#!/bin/bash

for ((n=0 ; n < 254 ; n+=1))
do
    ip=192.168.0.$n
    if ping -c 1 -w 1 $ip > /dev/null 2> /dev/null >> /etc/logping.txt; then  
        echo "${ip} is up" # output up
        # sintax >> /etc/logping.txt log with .txt format
    else
        echo "${ip} is down" # output down
    fi
done

192.168.0.0 is down
192.168.0.1 is up
192.168.....
...
.
.
.
.
192.168.0.220