Convert from Base $10$ to Binary. Show your method, show your work.

$($a$)157$

$($b$)19$

Convert from Binary to Base $10.$ Show your method, show your work.

$($a$)1011$

$($b$)010111011$

$($a$)$ Write a truth table for the following Boolean expression: $A^{\text{'}}+BC=Y$

$($b$)$ Write the Full Boolean Expression for Y from the truth table.

$($bonus$)$ Use Boolean theorems to reduce the full $Y$ equation from $($b$)$ to the reduced $Y$

equation given in $($a$).$ Indicate each reduction used and corresponding theorems.

Create a Logic Circuit for each Boolean equation.

$($a$)Y=AB+CD$

$($b$)$

D$)*$Note: Do not distribute the $A.$