QuineMcCluskey Algorithm


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1 QuineMcCluskey Algorithm Useful for minimizing equations with more than 4 inputs. Like Kmap, also uses combining theorem Allows for automation Chapter <>
2 Edward McCluskey (9906) Pioneer in Electrical Engineering First president of IEEE Professor at Princeton, then Stanford 955: QuineMcCluskey Algorithm Chapter <>
3 QuineMcCluskey Algorithm Method:. s Table: List each minterm, sorted by the number of s it contains. Combine minterms.. Prime Implicant Table: When you can t combine anymore, list prime implicants and the minterms they cover. 3. Select Prime to cover all minterms. Chapter <3>
4 QuineMcCluskey Example ABC Y Chapter <4>
5 s Table QuineMcCluskey Example ABC Y of 's 0 Size 000 m0 00 m 00 m 0 m3 0 m5 0 m6 Order the minterms by the number of s they have. Chapter <5>
6 s Table QuineMcCluskey Example ABC Y of 's 0 Size 000 m0 00 m 00 m 0 m3 0 m5 0 m6 Size 00 m(0,) 00 m(0,) 0 m(,3) 0 m(,5) 0 m(,3) 0 m(,6) Combine minterms in adjacent groups (starting with the top group). To combine terms, minterm can differ (be or 0) in only place  indicates don t care Chapter <6>
7 s Table QuineMcCluskey Example ABC Y of 's 0 Size 000 m0 00 m 00 m 0 m3 0 m5 0 m6 Size 00 m(0,) 00 m(0,) 0 m(,3) 0 m(,5) 0 m(,3) 0 m(,6) Size m(0,,,3) Combine minterms in adjacent groups (starting with the top group). To combine terms, minterm can differ (be or 0) in only place  (don t care) acts like another variable (0,, ) Match up  first. Chapter <7>
8 s Table QuineMcCluskey Example ABC Y of 's 0 Size 000 m0 00 m 00 m 0 m3 0 m5 0 m6 Size 00 m(0,) 00 m(0,) 0 m(,3) 0 m(,5)* 0 m(,3) 0 m(,6)* Size m(0,,,3)* List prime implicants: Largest implicants containing a given minterm For example m(0,) is an implicant but not a prime implicant, because m(0,,,3) is a larger implicant containing those minterms. However, m(,5) is a prime implicant no larger implicant exists that contains minterm 5. Chapter <8>
9 Prime Implicant Table s Table QuineMcCluskey Example ABC Y of 's 0 Size 000 m0 00 m 00 m 0 m3 0 m5 0 m6 Size 00 m(0,) 00 m(0,) 0 m(,3) 0 m(,5)* 0 m(,3) 0 m(,6)* Size m(0,,,3)* List prime implicants. Prime m(0,,,3) m(,5) m(,6) Minterms ABC Show which of the required minterms each includes. Chapter <9>
10 Prime Implicant Table s Table QuineMcCluskey Example ABC Y of 's 0 Prime m(0,,,3) m(,5) m(,6) Size 000 m0 00 m 00 m 0 m3 0 m5 0 m6 Minterms Size 00 m(0,) 00 m(0,) 0 m(,3) 0 m(,5)* 0 m(,3) 0 m(,6)* Size m(0,,,3)* ABC Select columns with only. Corresponding prime implicants must be included in equation. Chapter <0>
11 Prime Implicant Table s Table QuineMcCluskey Example ABC Y of 's 0 Prime m(0,,,3) m(,5) m(,6) Size 000 m0 00 m 00 m 0 m3 0 m5 0 m6 Minterms Size 00 m(0,) 00 m(0,) 0 m(,3) 0 m(,5)* 0 m(,3) 0 m(,6)* Size m(0,,,3)* ABC Select columns with only. Corresponding prime implicants must be included in equation. Chapter <>
12 Prime Implicant Table s Table QuineMcCluskey Example ABC Y of 's 0 Prime m(0,,,3) m(,5) m(,6) Size 000 m0 00 m 00 m 0 m3 0 m5 0 m6 Minterms Size 00 m(0,) 00 m(0,) 0 m(,3) 0 m(,5)* 0 m(,3) 0 m(,6)* Y = A + BC + BC ABC Chapter <> Size m(0,,,3)* Select columns with only. Corresponding prime implicants must be included in equation.
13 QuineMcCluskey Example ABCD Y Chapter <3>
14 s Table QuineMcCluskey Example ABCD Y of 's 3 Size 000 m 000 m 000 m4 000 m8 00 m3 00 m6 00 m9 00 m0 0 m4 Chapter <4>
15 s Table QuineMcCluskey Example ABCD Y of 's 3 Size 000 m 000 m 000 m4 000 m8 00 m3 00 m6 00 m9 00 m0 0 m4 Size 00 m(,3) 00 m(,9) 00 m(,3) 00 m(,6) 00 m(,0) 00 m(4,6) 00 m(8,9) 00 m(8,0) 0 m(6,4) 0 m(0,4) Chapter <5>
16 s Table QuineMcCluskey Example ABCD Y of 's 3 Size 000 m 000 m 000 m4 000 m8 00 m3 00 m6 00 m9 00 m0 0 m4 Size 00 m(,3) 00 m(,9) 00 m(,3) 00 m(,6) 00 m(,0) 00 m(4,6) 00 m(8,9) 00 m(8,0) 0 m(6,4) 0 m(0,4) Size m(,6,0,4) Chapter <6>
17 s Table QuineMcCluskey Example ABCD Y of 's 3 Size 000 m 000 m 000 m4 000 m8 00 m3 00 m6 00 m9 00 m0 0 m4 Size 00 m(,3)* 00 m(,9)* 00 m(,3)* 00 m(,6) 00 m(,0) 00 m(4,6)* 00 m(8,9)* 00 m(8,0)* 0 m(6,4) 0 m(0,4) Size m(,6,0,4)* Chapter <7>
18 Prime Implicant Table s Table QuineMcCluskey Example ABCD Y of 's 3 Size 000 m 000 m 000 m4 000 m8 00 m3 00 m6 00 m9 00 m0 0 m4 Prime m(,6,0,4) m(,3) m(,9) m(,3) m(4,6) m(8,9) m(8,0) Size 00 m(,3)* 00 m(,9)* 00 m(,3)* 00 m(,6) 00 m(,0) 00 m(4,6)* 00 m(8,9)* 00 m(8,0)* 0 m(6,4) 0 m(0,4) Minterms Chapter <8> Size m(,6,0,4)* ABCD
19 Prime Implicant Table QuineMcCluskey Example ABCD Y Prime m(,6,0,4) m(,3) m(,9) m(,3) m(4,6) m(8,9) m(8,0) Minterms ABCD Chapter <9>
20 Prime Implicant Table QuineMcCluskey Example ABCD Y Prime m(,6,0,4) m(,3) m(,9) m(,3) m(4,6) m(8,9) m(8,0) Minterms ABCD Chapter <0>
21 Prime Implicant Table QuineMcCluskey Example ABCD Y Prime m(,6,0,4) m(,3) m(,9) m(,3) m(4,6) m(8,9) m(8,0) Minterms ABCD Chapter <>
22 Prime Implicant Table QuineMcCluskey Example ABCD Y Prime m(,6,0,4) m(,3) m(,9) m(,3) m(4,6) m(8,9) m(8,0) Minterms ABCD Chapter <>
23 Prime Implicant Table QuineMcCluskey Example ABCD Y Prime m(,6,0,4) m(,3) m(,9) m(,3) m(4,6) m(8,9) m(8,0) Minterms ABCD Y = CD + ABD + ABC Chapter <3>
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