Design a combinational circuit that takes four inputs $($

E

$$

$($the

enable

$),$A$,$B$,$ and C $),$ has four outputs $($X$,$Y$,$Z$,$ and S $($the end of sequence flag$))$ and meets the following specifications. $$ If ABC$=111$ then, regardless of the value of E$,$ the end of sequence flag S$=1$ else S$=0.$ If E$=1$ then XYZ$=$ABC. $$ If E$=0$ and ABC

$$

$=111$ then XYZ should be set to the code after ABC in this list: $000,100,101,001,011,010,110,111.$ So if ABC$=010$ then XYZ$=110.$ This is a type of Gray code sequence. $$ If E$=0$ and ABC$=111,$ then XYZ may be set to anything $($this is called a "don't care" and should be represented in the truth tables and K$-$maps with an$\backslash$times $.$ Notice that this is essentially a description of a four input, four output truth table a$.$Pre$-$Lab$>$ Create a truth table $($with the operands in this order E$,$A$,$B$,$C$,$X$,$Y$,$Z$,$S $)$ for this combinational circuit's function. The first three lines of the truth table look like this: b$.$Pre$-$Lab$>$ Write Boolean expressions for each output. Write the expressions as sum of minterms. c$.$ PPre$-$Lab$>$ Simplify each expression using a K$-$map $(4$ variable K$-$maps will be used$).($Show the maps, minterm groupings, and final expressions. Remember there is a convenient K$-$map template that is available if desired in the moodle resources section.$)$ d$.$ Pre$-$Lab$>$ Create the logic circuit.