Converting a Real Number (between 0 and 1) to Binary String
Last Updated :
13 Oct, 2022
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Given a real number between 0 and 1 (e.g., 0.72) that is passed in as a double, print the binary representation. If the number cannot be represented accurately in binary with at most 32 characters, print” ERROR:’
Examples:
Input : (0.625)10 Output : (0.101)2 Input : (0.72)10 Output : ERROR
Solution: First, let’s start off by asking ourselves what a non-integer number in binary looks like. By analogy to a decimal number, the binary number 0 .1012 would look like:
0. 1012 = 1 * 1/21 + 0 *1/22 + 1 * 1/23 .
Method 1: Multiply the decimal part by 2
To print the decimal part, we can multiply by 2 and check if 2*n is greater than or equal to 1. This is essentially “shifting” the fractional sum. That is:
r = 210 * n; = 210 * 0.1012; = 1 * 1/20 + 0 *1/21 + 1 * 1/22; = 1.012;
If r >= 1, then we know that n had a 1 right after the decimal point. By doing this continuously, we can check every digit.
C++
// C++ program to binary real number to string#include <iostream>#include<string>using namespace std;// Function to convert Binary real// number to Stringstring toBinary(double n){ // Check if the number is Between 0 to 1 or Not if (n >= 1 || n <= 0) return "ERROR"; string answer; double frac = 0.5; answer.append("."); // Setting a limit on length: 32 characters. while (n > 0) { //Setting a limit on length: 32 characters if (answer.length() >= 32) return "ERROR"; // Multiply n by 2 to check it 1 or 0 double b = n * 2; if (b >= 1) { answer.append("1"); n = b - 1; } else { answer.append("0"); n = b; } } return answer;}// Driver codeint main(){ // Input value double n = 0.625; string result = toBinary(n); cout<<"(0"<< result <<") in base 2"<<endl; double m = 0.72; result= toBinary(m); cout<<"("<<result<<")"<<endl; }// This code is contributed by Himanshu Batra |
Java
// Java program to Binary real number to String.import java.lang.*;import java.io.*;import java.util.*;// Class Representation of Binary real number// to Stringclass BinaryToString{ // Main function to convert Binary real number // to String static String printBinary(double num) { // Check Number is Between 0 to 1 or Not if (num >= 1 || num <= 0) return "ERROR"; StringBuilder binary = new StringBuilder(); binary.append("."); while (num > 0) { /* Setting a limit on length: 32 characters, If the number cannot be represented accurately in binary with at most 32 character */ if (binary.length() >= 32) return "ERROR"; // Multiply by 2 in num to check it 1 or 0 double r = num * 2; if (r >= 1) { binary.append(1); num = r - 1; } else { binary.append(0); num = r; } } return binary.toString(); } // Driver Code public static void main(String[] args) { double num1 = 0.625; // Input value in Decimal String output = printBinary(num1); System.out.println("(0" + output + ") in base 2"); double num2 = 0.72; output = printBinary(num2); System.out.println("(" + output + ") "); }} |
Python3
# Python3 program to binary real number to string# Function to convert Binary real# number to Stringdef toBinary(n): # Check if the number is Between 0 to 1 or Not if(n >= 1 or n <= 0): return "ERROR" answer = "" frac = 0.5 answer = answer + "." # Setting a limit on length: 32 characters. while(n > 0): # Setting a limit on length: 32 characters if(len(answer) >= 32): return "ERROR" # Multiply n by 2 to check it 1 or 0 b = n * 2 if (b >= 1): answer = answer + "1" n = b - 1 else: answer = answer + "0" n = b return answer# Driver codeif __name__=='__main__': n = 0.625 result = toBinary(n) print("(0", result, ") in base 2") m = 0.72 result = toBinary(m) print("(", result, ")")# This code is contributed by# Sanjit_Prasad |
C#
