Question

ConvertingDecimalValuesintoBina ry,andViceVersa. PartA Being able to convert decimal values to binary (and vice versa) is very important in networking because this is the basis for how subnetting is done. You may have done some
of these exercises in high school and probably didn’t know why it was important to be able to convert decimal values into binary, and vice versa. This hands-on activity will help yourecallhowthisisdoneorwillteachhowtodoitincase youneverseenthisbefore.
152 Chapter 5 Network and Transport Layers
As you know, an IPv4 address consists of 32 bits that have been separated into 4 bytes (sometimes called octets), for example, 129.79.126.1. This is called the dotted decimal address. Each byte has 8 bits, and each of these bits can assumeavalueof0or1.Thefollowingtableshowshowwe converteachbinarypositiontoadecimalvalue:
Binaryposition 27 26 25 24 23 22 21 20 Decimalvalue 128 64 32 16 8 4 2 1
To practice the conversion from binary to decimal, let’s doacoupleproblemstogether: 1. You have the following binary number: 10101010. Convertitintodecimal. 10101010=(1 ∗ 128)+(0 ∗ 64)+(1 ∗ 32) +( 0 ∗ 16)+(1 ∗ 8)+(0 ∗ 4) +( 1 ∗ 2)+(0 ∗ 1)=128 +31+8+2 = 170 2. You have the following binary number: 01110111. Convertitintodecimal. 01110111=(0×128)+(1 ∗ 64)+(1 ∗ 32) +( 1 ∗ 16)+(0 ∗ 8)+(1 ∗ 4) +( 1 ∗ 2)+(1 ∗ 1) =64+32+16+4+2+1 = 119 Itisimportanttonoticewhattherangeofpossibledecimal values for each byte is. The lower bound is given when each bit is 0 and the upper bound is when each bit is 1. So 00000000willgiveus0and11111111willgiveus255.This isthereasonwhyIPv4addressescannotgoabovethevalue of255. Deliverable Calculate the decimal values of the following binary numbers:11011011,01111111,10000000,11000000,11001101. PartB Nowlet’spracticetheconversionofdecimalvaluetobinary. This is a bit trickier. Start by finding the highest binary
position that is equal to or smaller than the decimal number we are converting. All the other placeholders to the left of this number will be 0. Then subtract the placeholder value from the number. Then find the highest binary position that is equal to or smaller than the remainder. Keep repeating these steps until the remainder is 0. Now, let’s practice. 3. Convert60intoabinarynumber. a. Theplaceholderthatisequaltoorlowerthan60is 32.Therefore,thefirsttwobitsfor60are0andthe third one is 1 − 001_ _ _ _ _ . The next step is to subtract32from60,whichequals60−32 = 28. b. The placeholder that is equal to or lower than 32 is 16, which is the fourth bit from the left. Therefore, our binary number will look like this: 0011_ _ _ _. The next step is to subtract 16 from 28,whichequals28−16 = 12. c. Theplaceholderthatisequaltoorlowerthan12is 8, and this is the fifth bit from the left. Therefore, ourbinarynumberwilllooklikethis:00111___. Thenextstepistosubtract8from12,whichequals 12−8 = 4. d. The placeholder that is equal to or lower than 4 is 4, andthisisthesixth bitfromtheleft. Therefore, our binary number will look like this: 001111_ _. Thenextstepistosubtract4from4,whichequals 4−4 = 0. e. Given that our remainder is 0, the additional bits are0,andwefindthatouranswer:60inbinaryis 00111100. 4. Convert182intoabinarynumber. 182=10110110 (Because182−128 = 54,54−32 = 22,22−16 = 6, and6−4 = 2)
Deliverable Calculate the binary value for each of the following binary numbers:126,128,191,192,223

Answer 1

Example , below is the method to convert decimal values to binary efficiently.

(12) base 10

Step 1)

12%2=0

12/2=6

Step 2)

6%2=0

6/2=3

Step-3)

3%2=1

3/2=1

Step 4)

1%2=1

1/2=0

Stop

compute result from behind

So binary value is (1100) base 2 for decimal value 12

Same steps are follwed in code to generate all answers asked.

Code:

#include <bits/stdc++.h>
using namespace std;

void ConvertToBinary(int decimal)
{
     
   int arr[32];

   int i = 0;
  
   // till value is greater than 0, keep taking modulo 2
   while (decimal > 0) {

      
       arr[i] = decimal % 2;
       decimal = decimal / 2;
       i++;
   }

// print elements from right to left
   for (int k = i - 1; k >= 0; k--)
       cout << arr[k];
       cout<<"\n";
}

int main()
{
// main method for fetching results
int t=6;
while(t--){
int n;
   cin>>n;
   ConvertToBinary(n);
}
   return 0;
}

Screenshot :

Input:

Output: