Basic: Decimal to Binary

For instance, we have number `7`

, which is base-10 number. Then, we need to convert to base-2 (binary) system.

The base-2 system uses the **addition of power of 2's** to get the number we have in another radix system. So, to get the value from the other base system (base-10 for example), we continuously divide that number with 2, and take **the remainder of each division**.

In paper and pen scribbling math, we do this:

7 : 2 -> closest multiplier is 3, remainder **1**

3 : 2 -> closest multiplier is 1, remainder **1**

1 : 2 -> the only multiplier is 0, remainder **1**

Put all remainders as a number, take each from the **BOTTOM**: **1 ► 1 ► 1**

So, 7_{10} (decimal) = `111`

(base-2 or binary system)_{2}

Or, we could use the addition method of power of 2:

Look at the multiplier (1), read it from the **LEFT**: **1 ► 1 ► 1**

Meaning, again, 7_{10} (decimal) = `111`

(base-2 or binary system)_{2}

To learn more about the base-10 to base-2 conversion (and vice versa) there's this explanation

JavaScript: Decimal to Binary

Use `toString(2)`

to convert the base-10 (decimal) input to base-2 (binary) system. Hence, the 2 as argument's value in that `toString()`

function. The output is `String`

type.

Example:

To convert the output to number, use `Number()`

. Like so:

This method also works for **negative** number.

For floating number (number with decimal point), this method will also work (but with some limitation for the radix point, the approximation).

Example:

JavaScript: One Base to Another Base

Basically, we implement `toString()`

to convert one base to another:

BUT, that **only works for decimal input**. For other base input, we need one preliminary step to convert it to its actual base, then we can convert it to another base.

It's using `parseInt(input, radix)`

function.

The `radix`

value ranges from **2** (base-2) to **36** (base-36).

For instance, converting base-16 (hexadecimal) 21 to decimal:

So then ► 21_{16} = 33_{10}

Converting base-2 (binary) 11011 to base-8 (octal):

► 11011_{2} = 33_{8}

Converting base-12 (dozenal) 322 to base-5 (pental):

► 322_{12} = 3313_{5}

JavaScript: Conversion Error

If the input cannot be converted, usually because of the input error, the output will produce `NaN`

.

If the error because of the unsupported `radix`

value in `toString`

, the browser will throw `RangeError`

exception.

JavaScript: Base Conversion Formula

You could also put preceding filter before `parseInt`

to make sure the input is valid, or in between `parseInt`

and `toString()`

or something else you might like to put.

For example, let's create a function named `radix_converter`

. This function has 3 arguments: `input`

, `from_base`

, and `to_base`

. It will return the value from that "base conversion formula" above:

That's All...

Oh wait, there's an application which can accommodate until base-62

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