Consider a circuit that accepts as inputs four bits x$\_(2),$x$\_(1),$x$\_(0).$ These specify which of

the digits in your $7-$digit student ID to choose. Consider a circuit with four outputs

y$\_(3),$y$\_(2),$y$\_(1),$y$\_(0)$ that produce the corresponding digit.

For instance, suppose that your student ID is $3451234.$ Given an input of $101$ for

x$\_(2),$x$\_(1),$x$\_(0),$ the circuit should produce the fifth digit $($starting at zero$)$ so $"4"$ in the

example above, so $0100$ for y$\_(3),$y$\_(2),$y$\_(1),$y$\_(0).$

Truth Table Design

Fill in the following truth table. Include "don't care" outputs when appropriate.

Write a minimal AND$-$OR $($i$.$e$.,$ sum of products$)$ two$-$level expression for this

function.

Write a minimal NAND$-$NAND two$-$level expression for this function.

Write a minimal OR$-$NAND two$-$level expression for this function.

Write a minimal NOR$-$OR two$-$level expression for this function.

Write a minimal OR$-$AND $($i$.$e$.,$ product$-$of$-$sums$)$ two$-$level expression for this

function.

Write a minimal NOR$-$NOR two$-$level expression for this function.

Write a minimal AND$-$NOR two$-$level expression for this function.

Write a minimal NAND$-$AND two$-$level expression for this function.

Write an XNF expression for this function.