Bitwise Operations

Bitwise operations are used to perform an action on the bits (the 1's and 0's) of a number. Understanding what bitwise operators do requires you to understand how to convert from decimal to binary and from binary to decimal.

In this article a "binary" formatted number (which represents the "bits" of a number) will be written with a ²... and a decimal number with a ¹⁰

Converting from decimal to binary and from binary to decimal

For example 11010011² is equal to 21110¹⁰, and 14310¹⁰ is qual to 10001111^2...

From decimal to binary

If we have a decimal number, 783 for example, you can convert it to a decimal number using this way:

Division:	783 / 2	391 / 2	195 / 2	97 / 2	48 / 2	24 / 2	12 / 2	6 / 2	3 / 2	1 / 2
Quotient:	391	195	97	48	24	12	6	3	1	0
Remainder:	1	1	1	1	0	0	0	0	1	1

You have to stop dividing if the quotient is 0.

Now, read the sequence of remainders from right to left, then you get the binary number 1100001111.

Negative decimal number to binary

For example: -783

1. Take the binary form of 783: 0000001100001111
2. Invert it: 1111110011110000
3. Add up 1111110011110000 with 1
4. So, -783¹⁰ is 11111100111100012

How you can be sure this number is negative? It depends on the data type. If the data type is an Int16, then if the first bit is a 0, then the number is positive. If the first bit is a 1, the number is negative. So, 1111110011110000 (Int16) is -783, but for an unsigned number, UInt16 for example, the first number DOESN'T tell whether the number is negative or not. For an UInt16 for example, we can be sure it's positive because it's unsigned. So, 1111110011110000 as an UInt16 is 64752.

In Sphere objects, an example of a 16 bit integer would be MORE1 or MORE2... as to whether it's value is interpreted as signed or not is up to the system or script that is using it. For example, the MORE1 and MORE2 on a Magery spellbook (an object with TYPE=t_spellbook), the value in MORE1 and MORE2 is an unsigned integer. And each bit in that number corresponds to a spell... MORE1 holds the first 32 spells (circles 1-4) and MORE2 is the last 32 spells (circles 5-8).