Consider a digital circuit that has three inputs A$,$ B$,$ and C and four outputs X$,$ Y$,$ Z and F $($Flag$).$ Let

$A,B,$ and $C$ be the unsigned binary representation of the number $W$ where $W$ can take values from $0$

to $7.$ If $W$ is in the range between $0$ and $4,$ then the outputs $x,Y,$ and $Z$ should be the unsigned binary

representation of $(W+3)$ and the Flag $(F)$ must be $0.$ For example, if $W=2$ then ABC$=010,$ and therefore

the outputs X Y Z should be $101($equivalent to $5)$ and F must be $0$ and so on$.$ If $W$ is equal to $5,6,$ or $7,$

the outputs X Y Z must be $000$ and the Flag $($F$)$ must be $1.$

Design a digital circuit using a minimum number of components from the following list:

Decoders

Encoders

Multiplexers

Logic gates $($AND$,$ NAND, OR$,$ NOR, XOR, NOT gates$).$