$1.$ Simplify the following expressions into a minimum SOP form using algebraic rules.

The size of the minimum SOP form solution is shown in parentheses.

$f(a,b,c)=(a^{\text{'}}b{)}^{\text{'}}(a+c^{\text{'}})+b{c}^{\text{'}}$

$(2$ terms, $2$ literals$)$

$g(a,b,c)={\displaystyle \underset{?}{\overset{?}{}}}m(0,2,4,5)$

$(2$ terms, $4$ literals$)$

$h(a,b,c)=(a^{\text{'}}+b{)}^{\text{'}}+ab{c}^{\text{'}}+a^{\text{'}}b{c}^{\text{'}}$

$(2$ terms, $4$ literals$)$

Find the complement of the following expression. Then, simplify the complement as

much as you can. Final answer should be in SOP form. $($Only single variables may

be complemented in your answer $---(a+b{)}^{\text{'}}$ is not acceptable part of answer

format$).$ Minimum size is $4$ terms, $4$ literals.

$f(w,x,y,z)=(x{z}^{\text{'}}+y)(wx)(z^{\text{'}})(w^{\text{'}}+y^{\text{'}})$

Consider the following function with don't cares:

$g(a,b,c)=m(0,5,6)+d(1,2,4)$

Determine if any of the following expressions can be used as solutions for $g?$ Explain

your answers.

$p=a^{\text{'}}+b^{\text{'}}{c}^{\text{'}}$

$q=b^{\text{'}}+a{c}^{\text{'}}$

$r=c^{\text{'}}+a{b}^{\text{'}}$

Draw the diagram of the following expressions two different ways: first using any

gates you like and then secondly using only NAND gates. Assume all inputs are

available both uncomplemented and complemented.

Do not simplify equations IN ANY WAY.

$f(w,x,y,z)=y+w{x}^{\text{'}}{y}^{\text{'}}{z}^{\text{'}}+w{x}^{\text{'}}{z}^{\text{'}}$

$g(a,b,c,d)=[(a^{\text{'}}+b{d}^{\text{'}})c^{\text{'}}+a{b}^{\text{'}}]+d$