Final answer:
To find the minimum AND-OR expression for x(a,b,c) = ∑(2,3,4,6,7), we can use a Karnaugh map. After constructing the map and grouping the 1s, we find that the expression is x(a,b,c) = b&c + a&b.
Step-by-step explanation:
For x(a,b,c) = ∑(2,3,4,6,7), we can use a Karnaugh map to find the minimum AND-OR expression.First, we construct a Karnaugh map for x(a,b,c) using the values given in the sum of minterms (∑) expression. The map will have three variables: a, b, and c.Next, we group the 1s (values included in the sum of minterms) in the Karnaugh map to find the minimal AND-OR expression. In this case, we have two groups: one with four 1s and one with two 1s. The grouping results in the expression: x(a,b,c) = b&c + a&b.To find the minimum AND-OR expression for the given function using a Karnaugh map (K-map), we list the minterms provided in the question. The question asks for simplification of two separate sums of minterms:
b) Σ(2,3,4,6,7)d) Σ(0,1,2,3,4,6)To solve part b), we create a 3-variable Karnaugh map representing each minterm with a '1'. Then, we group the adjacent ones to form the largest possible groups following the power of two (1, 2, 4...). After grouping, we derive the AND-OR expression from the groups created on the map. The variables that remain the same within a group represent the terms in our expression, and the overall result should be the simplified sum of the product terms.For part d), we follow the same process, noting that the minterms include both those from part b) and additional ones, which might create larger groups and further simplify the expression.