You need to design a combinational logic circuit that outputs '1' if a 4-bit binary input (N3, N2, N1, N0) is a prime number (considering primes > 1). What is the minimum number of product terms required for a sum-of-products (SOP) implementation after Karnaugh map minimization?
The prime numbers in the 4-bit range [0-15] are 2, 3, 5, 7, 11, 13. The corresponding minterms are m2, m3, m5, m7, m11, m13. Placing these on a 4-variable K-map allows for minimization. The optimal groupings are: (m2, m3) -> N3'N2'N1; (m5, m7) -> N3'N2N0; (m3, m11) -> N2'N1N0; and (m5, m13) -> N2N1'N0. This results in a minimal SOP expression with 4 product terms: F = N3'N2'N1 + N3'N2N0 + N2'N1N0 + N2N1'N0.
