Questions

Simplify the following Boolean functions using k$-$maps. Prove each with truth

table. Draw each reduced circuit in Digital.

a$.F(x,y,z)={\displaystyle \underset{?}{\overset{?}{}}}(0,2,3,4,6)$

b$.F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}(0,2,8,10,15)$

With the following Boolean function with the don't$-$care conditions $d.$

$F(w,x,y,z)={\displaystyle \underset{?}{\overset{?}{}}}(0,1,2,3,7,8,10)$

$d(w,x,y,z)={\displaystyle \underset{?}{\overset{?}{}}}(5,6,11,15)$

a$.$ Build a truth table

b$.$ Write the non reduced algebraic function for $F$

c$.$ Reduce using a K$-$Map

d$.$ Draw the circuit for $F$ found in $c.$

Design a combinational circuit with four inputs $x_3,x_2,x_1,x_0$ and three

outputs A$,$ B$,$ C$.x_3,x_2,x_1,x_0$ represents a binary number with $x_0$

representing the lowest significant $($right most$)$ bit and $x_3$ being the highest $($left

most$)$ bit. A will be true when the input is even. $B$ will be true when the input is a

$((($prime number greater than $2)$ or $15)$ and not $11).$ C will be true when the input

is divisible by $4($zero is divisible as well$).$

a$.$ Give the reduced algebraic equations for $A,B,$ and $C$ using K$-$Maps.

b$.$ Draw the circuit in Digital. The inputs and outputs should be labeled in Digital,

You may use multi input and$/$or gates, however, no bus lines vet.