// C# program to Binary real number to String. using System;using System.Text;// Class Representation of Binary real number // to String class BinaryToString { // Main function to convert Binary real number // to String static String printBinary(double num) { // Check Number is Between 0 to 1 or Not if (num >= 1 || num <= 0) return "ERROR"; StringBuilder binary = new StringBuilder(); binary.Append("."); while (num > 0) { /* Setting a limit on length: 32 characters, If the number cannot be represented accurately in binary with at most 32 character */ if (binary.Length >= 32) return "ERROR"; // Multiply by 2 in num to check it 1 or 0 double r = num * 2; if (r >= 1) { binary.Append(1); num = r - 1; } else { binary.Append(0); num = r; } } return binary.ToString(); } // Driver Code public static void Main() { double num1 = 0.625; // Input value in Decimal String output = printBinary(num1); Console.WriteLine("(0 " + output + ") in base 2"); double num2 = 0.72; output = printBinary(num2); Console.WriteLine("(" + output + ") "); } } |
PHP
<?php// PHP program to binary real number// to string// Function to convert Binary real// number to Stringfunction toBinary($n){ // Check if the number is Between // 0 to 1 or Not if ($n >= 1 || $n <= 0) return "ERROR"; $answer = ""; $frac = 0.5; $answer .= "."; // Setting a limit on length: 32 characters. while ($n > 0) { //Setting a limit on length: 32 characters if (strlen($answer) >= 32) return "ERROR"; // Multiply n by 2 to check it 1 or 0 $b = $n * 2; if ($b >= 1) { $answer .= "1"; $n = $b - 1; } else { $answer .= "0"; $n = $b; } } return $answer;}// Driver code// Input value $n = 0.625; $result = toBinary($n);echo "(0" . $result . ") in base 2\n";$m = 0.72;$result= toBinary($m);echo "(" . $result . ")"; // This code is contributed by mits?> |
Javascript
<script>// JavaScript program to binary real number to string// Function to convert Binary real// number to Stringfunction toBinary(n){ // Check if the number is Between 0 to 1 or Not if(n >= 1 || n <= 0) return "ERROR" let answer = "" let frac = 0.5 answer = answer + "." // Setting a limit on length: 32 characters. while(n > 0){ // Setting a limit on length: 32 characters if(answer.length >= 32){ return "ERROR" } // Multiply n by 2 to check it 1 or 0 b = n * 2 if (b >= 1){ answer = answer + "1" n = b - 1 } else{ answer = answer + "0" n = b } } return answer}// Driver codelet n = 0.625let result = toBinary(n)document.write(`(0 ${result}) in base 2`,"</br>")let m = 0.72result = toBinary(m)document.write(`(${result})`,"</br>")// This code is contributed by Shinjanpatra</script> |
Output:
(0.101) in base 2 (ERROR)
Method 2
Alternatively, rather than multiplying the number by two and comparing it to 1, we can compare the number to . 5, then . 25, and so on. The code below demonstrates this approach.
C++
// C++ program to Binary real number to String.#include <iostream>#include<string>using namespace std;// Function to convert Binary real// number to Stringstring toBinary(double n){ // Check if the number is Between 0 to 1 or Not if (n >= 1 || n <= 0) return "ERROR"; string answer; double frac = 0.5; answer.append("."); // Setting a limit on length: 32 characters. while (n > 0) { // 32 char max if (answer.length() >= 32) return "ERROR"; // compare the number to .5 if (n >= frac) { answer.append("1"); n = n- frac; } else { answer.append("0"); } frac /= 2; } return answer;}// Driver codeint main(){ // Input value double n = 0.625; string result = toBinary(n); cout<<"(0"<< result <<") in base 2"<<endl; double m = 0.72; result= toBinary(m); cout<<"("<<result<<")"<<endl; } |
Java
// Java program to Binary real number to String.import java.lang.*;import java.io.*;import java.util.*;// Class representation of Binary real number// to Stringclass BinaryToString{ // Main function to convert Binary real // number to String static String printBinary(double num) { // Check Number is Between 0 to 1 or Not if (num >= 1 || num <= 0) return "ERROR"; StringBuilder binary = new StringBuilder(); double frac = 0.5; binary.append("."); while (num > 0) { /* Setting a limit on length: 32 characters, If the number cannot be represented accurately in binary with at most 32 characters */ if (binary.length() >= 32) return "ERROR"; // It compare the number to . 5. if (num >= frac) { binary.append(1); num -= frac; } else binary.append(0); // Now it become 0.25 frac /= 2; } return binary.toString(); } // Driver Code public static void main(String[] args) { double num1 = 0.625; // Input value in Decimal String output = printBinary(num1); System.out.println("(0" + output + ") in base 2"); double num2 = 0.72; output = printBinary(num2); System.out.println("(" + output + ") "); }} |
