separate each minterm into groups according to the numbers of 1s’ in its binary form. § Determination of Prime Implicants: (using XY+XY’=X)
EX : group 0 0 0 0 0 0 1 0 0 0 1 group 1 2 0 0 1 0 8 1 0 0 0 5 0 1 0 1 6 0 1 1 0 group 2 9 1 0 0 1 10 1 0 1 0 group 3 7 0 1 1 1 14 1 1 1 0

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(3) Two terms can be combined if they differ in exactly one variable. Comparison of terms in non-adjacent groups is unnecessary since such terms will always differ from at least two variables and can not be combined using XY+XY’=X.) Comparison of terms within a group is unnecessary since two terms with the some number of 1s’ must differ from at least two variables . Only terms in adjacent groups need to be compared .
(4) Make a table as follows : column 1 group 0 0 0000 1 0001 group 1 2 0010 8 1000 5 0101 6 0110 group 2 9 1001 10 1010 group 3 7 0111 14 1110

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Column 2 0,1 000- 5,7 01-1 0,2 00-0 6,7 011- 0,8 -000 6,14 -110 1,5 0-01 10,14 1-10 1,9 -001 2,6 0-10 2,10 -010 8,9 100- 8,10 10-0
Column 3 0,1,8,9 -00- 0,2,8,10 -0-0 0,8,1,9 -00- 2,6,10,14 --10 2,10,6,14 --10

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The terms of which have not been checked off (because they can not be combined with other terms) are called prime implicants . From the decimal in column , we can find the prime implicants in column I. From the decimal in column , we can find the prime implicants in column .
After inspection of the table, the function can be expressed by the sum of its prime implicants. F=(1,5)+(5,7)+(6,7)+(0,1,8,9)+(0,2,8,10)+(2,6,10,14) =A’C’D+A’BD+A’BC+B’C’+B’D’+CD’

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(5) Using the consensus theorem to eliminate redundant terms.
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LOGIC6_r2 - Chapter 6 Quine-McCluskey Method Microwave...

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