Consider the need for a BCD to $7-$segment decoder. While chips exist for this, you want to design this using basic AND, OR$,$ XOR, and NOT gates. Refer to Figure $4\mathrm{.}6$ in An Animated Introduction text. The truth table is shown in Figure $4\mathrm{.}7.$ Design a circuit which will be part of a complete decoder which will implement the $\text{'}$b$\text{'}$ segment of the display.

$($b$)$

$\backslash$table$[[3\mathrm{.}13\mathrm{.}16,$a$,$b$,$c$,$d$,-,f,9],[0000,2,1,1,1,1,1,0],[0001,0,1,1,0,0,0,0],[0010,3,1,0,1,1,0,1],[0011,1,1,4,1,0,0,1],[0100,0,1,1,0,0,1,1],[0101,1,0,1,1,0,1,1],[0110,1,0,1,1,1,1,1],[0111,4,1,1,0,0,0,0],[1000,1,1,1,1,1,1,1],[1001,1,1,1,1,0,1,1],[$Others$,,,$x$,$K$,,*,$x$]]$

$($a$)$

$($b$)$

PLEASE DRAW OUT THE CIRCUIT