The aim is to design a seven segment decoder as follows:

Complete the truth table.

Obtain the Boolean equations.

Simplify it using K$-$Map.

Implement the design using logisim software $.$

Segment a is activated for the digits $0,2,3,5,6,7,8,$ and $9$

$\backslash$table$[[,$BCD Inputs,Segment outputs$],[$N$.,$A$,$B$,$C$,$D$,$a$,$b$,$c$,$d$,$e$,$f$,$g$],[0,0,0,0,0,1,,,,,,],[1,0,0,0,1,0,,,,,,],[2,0,0,1,0,1,,,,,,],[3,0,0,1,1,1,,,,,,],[4,0,1,0,0,0,,,,,,],[5,0,1,0,1,1,,,,,,],[6,0,1,1,$o$,1,,,,,,],[7,$o$,1,1,1,1,,,,,,],[8,1,$o$,0,$o$,1,,,,,,],[9,1,0,0,1,1,,,,,,],[10,1,$o$,1,$o$,,,,,,,],[11,1,$o$,1,1,,,,,,,],[12,1,1,0,$o$,,,,,,,],[13,1,1,0,1,,,,,,,],[14,1,1,1,$o$,,,,,,,],[15,1,1,1,1,,,,,,,]]$

$a\frac{?}{b}=ar\frac{A}{b}ar\frac{B}{b}ar\frac{C}{b}ar(D)\frac{+}{b}ar\frac{A}{b}ar(B)\frac{C}{b}ar(D)\frac{+}{b}ar\frac{A}{b}ar(B)CD\frac{+}{b}ar(A)\frac{B}{b}ar(C)D\frac{+}{b}ar(A)B\frac{C}{b}ar(D)\frac{+}{b}ar(A)BCD+\frac{A}{b}ar\frac{B}{b}ar\frac{C}{b}ar(D)+\frac{A}{b}ar\frac{B}{b}ar(C)D$

the minimized expression for segment a is

$a=A+C+BD\frac{+}{b}ar\frac{B}{b}ar(D)$