$1\mathrm{.}2$ Arithmetic CircuitImplement a full$-$adder using a $38$ decoder with active$-$low outputs, active

high data inputs, and active high enable input. Use the gate substitution method

given in class.

Table $1$ shows the four arithmetic instructions to be implemented, along with their binary

encodings; that is$,$ their mapping to selection lines $($S$1$ and S$0).$ You must not change the

selection$-$line bindings of these operations, but use them as given below.

Table $1$: Function table for arithmetic circuit.

Using the exact procedure given in class, determining F$0-$ the logic function that controls the

carry into the first stage of the ALU. Show all of your work, including the truth table, logic

expression, and gate$-$level implementation in the box below.

Next, following the procedure given in class, determine logic expression F$1-$ the decoding logic

used to manipulate the data appearing on the B input of the full$-$adder. Show all of your work,

including the initial truth table, canonic SoP logic expression, minimized SoP logic equation, the

$K-$map used to find the latter, and the gate$-$level implementation. When drawing the latter, simply

show a single $1-$bit slice using a single full$-$adder module.