$(15p)m=$keymod$8(m=47$mod$8=7).$ Find your $m.,m=$dotsdotsmod$8=$dotsdots

$n$ is the binary equivalent of $m(n=7={111}_2)n$:dots...

Design a gray code, for the digits of octal $($base $8)$ numbering system. The code for digit $"0"$

should be $"n".($Code of digit $"0"$: $111)$ Keep in mind that the codes of $"0"$ and $"7"$ should

also have a $1-$bit difference $($only one bit should change between the two codes$).$

Write down the codes for your digits on the table below.

a$)(10$p$)$ Find the complement of the simplified version of $F_1$ in question $4$ using DeMorgan's

rule and algebraic methods.

b$)(15$ p$)$ Draw the truth table of the simplified version of $F_1$ in question $4.$ Obtain the truth

table of the complement of this function $($add a column$).$ Simplify this complement from its

truth table using algebraic methods. Did you end up with the same expression in part a$?$ Do

these two methods always result in identical expressions? Explain...

key is $38$