Difference between revisions of "Bitwise Operations"
m (→Converting from decimal to binary and from binary to decimal) |
m (→Converting from decimal to binary and from binary to decimal) |
||
| Line 5: | Line 5: | ||
==Converting from decimal to binary and from binary to decimal== | ==Converting from decimal to binary and from binary to decimal== | ||
| − | For example 11010011<sup>2</sup> is equal to 21110<sup>10</sup>, and 14310<sup>10</sup> is | + | For example 11010011<sup>2</sup> is equal to 21110<sup>10</sup>, and 14310<sup>10</sup> is equal to 10001111<sup>2... |
;From decimal to binary | ;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: | |
{|border=1 cellpadding=5 | {|border=1 cellpadding=5 | ||
| Line 19: | Line 19: | ||
|Remainder: ||1 ||1 ||1 ||1 ||0 ||0 ||0 ||0 ||1 ||1 | |Remainder: ||1 ||1 ||1 ||1 ||0 ||0 ||0 ||0 ||1 ||1 | ||
|} | |} | ||
| − | |||
| − | Now, read the sequence of remainders from '''right to left''', | + | ...Now, read the sequence of remainders from '''right to left''', to arrive at the binary number 1100001111. |
;Negative decimal number to binary | ;Negative decimal number to binary | ||
| Line 29: | Line 28: | ||
# Take the binary form of 783: 0000001100001111 | # Take the binary form of 783: 0000001100001111 | ||
# Invert it: 1111110011110000 | # Invert it: 1111110011110000 | ||
| − | # | + | # Then add 1 to it |
| − | # So, -783<sup>10</sup> is | + | # So, -783<sup>10</sup> is 1111110011110001<sup>2</sup> |
| − | + | 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, 1111110011110001<sup>2</sup> is equal to -783<sup>10</sup> 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, 1111110011110001<sup>2</sup> is equal to 64752<sup>10</sup>. | ||
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). | 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). | ||
Revision as of 22:01, 28 March 2013
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 100011112...
- 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
- Take the binary form of 783: 0000001100001111
- Invert it: 1111110011110000
- Then add 1 to it
- 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).
