A. If (12P)3-(123)p, then value of P is infeasible.
B. The simplified sum of product form of the Boolean expression is (𝑃+𝑄̅+𝑅̅).(𝑃+𝑄̅+𝑅).(𝑃+𝑄+𝑅̅) 𝑖𝑠 (𝑃+𝑄̅.𝑅̅). C. The minimum number of D flip-flops needed to design a mod (258) counter is 8. Choose Correct OptionsStatement A: \((12P)_3 = (123)_P\). The digit P is used in base 3, so P < 3. But \((123)_P\) uses the digit 3, so P > 3. Both can't be true, so P is infeasible. True.
Statement B: \((P+\bar{Q}+\bar{R})(P+\bar{Q}+R) = P + \bar{Q}\) (since \((X+\bar{R})(X+R) = X\)).
Then \((P+\bar{Q})(P+Q+\bar{R}) = P + \bar{Q}(Q+\bar{R}) = P + \bar{Q}\bar{R}\). True.
Statement C: a mod-258 counter needs \(\lceil \log_2 258 \rceil = 9\) flip-flops, since \(2^8 = 256 < 258\). So 8 is wrong. False.
Answer: (B) A and B only
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