bitmask question?

Question

I have the follow:

public static final int LIMIT_ONE = 1;
public static final int TRADEABLE = (1 << 1);
public static final int SELLABLE = (1 << 2);
public static final int STORABLE = (1 << 3);
public static final int STORABLE_IN_WH = (1 << 4);
public static final int STORABLE_IN_LEGION_WH = (1 << 5);
public static final int BREAKABLE = (1 << 6);
public static final int SOUL_BOUND = (1 << 7);
public static final int UNK9 = (1 << 8);
public static final int UNK10 = (1 << 9);
public static final int UNK11 = (1 << 10);
public static final int CAN_COMPOSITE_WEAPON = (1 << 11);
public static final int BLACK_CLOUD_TRADERS = (1 << 12);
public static final int CAN_SPLIT = (1 << 13);
public static final int UNK15 = (1 << 14);
public static final int UNK16 = (1 << 15);

and I wanted to understand how it is calculated to give the follow result, for example: 12414

I am really clueless on how the bitmask work and if any one could perhaps give some tips and explain how it goes to that number I would appreciate very much.

Answer 1

The expression (1 << n) is equivalent to 2 raised to the power of n.

When you write (1 << n) | (1 << m) this is the same as (1 << n) + (1 << m) as long as n and m are different. So you can think of it in terms of simple additions if you wish.

The number 12414 in binary is 11000001111110 so it is the sum (or bitwise OR) of the following flags:

TRADEABLE                1 << 1  =     2
SELLABLE                 1 << 2  =     4
STORABLE                 1 << 3  =     8
STORABLE_IN_WH           1 << 4  =    16
STORABLE_IN_LEGION_WH    1 << 5  =    32
BREAKABLE                1 << 6  =    64
BLACK_CLOUD_TRADERS      1 << 12 =  4096
CAN_SPLIT                1 << 13 =  8192
========================================
                         Total   = 12414

Note that the flags that are included correspond to the bits that are set in the binary representation of 12414, when read right-to-left.

Answer 2

12414 in binary is:

Binary number: 1  1  0  0  0  0  0  1  1  1  1  1  1  0
-------------------------------------------------------
Bit positions: 13 12 11 10 9  8  7  6  5  4  3  2  1  0

Look at which bits are 1. Those are the flags that are set in the bitmask, which is created by using the bitwise OR operator to combine the flags:

bitmask = TRADEABLE | SELLABLE | STORABLE | STORABLE_IN_WH | STORABLE_IN_LEGION_WH | BREAKABLE | BLACK_CLOUD_TRADERS | CAN_SPLIT;

To further explain this, STORABLE = (1 << 3); means that STORABLE is equal to the number one (binary 1, falling only in bit position 0) shifted to the left by 3 places. Note that STORABLE = Math.pow(2, 3); would be equivalent. Because none of the bits overlap among the flags, we can combine all of them into a single int and then split them apart later.

We can check for the existence of flags using the bitwise AND operator, which will return a non-zero value if the flag is set and a zero value if the flag is not set:

if(bitmask & TRADEABLE != 0) {
    // This item can be traded
} else {
    // This item cannot be traded
}

We can set, clear, or toggle flags like this:

bitmask |= TRADEABLE; // Sets the flag using bitwise OR
bitmask &= ~TRADEABLE; // Clears the flag using bitwise AND and NOT
bitmask ^= TRADEABLE; // Toggles the flag using bitwise XOR 

Answer 3

a << b shifts the bits in a b values to the left, padding the new bits on the right with zeroes. 1 << n equates to an integer with only the nth bit (counting from 0 from the right) set, which is equivalent to 2ⁿ.

12414 is 11000001111110 in binary. Therefore it is produced by summing the constants listed below. You can work this out by seeing the bit 1 from the right is set, therefore TRADEABLE is "set"; bit 7 is not set (it's 0), therefore SOUL_BOUND is not "set". Note how the bit numbers associate with the declared values of (1 << n).

TRADEABLE
SELLABLE
STORABLE
STORABLE_IN_WH
STORABLE_IN_LEGION_WH
BREAKABLE
BLACK_CLOUD_TRADERS
CAN_SPLIT

Answer 4

I don't understand the question "how it is calculated to give the follow result". (What is calculated?)

The main thing to understand is that all computer values are stored in binary. Any number will be a combination of 0 and 1 bit. Some numbers only have one 1 bit.

http://en.wikipedia.org/wiki/Mask_(computing)

Answer 5

My guess would be that you take some number, such as your example 12414, and figure out what properties are contained within it.

For example, since 12414 is 11000001111110 in binary, whatever it is attached to is tradeable, because ANDing this number with the mask will give you a 1 in the second bit.

Answer 6

In binary, 12414 is 11000001111110. LIMIT_ONE in binary is 1 and the <<, which is the bitshift operator moves the zero to the left padding with a zero on the right. Therefore, tradeable in binary is 10 and so on until unk16, which ends up being 1000000000000000. Now you put these values together using bitwise OR, which basically puts a 1 on each position where at least one of its operand has a one on that position (the pipe operator '|' is used in most languages).

Example:

100 | 10 = 110

Therefore, to get to 12414, you need to do a bitwise OR on the following variables: unk16, unk15, tradeable, selleable, storeable, storeable in wh, storeable in legion wh and breakable. The combination of ones on the different positions in each of these variables gives you binary 11000001111110, which turns out to be 12414 in decimal.

This is probably the simplest way to explain it, if you want to know more, you should read up on bitwise operators and how binary representation of numbers works.

To find out which of the flags the number 12414 has, you can use the & (bitwise AND) operator and do a zero check. For example:

6 & 2 = 2 (110 has a 1 on the same position as 2, which is 010)
6 & 1 = 0 (110 does not have a 1 on the same position as 1, which is 001)