Question

C++

Convert a Number from Binary to Decimal using a stack: The language of a computer is a sequence of Os and 1s. The numbering system we use is called the decimal system, or base 10 system. The numbering system that the computer uses is called the binary system, or base 2 system. The purpose of this exercise is to write a function to convert a string representing a binary number from base 2 to base 10. To convert a number from base 2 to base 10, we first find the weight of each bit in the binary number. The weight of each bit in the binary number is assigned from right to left. The weight of the rightmost bit is 0. The weight of the bit immediately to the left of the rightmost bit is 1. the weight of the bit immediately to the left of it is 2, and so on. Consider the binary number 1001101. The weight of each bit is as follows: weight 6543210 1001101 We use the weight of each bit to find the equivalent decimal number. For each bit, we multiply the bit by 2 to the power of its weight, and then we add all of the numbers. For the binary number 1001101, the equivalent decimal number is 77. To write a program that converts a binary number into the equivalent decimal number, we note two things: (1) The weight of each bit in the binary number must be known, and (2) the weight is assigned from right to left. Because we do not know in advance how many bits are in the binary number, we must process the bits from right to left. After processing a bit, we can add 1 to its weight, giving the weight of the bit immediately to its left. Also, each bit must be extracted from the binary number and multiplied by 2 to the power of its weight. Write a program that reads a string of zeros and ones representing a binary number and uses a stack to convert a binary number into an equivalent decimal number. Test your function for the following values: 11000101, 10101010, 11111111, 10000000, 1111100000

Answer 1

code

#include<bits/stdc++.h>
using namespace std;
int binToDeci(string s){
// stack for
   stack<int> st;
// vector for storing weights
   std::vector<int> weight;
   int k=0;
   for (auto i:s)
   {
       weight.push_back(k++);
       st.push(i-'0');
   }

// reverse the vector weight
   reverse(weight.begin(),weight.end());

// variable for storing decimal
   int ans=0;

   while(!st.empty()){
       ans+=st.top()*(1<<weight[k-1]);
       k--;
       st.pop();
   }

   return ans;
  
}
//main function
int main()
{
   cout<<"enter a binary string\n";
   string s;
   cin>>s;
   cout<<"Decimal for "<<s<<" value is : "<<binToDeci(s)<<endl;
}

screenshot

i 4 #include<bits/stdc++.h> using namespace std; int binToDeci(string s) { // stack for stack int> st; vector for storing weights std::vector<int> weight; int k=0; for (auto i:s) 10 12 weight.push_back(k++); st.push(i-'0'); 13 14 15 // reverse the vector weight 16 . reverse (weight.begin(), weight.end(); 17 187 // variable for storing decimal int ans=0; 19 20 NNNNNNNN while(!st.empty()) { ans+=st.top() *(1<<weight[k-1]); k--; st.pop(); return ans; 28 29 30 31 32 33 34 } 7/main function int main() { cout<<"enter a binary string\n"; string s; cin>>s; cout<<"Decimal for "<<s<<" value is : "<<binToDeci(s)<<endl; } 35 36 37

sample output

[pp]$ g++ stack.cpp [pp]$ ./a.out enter a binary string 11000101 Decimal for 11000101 value is : 197 [pp]$ ./a.out enter a binary string 10101010 Decimal for 10101010 value is : 170 [pp]$ ./a.out enter a binary string 11111111 Decimal for 11111111 value is : 255 [pp]$ ./a.out enter a binary string 10000000 Decimal for 10000000 value is : 128 [pp]$ ./a.out enter a binary string 1111100000 Decimal for 1111100000 value is : 992, [pp]$ 1

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