This is the fifth post of my "Data Structures & Algorithms Collection" series. In this blog post I'll walk through a sample bit manipulation problem.

Given a real number between 0 and 1 (e.g. 0.77) that is passed in as a double, output the binary representation. If the number cannot be printed accurately with 32 characters, an error should be thrown.

How are real binary numbers represented?

• 1 / 2^1 = 0.5
• 1 / 2^2 = 0.25
• 1 / 2^3 = 0.125
• ...

By knowing that, one way is to repeatedly shift the number left by 1 and check whether the number is > 1 - in this case the MSB (most significant bit) was set. We can append 1 to the output and subtract 1, else we just append 0 to the result.

Here's the source code:

class BinaryToStringConverter {

    private let errorString = "ERROR"

    func binaryRepresentation(of number: Double) -> String {
        var binary = "."
        var currentNumber = number

        if currentNumber <= 0 || currentNumber >= 1 {
            return errorString
        }

        while currentNumber > 0 {
            if binary.count >= 32 {
                return errorString
            }

            let digit = currentNumber * 2 //Same as shift left by 1
            binary.append(digit >= 1 ? "1" : "0")
            currentNumber = digit >= 1 ? digit - 1 : digit
        }

        return binary
    }
}

You can also check it out in my repository:

Binary To String Converter