QuineMc Clusky Minimization Method Discussion D 3 2

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Quine-Mc. Clusky Minimization Method Discussion D 3. 2

Quine-Mc. Clusky Minimization Method Discussion D 3. 2

Quine-Mc. Cluskey Method • Tabular Representations • Prime Implicants • Essential Prime Implicants

Quine-Mc. Cluskey Method • Tabular Representations • Prime Implicants • Essential Prime Implicants

Tabular Representations YZ WX 00 W'X 01 -- WY'Z 1 -01 01 11 00

Tabular Representations YZ WX 00 W'X 01 -- WY'Z 1 -01 01 11 00 01 10 1 1 11 1 10 1 W'YZ' 0 -10 XY -11 - F = XY + W'YZ' + WY'Z + W'X

Prime Implicants F = XY'Z + X'Z' + X'Y Each product term is an

Prime Implicants F = XY'Z + X'Z' + X'Y Each product term is an implicant A product term that cannot have any of its variables removed and still imply the logic function is called a prime implicant.

Prime Implicants X YZ 00 01 11 0 1 1 -- 10 1 1

Prime Implicants X YZ 00 01 11 0 1 1 -- 10 1 1 F = YZ' + X 1 -10

Prime Implicants Minterm 0 1 2 3 4 5 6 7 X O 0

Prime Implicants Minterm 0 1 2 3 4 5 6 7 X O 0 0 0 1 1 Y O 0 1 1 Z O 1 0 1 F 0 0 1 1 1 1 X YZ 00 01 11 0 1 1 -- 10 1 1 1 F = YZ' + X -10

Finding Prime Implicants Step 1 2 4 5 6 7 0 1 1 1

Finding Prime Implicants Step 1 2 4 5 6 7 0 1 1 1 O 0 1 1 0 0 1 Step 3 Step 2 (2, 6) (4, 5) (4, 6) (5, 7) (6, 7) 1 1 1 0 0 1 - (4, 5, 6, 7) 1 - (4, 6, 5, 7) 1 - - All unchecked entries are Prime Implicants -10 1 -- YZ' X

Prime Implicants Minterm 0 1 2 3 4 5 6 7 X O 0

Prime Implicants Minterm 0 1 2 3 4 5 6 7 X O 0 0 1 1 1 Y O 0 1 1 Z O 1 0 1 F 0 0 1 1 1 1 X YZ 00 01 11 0 1 1 -- 10 1 1 1 F = YZ' + X -10

Essential Prime Implicants YZ WX 00 00 1 01 11 10 1 1 1

Essential Prime Implicants YZ WX 00 00 1 01 11 10 1 1 1 1 1 Find the essential prime implicants using the Q-M method.

Essential Prime Implicants minterms YZ WX 00 00 1 01 11 10 1 1

Essential Prime Implicants minterms YZ WX 00 00 1 01 11 10 1 1 1 1 1 0 1 2 8 3 5 10 7 14 15 0000 0001 0010 1000 0011 0101 1010 0111 1110 1111

Finding Prime Implicants Step 1 0 1 2 8 3 5 10 7 14

Finding Prime Implicants Step 1 0 1 2 8 3 5 10 7 14 15 0000 0001 0010 1000 0011 0101 1010 0111 1110 1111 Step 2 (0, 1) (0, 2) (0, 8) (1, 3) (1, 5) (2, 3) (2, 10) (8, 10) (3, 7) (5, 7) (10, 14) (7, 15) (14, 15) 00000 -0 -000 00 -1 0 -01 001 -010 10 -0 0 -11 01 -1 1 -10 -111 111 - Step 3 (0, 1, 2, 3) 00 -- (0, 2, 1, 3) 00 -- (0, 2, 8, 10) (0, 8, 2, 10) (1, 3, 5, 7) (1, 5, 3, 7) -0 -0 0 --1 6 Prime Implicants 1 -10 -111 111 - 00 --0 -0 0 --1

Find Essential Prime Implicants Prime Covered Implicant minterms * 1 -10 -111 11100 --0

Find Essential Prime Implicants Prime Covered Implicant minterms * 1 -10 -111 11100 --0 -0 0 --1 0 10, 14 7, 15 14, 15 0, 1, 2, 3 X 0, 2, 8, 10 X 1, 3, 5, 7 1 2 Minterms 3 5 7 8 X 10 14 X X X X 15 X X

3 Prime Implicants F = W'Z + WXY + X'Z' YZ WX 00 0

3 Prime Implicants F = W'Z + WXY + X'Z' YZ WX 00 0 --1 W'Z 00 1 01 11 X'Z' -0 -0 10 01 11 10 1 1 1 1 111 WXY

3 Prime Implicants F = W'Z + WXY + X'Z' YZ WX 00 0

3 Prime Implicants F = W'Z + WXY + X'Z' YZ WX 00 0 --1 W'Z 00 1 01 10 1 1 11 X'Z' 01 -111 1 1 -0 -0 1 -10 00 -- 111 WXY

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