A logic circuit realizing the function f has four inputs A,B,C, and D. The three inputs A,B, and c are the binary representation of the digits 0 through 7 with A being the most-significant bit. The input D is an odd-parity bit, i.e., the value of D such that A,B,C, and D always contain an odd number of 1's. (For example, the digit 1 is represented by ABC = 001 and D = 0, and the digit 3 is represented by ABCD = 0001.) The function f has a value 1 if the input digit is a prime number. (A number is prime if it is divisible only by itself and 1;1 is considered to be prime and 0 is not.) (a) List the minterms and don't-care minterms of f in algebraic form. (b) List the maxterms and don't-care minterms of f in algebraic form.
A logic circuit realizing the function f has four inputs A,B,C, and D. The three inputs A,B, and c are the binary representation of the digits 0 through 7 with A being the most-significant bit. The input D is an odd-parity bit, i.e., the value of D such that A,B,C, and D always contain an odd number of 1's. (For example, the digit 1 is represented by ABC = 001 and D = 0, and the digit 3 is represented by ABCD = 0001.) The function f has a value 1 if the input digit is a prime number. (A number is prime if it is divisible only by itself and 1;1 is considered to be prime and 0 is not.)
(a) List the minterms and don't-care minterms of f in algebraic form.
(b) List the maxterms and don't-care minterms of f in algebraic form.
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