$(15$ p$)$ Write down your key again. Key: $......$

Write your key in BCD code: $..................$

Write your key in $84-2-1$ code: $..................$

$m=3^{**}$ key $m$:dotsdots. $..$

Write $m$ in BCD code: $..................$

Write $m$ in Excess$-3$ code: $..................$

Some terms are listed in the table below.

$m=$ key mod$3(m=47$mod$3=2).$ Find your $m.m=$dotsdotsmod$3=$dotsdots

$n=$ key mod$5(n=47$mod$5=2).$ Find your $n.n=$dotsdotsmod$5=$dotsdots.

$p=$ key mod$8(p=47$mod$8=7).$ Find your $p.,p=$dotsdotsmod$8=$dotsdots

$F_1=t_m+t_n+t_p(F_1=t_2+t_2+t_7=xy{z}^{\text{'}}+x^{\text{'}}y)$

Find your $F_1.F_1=t_{\text{d}\text{o}\text{t}\text{s}}..+t_{...}+t_{.}=$

$(10$ p$)$ Using algebraic methods, simplify $F_1$ to minimum number of literals.

$F_2=t_{m+8}^{{?}^{?}}{t}_{n+8}^{{?}^{?}}{t}_{p+8},(F_1=t_{10}^{{?}^{?}}{t}_{10}^{{?}^{?}}{t}_{15}=(x+y^{\text{'}}+z^{\text{'}})(x+y^{\text{'}})),cdot{s}^{{?}^{?}}$: AND cdots

Find your $F_2.F_2=t_{\text{d}\text{o}\text{t}\text{s}}dot{s}^{{?}^{?}}{t}_{\text{d}\text{o}\text{t}\text{s}}dots{t}_{\text{d}\text{o}\text{t}\text{s}}..=$

$(10$ p$)$ Using algebraic methods, simplify $F_2$ to minimum number of literals.

key is $38$