Problem $5.(10$ points$)$ Let x$3$x$2$x$1$x$0$ be a $4-$bit binary number.

a$)$ Write an expression in Boolean algebra that evaluates to $1$ when an even number of bits of the

number is $$one$$ and $0$ otherwise. Submit a file named p$5$a$.$py$.$

Examples: $0110$ evaluates to $1$ but $0010$ evaluates to $0.$

b$)$ Write an expression in Boolean algebra that evaluates to $1$ when the number is an even number

and $0$ otherwise. Submit a file named p$5$b$.$py$.$

Examples: $1110$ evaluates to $1$ but $1011$ evaluates to $0.$

c$)$ Write an expression in Boolean algebra that evaluates to $1$ when the number is a non$-$zero

number and $0$ otherwise. Submit a file named p$5$c$.$py$.$

Examples: $1110$ evaluates to $1$ and $0001$ evaluates to $1$ but $0000$ evaluates to $0.$

d$)$ Write an expression in Boolean algebra that evaluates to $1$ when the number is not a non$-$zero

even number and the number does not have even number of $$one$$s$,$ and $0$ otherwise. Submit a file

named p$5$d$.$py$.$

Examples: $0000($it has even number of ones$)$ and $0011($it has even number of ones$)$ and $1110($it

is a non$-$zero even$)$ evaluate to $0$ but $0001$ and $1011$ evaluate to $1.$