Binary Conversion

It has been suggested that this page's contents be merged with the page Base Conversion. You can discuss this on the page's talk page. (February 2025)

For more information, see Binary number on Wikipedia.

This tutorial goes over the basics of converting numbers to/from binary.

Explanation

Binary is a base-2 numerical system that uses 2 digits: 0 and 1.

One use case in Scratch is packing together many boolean values for more efficient storage, especially useful for cloud variables which hold a limited number of digits. Booleans are binary, in that they can only be true or false.

In Scratch, what is often called a "binary number" is often a string consisting of of 0s and 1s.

Converting Numbers to Binary

In this example, note that the input number must be a non-zero positive integer.

to binary [19] // 19 in binary is 10011
define to binary (num)
set [remainder v] to (num)
set [binary v] to () // result is outputted to this variable as a string
repeat until <(remainder) = [0]>
set [binary v] to (join ((remainder) mod (2))(binary)) // join the binary digit to the result
set [remainder v] to ([floor v] of ((remainder) / (2)))
end

Padding Binary Numbers

It can be useful to insert zeroes to the start of a number so it has a fixed length. The script below will convert a binary number into a binary number of equal value, adding 0s.

pad binary number (10011) to length (8) // result is 00010011
define pad binary number (bin) to length (target length)
set [binary v] to (bin) // result is outputted to this variable as a string
repeat ((target length) - (length of (binary)))
set [binary v] to (join (0)(binary))
end

Lookup Table

In some use cases a lookup table is a suitable way to implement a base conversion. In Scratch they are implemented with lists. This method is computationally more performant at the cost of memory (to store every possible result).

As a simple example, to convert to a 4-digit binary number you would need a list of 16 items like this: 0, 1, 10, ... 1110, 1111

(item ((6) + (1)) of [binary lookup v]) // 6 in binary is 110 (note that we add 1 because lists are 1-indexed)

One advantage with this method is that if zero padding is needed, the list can store binary numbers with zero padding already computed.

Converting Numbers From Binary

A binary number can be converted using the following:

((0) + (join [0b] (binary number)))

This script works because JavaScript (what Scratch is built on) interprets strings with "0b" at the beginning as binary. Adding 0 to the string will convert the string into a number.

See Also

• Binary number on Wikipedia