Problem $4.$ Using a Decoder to represent a Boolean Equation $(5$ points$)$

For the following design problem, make a truth table that describes the problem, then and

draw a logic diagram of the circuit $($you can draw the diagram by hand$).$ The circuit should use

a $4$:$16$ Decoder with negated outputs $($low$)$ and any other logic gates: NOT, AND, OR$,$ NAND,

NOR, XOR. The logic gates in this design may have multibit inputs. A logical diagram should

contain block notations $($such as Full Adder, D Flip$-$Flop, Decoder, Multiplexer$)$ and gate

symbols $($such as AND, OR$,$ and NOT$).$

Hint $1$: Which logic gate can we use to combine different outputs of the decoder into a single output?

Hint $2$: Remember the logic value of an output of the decoder when it is "activated" $($or "chosen"$).$

Check the answer from Problem $2.$

SOLVE: Design a logic circuit that will output HIGH when the input is an odd number less than $8,$

and an even number greater than or equal to $8,$ and all inputs are smaller than $16.$ The input should

be a $4-$bit binary number. Design the circuit using a $4$:$16$ decoder and other gates.Problem $2.$ Understanding the Decoder $(5$ points$)$

Below on the left is the logic symbol for a $4$:$16$ Decoder, on the right is the circuit diagram

$($taken from DECODER$\_75154.$pdf$)$

Decoder Symbol

for Logic Diagram

IC Pinout