Let f be a Boolean expression in 8 variables which has true value exactly for 4 combinations out of 28 possible combinations. Then f can be expressed as sum of .......... min terms.
4
A minterm of n variables is a product term in which every variable appears exactly once, either complemented or uncomplemented. Each minterm is true for exactly one of the \(2^{n}\) input combinations, so a function in canonical sum-of-products form is the OR of one minterm per input combination for which the function is 1.
Here f has 8 variables, giving \(2^{8} = 256\) possible combinations, and f is true for exactly 4 of them. Each of those 4 true rows of the truth table contributes one minterm, and no other minterm may be included, because that would make f true for an extra combination.
So f is the sum of exactly as many minterms as true combinations. The numbers ten, eight and six do not match the count of true rows; eight is the number of variables, which decides the size of each minterm, not how many minterms appear.
4 option is correct.
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