Let a digital system E has four inputs, which are A$,$ B$,$ C and D $($A is the most

significant bit, while D is the least significant bit$).$ It has $2$ outputs, P and Q such

that :

$-$ P is $1$ when the inputs are a valid BCD code, and

$-$ Q is $1$ when the four input bit is equivalent to decimal number that perfectly

divisible $($without remainder$)$ by $2$ OR perfectly divisible by $3.$