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 equal to 10001111^2...

From decimal to binary

To convert the decimal number 783 to binary, you could think of it this way... divide the number by 2, over and over again and stop dividing if the quotient is 0. Here is a table that shows this concept:

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

...Now, read the sequence of remainders from right to left, to arrive at 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. Then add 1 to it
4. So, -783¹⁰ is 1111110011110001²

The convention for storing negative numbers is typically to use the first "bit" to represent the negative. If the first bit is 0, the number is positive, if the first bit is 1, the number is negative. This is called a "signed integer", because the first bit indicates the sign.

How you can be sure that a binary number is signed or not? It depends entirely on the code. So, 1111110011110001² is equal to -783¹⁰ if you consider it to be signed... but if you consider it an unsigned number, since the first bit does not indicate the number is negative, 1111110011110001² is equal to 64752¹⁰.

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).

From binary to decimal

If you have a signed binary number 0000000100010110² (notice the first bit is 0, therefore it is a positive number), then reverse the order of the bits (giving you 0110100010000000²), and use this method:

Bit b:	0	1	1	0	1	0	0	0	1	0	0	0	0	0	0	0
b * 2n	0 * 20	1 * 21	1 * 22	0 * 23	1 * 24	0 * 25	0 * 26	0 * 27	1 * 28	0 * 29	0 * 210	0 * 211	0 * 212	0 * 213	0 * 214	0 * 215
Result:	0	2	4	0	16	0	0	0	256	0	0	0	0	0	0	0

Now, you have to add up all results: 0 + 2 + 4 + 16 + 0 + 0 + 0 + 256 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 2 + 4 + 16 + 256 = 278

Negative binary number to decimal

For example, 1111111111010011²

1. Invert the binary number: (1111111111010011² becomes 0000000000101100²)
2. Convert it to a decimal number: 44¹⁰
3. Add 1: 45
4. Negate it: -45
5. Therefore, the negative binary number 1111111111010011² is equal to the decimal number -45¹⁰

The NOT Operator

==Left and right shift==