Topic: Digital Circuits
Simplified Boolean function $f(A,B,C,D)=\Sigma(0,2,4,5,6,7,8,10,13,15)$ in POS form is
- A. $(B'+D)(A'+B'+D)$
- B. $(B+D')(A+B'+D)$
- C. $(B+D)(B'+D')(A'+B)$
- D. $(B+D')(A'+B'+D)$
Answer: D. $(B+D')(A'+B'+D)$
Explanation: The given sum of minterms is $\Sigma(0,2,4,5,6,7,8,10,13,15)$. The Product of Sums (POS) form uses maxterms (the missing terms), which are $\Pi(1,3,9,11,12,14)$.
Plotting these maxterms (0s) on a 4-variable K-map:
- Minterms 1, 3, 9, 11 form a quad. In POS, this quad yields the sum term $(B+D')$.
- Minterms 12, 14 form a pair. This yields the sum term $(A'+B'+D)$.
Multiplying these terms provides the simplified POS expression: $(B+D')(A'+B'+D)$.