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Step 1 of 3 4.16DP In a 4-bit prime number detector, the input combinations of N = produces a 1 output for N= 1,2,3,5,7,11,13 and 0 for other values. Thus, the minterm list is, But according to the context, mathematicians will tell that 1 is not really a prime number. Therefore, the minterm list is, = The canonical sum of a logic function is a sum of the minterms corresponding to truth table rows (input combinations) for which the function produces a 1 output. Thus, the canonical sum of the function F is, = Step 2 of 3 The K-map for function is shown in Figure 1. AB 00 01 11 10 CD 00 01 1 1 11 1 1 1 10 1 Figure 1 Step 3 of 3 From the K-map in Figure 1, the minimum sum of products expression is, The following is the design for minimal sum for 4 bit prime detector: A A A'-B'-C - A' B B B' F C C C' D D D' Figure 2