Python3
# Python3 program to Binary real number to String.# Function to convert Binary real# number to Stringdef toBinary(n): # Check if the number is Between # 0 to 1 or Not if (n >= 1 or n <= 0): return "ERROR"; frac = 0.5; answer = "."; # Setting a limit on length: 32 characters. while (n > 0): # 32 char max if (len(answer) >= 32): return "ERROR"; # compare the number to .5 if (n >= frac): answer += "1"; n = n - frac; else: answer += "0"; frac = (frac / 2); return answer;# Driver code# Input value n = 0.625;result = toBinary(n);print("( 0", result, ") in base 2");m = 0.72;result = toBinary(m);print("(", result, ")"); # This code is contributed # by mits |
C#
// C# program to Binary real number to String. using System;// Class representation of Binary // real number to String class BinaryToString { // Main function to convert Binary // real number to String static string printBinary(double num) { // Check Number is Between // 0 to 1 or Not if (num >= 1 || num <= 0) return "ERROR"; string binary = ""; double frac = 0.5; binary += "."; while (num > 0) { /* Setting a limit on length: 32 characters, If the number cannot be represented accurately in binary with at most 32 characters */ if (binary.Length >= 32) return "ERROR"; // It compare the number to . 5. if (num >= frac) { binary += "1"; num -= frac; } else binary += "0"; // Now it become 0.25 frac /= 2; } return binary; } // Driver Code public static void Main() { double num1 = 0.625; // Input value in Decimal String output = printBinary(num1); Console.WriteLine("(0" + output + ") in base 2"); double num2 = 0.72; output = printBinary(num2); Console.WriteLine("(" + output + ") "); } } // This code is contributed by mits |
PHP
<?php// PHP program to Binary real number to String.// Function to convert Binary real// number to Stringfunction toBinary($n){ // Check if the number is Between // 0 to 1 or Not if ($n >= 1 || $n <= 0) return "ERROR"; $frac = 0.5; $answer = "."; // Setting a limit on length: 32 characters. while ($n > 0) { // 32 char max if (strlen($answer) >= 32) return "ERROR"; // compare the number to .5 if ($n >= $frac) { $answer.="1"; $n = $n - $frac; } else { $answer.="0"; } $frac = ($frac / 2); } return $answer;}// Driver code// Input value $n = 0.625;$result = toBinary($n);print("(0".$result.") in base 2\n");$m = 0.72;$result = toBinary($m);print("(".$result.")"); // This code is contributed // by chandan_jnu?> |
Javascript
<script>// Javascript program to Binary real // number to String. // Main function to convert Binary// real number to String function printBinary(num) { // Check Number is Between // 0 to 1 or Not if (num >= 1 || num <= 0) return "ERROR"; let binary = ""; let frac = 0.5; binary += "."; while (num > 0) { /* Setting a limit on length: 32 characters, If the number cannot be represented accurately in binary with at most 32 characters */ if (binary.length >= 32) return "ERROR"; // It compare the number to . 5. if (num >= frac) { binary += "1"; num -= frac; } else binary += "0"; // Now it become 0.25 frac = frac / 2; } return binary; } // Driver code// Input value in Decimal let num1 = 0.625; let output = printBinary(num1); document.write("(0" + output + ") in base 2" + "</br>"); let num2 = 0.72; output = printBinary(num2); document.write("(" + output + ") "); // This code is contributed by rameshtravel07</script> |
Output:
(0.101) in base 2 (ERROR)
Both approaches are equally good; choose the one you feel most comfortable with.
This article is contributed by Mr. Somesh Awasthi.
