Logic Gates are important to electronics everywhere! We describe logic gates using 1s and 0s. Where True or On is represented by 1 and False or Off is represented by 0. In programming terminology, this representation, or data type, is called Boolean. Where a value is represented by two choices, True or False.
2022-11-14
What are Logic Gates?
Types of Basic Logic Gates
There are several basic logic gates used in performing operations in digital systems. The common ones are;
- OR Gate
- AND Gate
- NOT Gate
- XOR Gate
Additionally, these gates can also be found in a combination of one or two.
OR Gate
In an OR gate, the output of an OR gate attains state 1 if one or more inputs attain state 1.
The Boolean expression of the OR gate is Y = A + B, read as Y equals A ‘OR’ B.
OR Logic Table
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
AND Gate
In the AND gate, the output of an AND gate attains state 1 if and only if all the inputs are in state 1.
The Boolean expression of AND gate is Y = A*B
AND Logic Table
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
NOT Gate
In a NOT gate, the output of a NOT gate attains state 1 if and only if the input does not attain state 1.
The Boolean expression of NOT gate is Y = \(\bar {A}\) It is read as Y equals NOT A. In Programming we use ! to mean not. So in programming the expression would be Y = !A or ‘Y equals NOT A’
NOT Logic Table
| A | Y |
|---|---|
| 0 | 1 |
| 1 | 0 |
Combining Gates
We can utilize the combination of the AND,OR and NOT gates to create our own logic tables such as the below.
| A | B | \(\bar {A}\) (NOT A) | \(\bar {A}\) + B ((NOT A) or B) |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 |
Combining Gates - Part 2
Follow along from right to left.It’s just simple arithmetic!
| A | B | A * B | A * B + A |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Combining Gates - Part 3
Somtimes it’s easier to assign new values. It makes logic easier to follow!
| A | B | A * B = Y | Y | \(\bar {B}\) | \(\bar {A}\) | Y + \(\bar {B}\) + \(\bar {A}\) |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 | 1 |
No Matter what value the above logic will ALWAYS return TRUE!
Combining Gates - Practice 1
| A | B | \(\bar {A}\) | \(\bar {B}\) | A * \(\bar {B}\) | \(\bar {A}\) * B | (A * \(\bar {B}\)) + (\(\bar {A}\)* B) |
|---|---|---|---|---|---|---|
| 0 | 0 | ? | ? | ? | ? | ? |
| 0 | 0 | ? | ? | ? | ? | ? |
| 0 | 0 | ? | ? | ? | ? | ? |
| 0 | 0 | ? | ? | ? | ? | ? |
Combining Gates - Practice 1 (SOLUTION)
| A | B | \(\bar {A}\) | \(\bar {B}\) | A * \(\bar {B}\) | \(\bar {A}\) * B | (A * \(\bar {B}\)) + (\(\bar {A}\)* B) |
|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
Combining Gates - Practice 2
| A | B | \(\bar {B}\) | (\(\bar {B}\) + B) * A | \(\bar {B}\) + (B * A) |
|---|---|---|---|---|
| 0 | 0 | ? | ? | ? |
| 0 | 1 | ? | ? | ? |
| 1 | 0 | ? | ? | ? |
| 1 | 1 | ? | ? | ? |
Combining Gates - Practice 2 (SOLUTION)
| A | B | \(\bar {B}\) | (\(\bar {B}\) + B) * A | \(\bar {B}\) + (B * A) |
|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 |
THE END
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