Page 44 - Computer science 868 Class 12
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0       1        3       2
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                                                         12      13       15      14
                                                          8       9       11      10

              Let us understand this better with the help of some examples.

              Example 7: Minimise a Boolean expression F(A, B, C) = Σ(0, 1, 2, 4, 6)
              Solution:                                 B'.C'    B'.C    B.C     B.C'

                                                  A'    1 0     1 1     0 3     1 2
                                                  A     1 4     0 5     0 7     1 6
              Quad 1: m +m +m +m  = C'
                               4
                           2
                        0
                                   6
              Pair1: m +m  = A'.B'
                      0
                         1
              Reduced SOP expression: A'.B'+C'
              Example 8: Given F(P, Q, R, S) = Σ(0, 2, 5, 7, 8, 10, 11, 13, 14, 15)
              Reduce the above expression by using a 4 – variable K-map, showing the various groups (i.e., octal, quads and pairs).
                                                                                                              [ISC 2010]
              Solution:                                R'.S'   R'.S    R.S     R.S'

                                               P'.Q'  1  0    0  1     0  3    1  2
                                                P'.Q  0  4    1  5     1  7    0  6
                                                P.Q    0     12   1     13   1     15   1     14
                                                P.Q'  1  8    0  9     1     11   1     10

              Quad 1: m +m +m +m  = Q.S
                               13
                                   15
                           7
                        5
              Quad 2: m +m +m +m  = P.R
                            11
                                     15
                                14
                        10
              Quad 3: m +m +m +m  = Q'.S'
                                   10
                        0
                               8
                           2
              Reduced SOP expression: Q'.S' + P.R + Q.S
              Example 9: Given F(A, B, C, D) = (A+B+C+D).(A+B+C+D').(A+B+C'+D').(A+B+C'+D).(A+B'+C+D').(A+B'+C'+D').(A'+B+C+D).
              (A'+B+C'+D).
              Reduce the above expression by using a 4 – variable K-map, showing the various groups (i.e., octal, quads and pairs).
                                                                                                              [ISC 2010]
                                                        C+D    C+D'    C'+D'    C'+D
                                                 A+B   0  0    0  1     0  3    0  2
                                                A+B'   1  4    0  5     0  7    1  6

                                                A'+B'   1     12   1     13   1     15   1    14
                                                A'+B   0  8    1  9     1     11   0     10
              Quad 1: M .M .M .M  = B+D
                           2
                        0
                                 10
                              8
              Quad 2: M .M .M .M  = A+B
                              2
                           1
                        0
                                 3
              Quad 3: M .M .M .M  = A+D'
                                 7
                        1
                              5
                           3
              Reduced POS expression: (A+B).(B+D).(A+D')
                4242  Touchpad Computer Science-XII
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