Given an fraction decimal number n and integer k, convert decimal number n into equivalent binary number up-to k precision after decimal point.
Input: n = 2.47, k = 5 Output: 10.01111 Input: n = 6.986 k = 8 Output: 110.11111100
A) Convert the integral part of decimal to binary equivalent
- Divide the decimal number by 2 and store remainders in array.
- Divide the quotient by 2.
- Repeat step 2 until we get the quotient equal to zero.
- Equivalent binary number would be reverse of all remainders of step 1.
B) Convert the fractional part of decimal to binary equivalent
- Multiply the fractional decimal number by 2.
- Integral part of resultant decimal number will be first digit of fraction binary number.
- Repeat step 1 using only fractional part of decimal number and then step 2.
C) Combine both integral and fractional part of binary number.
Let's take an example for n = 4.47 k = 3 Step 1: Conversion of 4 to binary 1. 4/2 : Remainder = 0 : Quotient = 2 2. 2/2 : Remainder = 0 : Quotient = 1 3. 1/2 : Remainder = 1 : Quotient = 0 So equivalent binary of integral part of decimal is 100. Step 2: Conversion of .47 to binary 1. 0.47 * 2 = 0.94, Integral part: 0 2. 0.94 * 2 = 1.88, Integral part: 1 3. 0.88 * 2 = 1.76, Integral part: 1 So equivalent bianry of fractional part of decimal is .011 Step 3: Combined the result of step 1 and 2. Final answer can be written as: 100 + .011 = 100.011
Program to demonstrate above steps:
Output: 100.011 110.11111
Time complexity: O(len(n))
Auxiliary space: O(len(n))
where len() is the total digits contain in number n.
This article is contributed by Shubham Bansal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Convert Binary fraction to Decimal
- Find ΔX which is added to numerator and denominator both of fraction (a/b) to convert it to another fraction (c/d)
- Number of substrings with odd decimal value in a binary string
- Sum of decimal equivalent of all possible pairs of Binary representation of a Number
- Convert a binary number to octal
- Convert a binary number to hexadecimal number
- Convert all substrings of length 'k' from base 'b' to decimal
- Maximum rational number (or fraction) from an array
- Largest proper fraction with sum of numerator and denominator equal to a given number
- Program for Decimal to Binary Conversion
- Program for Binary To Decimal Conversion
- Counting even decimal value substrings in a binary string
- Decimal representation of given binary string is divisible by 20 or not
- Decimal representation of given binary string is divisible by 10 or not
- Decimal representation of given binary string is divisible by 5 or not
Improved By : Ryuga