Create a truth table and then use a Karnaugh map to produce the MPOS equations for a Gray Code to BCD Converter. The converter should take a $4-$bit Gray Code number ABCD and convert it to its BCD equivalent, WXYZ$.$ For this problem, only find the equation for the output $x.($Use "don't cares" where possible.$)$

Assume the Gray Code used is as follows

Gray Code $-BCD$ Digit

$0000-7$

$0001-0$

$0010-8$

$0011-1$

$0110-9$

$0111-2$

$1000-6$

$1100-5$

$1110-4$

$1111-3$