We designed a number range detector in HW$3$ assignment. Let's upgrade the

number range detector. You need to design a combinational logic circuit in the black

bos

$3-$bit input: A$[2$:$0]($indicating a number between $O_{10}(={000}_2)$ and $7_{10}(={111}_2))$

Three $1-$bit outputs:

$($Lower Range$)LR=1,$ if the input $A[2$:$0]$ is in $0,10,10($it means between $0$ and $1,$

and $0$ and $1$ are included$),$ and the output $LR=0,$ otherwise.

$($Right Range$)RR=1,$ if the input $A[2$:$0]$ is in $210,510,$ and $RR=0,$ otherwise.

$($Upper Range$)R=1,$ if the input $A[2$:$0]$ is in $6,70,$ and $UR=0,$ otherwise.

$($For your information again, this kind of logic circuit can be used for a smart farm

system in maintaining temperature or humanity. For example, the number range $2-5$

represents temperature range $72-75.$ The output $F$ can be used to control an $\frac{A}{C}$ to turn

on or off.$)$

$2\mathrm{.}1.(5$ points$)$ Make a truth table for the number range detector. $($Make sure that you

use the same signal name that I provided in the drawing, namely, $A[2],A[1],A[0].$

$LR,RR,$ and $UR.)$

$2\mathrm{.}2.(5$ points$)$ With the truth table, express the Boolean functions for the number

range detector in sum of products $($i$.$e$.,$ minterms$).$ Since the system has three

outputs, you need to provide three Boolean functions.

$2\mathrm{.}3.(5$ points$)$ Design the number range system by using a decoder and $OR$ gates. To

minimize hardware resources to be wasted, you need to use just one decoder

and multiple $OR$ gates.