boolean and bitwise operations

== boolean logic ==

definition rougly equates to logic involving things that can be one of two states (true or false, 1 or 0)


== Basic boolean operations ==

=== NOT ===
negates a given input

Truth Table
 _______
| I | O |
|---|---|
| 0 | 1 |
|---|---|
| 1 | 0 |
|___|___|

The C language equivalent operator should be  !  (not 100% sure).

=== OR ===
takes two inputs and outputs 1 if AT LEAST ONE input is 1, or 0 if neither is.

The OR bitwise operator can be used to force a sequence of bits into their on (1) state.
In MIPS, you will occasionally see the OR instructiong being used to initialize a register to an immediate value.

The C language equivalent operator is  |

Truth Table
 _____________
| I1 | I2 | O |
|----|----|---|
| 0  | 0  | 0 |
|----|----|---|
| 1  | 0  | 1 |
|----|----|---|
| 0  | 1  | 1 |
|----|----|---|
| 1  | 1  | 1 |
|____|____|___|


=== AND ===
Takes two inputs and outputs 1 if BOTH inputs are 1, or 0 if neither is.

The AND bitwise operator can be used to capture a specific set of bits, ignoring the state of the rest.

The C language equivalent operator is  &

Truth Table
 _____________
| I1 | I2 | O |
|----|----|---|
| 0  | 0  | 0 |
|----|----|---|
| 1  | 0  | 0 |
|----|----|---|
| 0  | 1  | 0 |
|----|----|---|
| 1  | 1  | 1 |
|____|____|___|

=== XOR ===
Takes two inputs and outputs 1 if the inputs do not match, or 0 if they match

The XOR bitwise operator can be used to flip the state of a bit or sequence of bits

The C language equivalent operator is  ^


Truth Table
 _____________
| I1 | I2 | O |
|----|----|---|
| 0  | 0  | 0 |
|----|----|---|
| 1  | 0  | 1 |
|----|----|---|
| 0  | 1  | 1 |
|----|----|---|
| 1  | 1  | 0 |
|____|____|___|


== Bitwise Operations ==

Bitwise Operations perform multiple boolean operations within one instruction. This is done by comparing the bits
on the same position. For example, consider the simple example of 0x05 OR 0x0C.

5 = 0 1 0 1
C = 1 1 0 0

we start by performing a boolean OR with the rightmost bits of the two numbers (1, 0), giving us an output of 1

? = ? ? ? 1

Then we perform the same operation with the next columns as such:

? = ? ? 0 1 (0, 0 is 0)
? = ? 1 0 1 (1, 1 is 1)
E = 1 1 0 1 (0, 1 is 1)