How to convert a float to binary using javascript

Question

Here is the Example:

For example, suppose we have a float 13.4. In binary, it can be written as: 1101.01100110011001100110011001100110011兮.

Suppose the system stores bits up to 10 decimal places. So 13.4 is stored as: 1101.0110011001 (only 10 decimal places now)

Because of this change, if you convert 1101.0110011001 back to base 10, you get 13.399414. In essence 13.399414 is stored rather than 13.4 in this case!

So given a floating point in base 10, an integer n which represents the number of decimal places as defined above, output the stored value of the float to three decimal places.

So How can i convert using javascript:- input 13.4 and output 13.399

Number's in javascript have a toString method that should help - oh wait, you still want 13.4 to output as 13.399 - why? — Jaromanda X, Nov 16 '17 at 05:40
13.4 is 13.4 ... it isn't 13.399 ... what about 13.5, should that be 13.499? I guess I don't understand the question :p — Jaromanda X, Nov 16 '17 at 05:43
@JaromandaX I think the question is how to translate the story into actual Javascript code in order to get the same result. — icecub, Nov 16 '17 at 05:44
Possible duplicate of [How to convert a floating point number to its binary representation (IEEE 754) in Javascript?](https://stackoverflow.com/questions/3096646/how-to-convert-a-floating-point-number-to-its-binary-representation-ieee-754-i) — Andrew, Nov 16 '17 at 05:46
Which in turn really makes me wonder why ppl are upvoting this question. It shows no research efford. There is no code. Essentialy the questions is: _Please do my work for me_ — icecub, Nov 16 '17 at 05:46
`(parseInt((13.4 * 1024).toString(2),2)/1024).toFixed(3)` - the 1024 is 10 binary digits after the `.` — Jaromanda X, Nov 16 '17 at 05:46
`Number((parseInt((13.4 * 1024).toString(2),2)/1024).toFixed(3))` — Jaromanda X, Nov 16 '17 at 05:48
`In essence 13.399414 is stored rather than 13.4 in this case!` actually, I'd say, in essence, 13.399414 and 13.4 are equal in this arbitrary 10 binary digit system you've developed for no apparent reason — Jaromanda X, Nov 16 '17 at 05:52
@amitkumar If you're going to keep tacking on requests, can you at least explain _why_ you want to do this? — JLRishe, Nov 16 '17 at 06:22
`1101.0110011001` does not have 10 decimal digits in its fractional part, it does have 10 *binary* digits?! — Bergi, Nov 16 '17 at 07:07
"*So given a floating point in base 10*" - you mean represented as a string? — Bergi, Nov 16 '17 at 07:08

score 0 · Answer 1 · answered Nov 16 '17 at 06:58

0

Going off of the comment by @Jaromanda X

function cut(num, base, len) {
    base = Math.pow(2, base);
    return (parseInt((num * base).toString(2), 2) / base).toFixed(len);
}

answered Nov 16 '17 at 06:58

ShadowCommander

161
6

score 0 · Answer 2 · answered Nov 16 '17 at 07:16

You can get a number with a desired number of fractional digits by shifting it to the left by that number of places, dropping the remaining digits on the right by flooring it, and shifting it back right. This works in any base - base 2 in your case:

Math.floor(13.4 * 2**10) / 2**10
Math.floor(13.4 * Math.pow(2, 10)) / Math.pow(2, 10)
Math.floor(13.4 * (1<<10)) / (1<<10)

score 0 · Answer 3 · answered Sep 08 '21 at 16:12

You can use the Basenumber.js library. Just create an instance in decimal, an parse it to binary:

// Set precision decimals you want
Base.setDecimals(100);

// create instance in decimal
let x = Base(13.4);

// Transform x to binary
let y = x.toBin();

console.log(x.valueOf());
console.log(y.valueOf());

// Transform y to decimal again
let z = y.toDec();

// Since 13.4 has no exact binary representation it would not be accurate
console.log(z.valueOf());

// But you can round the value so get again 13.4
let rounded = z.round(10);   // round 10 decimals

console.log(rounded.valueOf());

<script src='https://cdn.jsdelivr.net/gh/AlexSp3/Basenumber.js@main/BaseNumber.min.js'></script>

How to convert a float to binary using javascript

3 Answers3