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Step of 2 4.060E (a) Write the given Karnaugh map for 6-variable function is shown in Figure 1. W W WX WX YZ 00 01 10 YZ 00 01 11 10 0 4 12 8 16 20 28 24 00 00 UVYZ 17 25 01 1 1 1 01 1 1 3 7 15 11 19 23 31 27 11 11 1 1 Y Y 10 2 6 14 10 10 18 22 30 26 U,V=0,0 U,V=0,1 X W X W WX WX YZ 00 01 11 10 YZ 00 01 11 10 32 00 36 44 40 00 48 52 60 56 33 32 41 1 1 01 49 57 01 1 z 35 39 47 43 II 51 55 63 59 11 Y Y 10 34 38 46 42 10 50 54 62 58 X X Figure 1 In the logical expression involving six variables, K map will get three dimensional picture with the overlapping of two dimensional planes and hence the cells that are in same relative position of two dimensional (four variable) K-map will become adjacent one that can be grouped together. Hence the squares that are adjacent vertically as shown above can be grouped together. Therefore, from Figure 1, the final expression Fis Step 2 (b) Write the given Karnaugh map for 6-variable function is shown in Figure 2. W W WX WX YZ 00 01 II 10 YZ 00 01 11 10 12 16 20 28 00 1 1 1 00 I 5 13 9 17 21 29 25 01 01 3 7 15 19 23 31 27 11 Y Y 10 2 6 14 10 10 18 22 30 26 U,V=0,0 X WX W X WX W YZ 00 01 10 YZ 01 11 10 00 44 1 00 52 60 33 7 45 41 49 01 53 61 57 01 U.V.W.X.Z 35 3b 47 43 11 1 51 55 63 59 Y Y 38 46 42 10 54 62 58 1 X X Figure 2 In the logical expression involving six variables, K map will get three dimensional picture with the overlapping of two dimensional planes and hence the cells that are in the same relative position of two dimensional (four variable) K-map will become adjacent one that can be grouped together. Hence the squares that are adjacent vertically as shown above can be grouped together. Therefore, the final expression F is (c) Write the given function = Karnaugh map for 6-variable function is shown in Figure 3. W W WX YZ 00 01 10 00 01 " to 0 8 20 24 00 1 1 00 1 1 1 9 21 25 01 1 01 1 1 Z 7 11 19 23 1 27 1 1 Y Y 10 10 10 22 1 1 30 26 X W X WX W YZ 00 01 10 YZ 00 01 II 10 V-W-X 32 36 44 00 40 00 48 52 60 56 1 33 37 45 41 49 01 53 57 01 2 35 39 47 43 11 55 1 59 Y Y 10 38 46 42 10 54 58 U,V=1,0 X X Figure 3 In the logical expression involving six variables, K map will get three dimensional picture with the overlapping of two dimensional planes and hence the cells that are in the same relative position of two dimensional (four variable) K-map will become adjacent one that can be grouped together. Hence the squares that are adjacent vertically as shown above can be grouped Therefore, the final expression