A logic circuit realizing the function f has four inputs a$,$ b$,$ c$,$ 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; that is$,$ the value of d is such that a$,$ b$,$ c$,$ and d always contains 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 $=0111.)$ The function f has 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