$134$

Chapter $3$ Minimize gate levels

$($c$)F(A,B,C,D)=(0,1,3,7,8,9,10,13,15)$

Using the K$-$map for $F$ and $F^{\text{'}},$ transform the following Boolean functions from

$3\mathrm{.}11$ the sum form of the product to the simplified sum form of the product.

$F(w,x,y,z)=$Degrees$(1,2,4,5,9,10,13,14)$

$12$ Simulate the following Boolean functions.

$(($a$)F(A,B,C,D)=(0,1,6,7,8,10,12,14)$

$($b$)F(A,B,C,D)=(0,2,5,8,10,15)$

$3\mathrm{.}13$ Simplify the following expression into the product form of $(1)$ the sum of the products and

$(2)$ the sum of the products.

$($b$)A^{\text{'}}B+A^{\text{'}}{B}^{\text{'}}C+CD$

$A^{\text{'}}{B}^{\text{'}}{D}^{\text{'}}+A^{\text{'}}D+BCD+B{C}^{\text{'}}{D}^{\text{'}}$

Using only a smaller number of literals, there are three possible ways to express the next

$3\mathrm{.}14$ Boolean function

$$ present something.

$A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}+A^{\text{'}}CD+A^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}+A^{\text{'}}BD+$ABC$+A{B}^{\text{'}}C$

$3\mathrm{.}15$

Simulate the following Boolean function $F$ with the condition d of don't care, and express it in the sum form of minimal terms.

$($a$)F(x,y,z)=(0,3,5)$

$d(x,y,z)=(1,6,7)$ b$)(b{)}^{**}F(A,B,C,D)=(1,2,4,6,12)$

$($c$)F(A,B,C,D)=(3,5,6,11)$

$($d$)$

$F(A,B,C,D)=(4,5,8,9,14,15)$

$d(A,B,C,D)=(2,3,12,13)$

$3\mathrm{.}16$ Simplify the following function and implement it as a $2-$level NAND gate circuit.

$($a$)F(A,B,C,D)=A^{\text{'}}{B}^{\text{'}}C+A^{\text{'}}BC+$ABC

$($b$)F(A,B,C,D)=A^{\text{'}}C{D}^{\text{'}}+A^{\text{'}}BD+$ABD$+A{B}^{\text{'}}CD$

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

$($d$)F(A,B,C,D)=A{B}^{\text{'}}{D}^{\text{'}}+AD+A^{\text{'}}BD$

$3\mathrm{.}17*$ Draw $($a$)$ a NAND logical diagram and $($b$)$ a NOR logical diagram that implements the complement of the following function.

$F(A,B,C,D)=(0,2,4,5,8,9,10,11)$

$3\mathrm{.}18$ Draw a logic diagram using $($a$)$ only the $2-$input NOR gate to implement the following function, and $($b$)$ repeat it for the NAND logic diagram.

$F(A,B,C,D)=(Ao+B{)}^{\text{'}}(Co+D)$

$19$ Simplify the following function and implement it as a $2-$level NOR gate circuit