Logic Gates
All logic gates work on Input/Process/Output model (just like a computer, but much more simple)
AND (one and the other)
| Truth Table | Diagram | |||
|---|---|---|---|---|
A 0 0 1 1 |
B 0 1 0 1 |
Q 0 0 0 1 |
 |
|
OR (one or the other or both)
| Truth Table | Diagram | |||
|---|---|---|---|---|
A 0 0 1 1 |
B 0 1 0 1 |
Q 0 1 1 1 |
 |
|
NOT (this is a unary operation, there is only one input)
| Truth Table | Diagram | ||
|---|---|---|---|
A 0 1 |
Q 1 0 |
 |
|
NAND (this is simply a combination of NOT and AND)
| Truth Table | Diagram | |||
|---|---|---|---|---|
A 0 0 1 1 |
B 0 1 0 1 |
Q 1 1 1 0 |
 |
|
NOR (for both NAND and NOR, notice the little circle at the front? that's the NOT component)
| Truth Table | Diagram | |||
|---|---|---|---|---|
A 0 0 1 1 |
B 0 1 0 1 |
Q 1 0 0 0 |
 |
|
XOR
| Truth Table | Diagram | |||
|---|---|---|---|---|
A 0 0 1 1 |
B 0 1 0 1 |
Q 0 1 1 0 |
 |
|
XNOR
| Truth Table | Diagram | |||
|---|---|---|---|---|
A 0 0 1 1 |
B 0 1 0 1 |
Q 1 0 0 1 |
 |
|
Combinations are fun. They require 3 variables and 8 different decisions to be made.
| A | B | C | Q | |
|---|---|---|---|---|
0 0 0 0 1 1 1 1 |
0 0 1 1 0 0 1 1 |
0 1 0 1 0 1 0 1 |
0 0 0 0 0 0 1 0 |
 |
Simple Adder
The most basic application of these logic gates is to set up a system that will add two binary numbers together. This is called a 'simple adder'.
First, let's take a look at how adding in binary works (with one digit)
It seems like we get a 1 in the ones column when the values we're adding together are different and 0 when they're the same. That corresponds with XOR. For the second column, we need 1 when both numbers being added are 1 and 0 otherwise, that's AND.
