More Boolean

a$)10110110$ OR $11000011=$

b$)10101001$ AND $10110111=$

c$)$ Implement $xy+x^{\text{'}}{y}^{\text{'}}+y^{\text{'}}z$ with NAND and inverter gates.

d$)$ Write a truth table for $($b$+$cd$)($c$+$bd$)$ and express the function as a sum of minterms and a product of maxterms.

e$)$ Convert to the other canonical form $F(A,B,C,D)=(2,7,8,15).$

f$)$ Convert $x^{\text{'}\text{'}}+x(x+y^{\text{'}})(y+z^{\text{'}})$ into the sum of products and the product of sums.

Karnaugh Maps

Simplify parts a through d using Karnaugh maps

a$)F(x,y,z)=(0,2,4,5)$

b$)F(x,y,z)=x^{\text{'}}{y}^{\text{'}}+yz+x^{\text{'}}y{z}^{\text{'}}$

c$)F(w,x,y,z)=(2,3,12,13,14,15)$

d$)x^{\text{'}\text{'}}z+w^{\text{'}}x{y}^{\text{'}}+w(x^{\text{'}}y+x{y}^{\text{'}})$

e$)$ Find minterms of $xy+yz+x{y}^{\text{'}}z$ by plotting it in a Karnaugh map.

f$)$ Find all the prime implicants of $F(w,x,y,z)=(0,2,4,5,6,7,8,10,13,15)$ Determine which are essential.

g$)$ Simplify F $($A$,$ B$,$ C$,$ D$)=(1,3,4,5,10,11,12,13,14,15)$ using essential prime implicants.

More Karnaugh Maps and Circuits

Use Karnaugh maps in parts a through $e.$

a$)$ Simplify $A^{\text{'}}{C}^{\text{'}}+B^{\text{'}}{C}^{\text{'}}+BC+AB$ into the sum of products and the product of sums.

b$)$ Simplify using the don't care conditions.

$F(A,B,C,D)=(0,6,8,13,14)$

$d(A,B,C,D)=(2,4,10)$

c$)$ Simplify $F(A,B,C,D)=A{C}^{\text{'}}{D}^{\text{'}}+AC+$ABC$+A{B}^{\text{'}}C+A^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$

And implement it with two level NAND gate circuit.

d$)$ Simplify $F=w{x}^{\text{'}}+y^{\text{'}}{z}^{\text{'}}+w^{\text{'}}y{z}^{\text{'}}$ and implement it with two level NOR gate circuit.

e$)$ Implement the following Boolean function F$,$ using the two$-$level forms of logic NANDAND, and NOR$-$OR:

$F(A,B,C,D)=(0,4,8,9,10,11,12,14)$