a)
A | B | F |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
F(min) = (A'*B)+(A*B')
F(max) = (A+B)*(A'+B')
b)
A | B | C | F |
0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 1 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 |
F(min) = (A'*B*C')+(A'*B*C)+(A*B'*C')+(A*B*C')
F(max) = (A+B+C)*(A+B+C')*(A'+B+C')*(A'+B'+C')
c)
A | B | C | D | F |
0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 0 |
F(min) = (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')
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