Exercise $2(6$ points$)$ A combinational circuit has a $4$ bit input $A=a_3{a}_2{a}_1{a}_0$ representing a two's complement number, and outptus $Z=z_1{Z}_0$ as an unsigned binary number, such that:

$Z=1se4A7$

$Z=2se-3A<mn\; id="EditorElement\_1387525">4</mn>$

$Z=3seA=-8$

Write down:

The corresponding truth table

The minimal POS form for $z_0$

The all$-$NAND and all$-$NOR form for $z_0($NOT gates are allowed, i$.$e$.,$ you don't need to translate NOT with NAND$/$NOR$)$

$z_0$ using only three $2$:$1$ multiplexers