Skip to content

Enhancement: Add Boolean expressions to all logic gates in Chapter 4 #477

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
haaasini01 wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Enhancement: Add Boolean expressions to all logic gates in Chapter 4 #477

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
105 changes: 56 additions & 49 deletions docs/chapter4/4gates.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -55,16 +55,17 @@ Each of the gates included in the CircuitVerse library can be customized for mul

## AND Gate

AND gate gives a HIGH output only if all input values are HIGH. Refer Table 4.25.
AND gate gives a HIGH output only if all input values are HIGH.
**Boolean Expression:** `Y = A · B`

Table 2.5: Two-input AND gate truth table
Table 4.25: Two-input AND gate truth table
| A (Input 1) | B (Input 2) | Y = (A · B) |
| ----------- | ----------- | ----------- |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

| Input 1 | Input 2 | Output |
| ------- | ------- | ------ |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

You can verify the behavior of the **AND gate** circuit element in the live circuit of a two-input AND gate embedded below:

Expand All @@ -83,16 +84,17 @@ You can verify the behavior of the **AND gate** circuit element in the live circ

## OR Gate

OR gate produces a HIGH output only if any of the input values are HIGH. Refer Table 4.26.
OR gate produces a HIGH output only if any of the input values are HIGH.
**Boolean Expression:** `Y = A + B`

Table 2.6: Two-input OR gate truth table
Table 4.26: Two-input OR gate truth table

| Input 1 | Input 2 | Output |
| ------- | ------- | ------ |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
| A (Input 1) | B (Input 2) | Y = (A + B) |
| ----------- | ----------- | ----------- |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |

You can verify the behavior of an **OR gate** circuit element in the live circuit embedded below:

Expand All @@ -111,14 +113,15 @@ You can verify the behavior of an **OR gate** circuit element in the live circui

## NOT Gate

NOT gate inverts the input as an output. It is also known as an inverter. Refer Table 4.27.
NOT gate inverts the input as an output. It is also known as an inverter.
**Boolean Expression:** `Y = ¬A`

Table 4.27: NOT gate truth table

| Input | Output |
| ----- | ------ |
| 0 | 1 |
| 1 | 0 |
| A (Input) | Y = (¬A) |
| --------- | -------- |
| 0 | 1 |
| 1 | 0 |

You can verify the behavior of an **NOT gate** circuit element in the live circuit embedded below:

Expand All @@ -137,16 +140,17 @@ You can verify the behavior of an **NOT gate** circuit element in the live circu

## XOR Gate

XOR gate produces a HIGH output only if both inputs aren't the same. Refer Table 4.28.
XOR gate produces a HIGH output only if both inputs aren't the same.
**Boolean Expression:** `Y = A ⊕ B`

Table 4.28: Two-input XOR gate truth table

| Input 1 | Input 2 | Output |
| ------- | ------- | ------ |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| A (Input 1) | B (Input 2) | Y = (A ⊕ B) |
| ----------- | ----------- | ------------ |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

You can verify the behavior of an **XOR gate** circuit element in the live circuit embedded below:

Expand All @@ -163,16 +167,17 @@ You can verify the behavior of an **XOR gate** circuit element in the live circu

## NAND Gate

NAND gate, a combination of an AND gate and a NOT gate connected together in series, produces the inverted output of an AND gate––produces a LOW output when all the inputs are HIGH. Refer Table 4.29.
NAND gate, a combination of an AND gate and a NOT gate connected together in series, produces the inverted output of an AND gate––produces a LOW output when all the inputs are HIGH.
**Boolean Expression:** `Y = ¬(A · B)`

Table 4.29: Two-input NAND gate truth table

| Input 1 | Input 2 | Output |
| ------- | ------- | ------ |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| A (Input 1) | B (Input 2) | Y = (¬(A · B)) |
| ----------- | ----------- | -------------- |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

You can verify the behavior of an **NAND gate** circuit element in the live circuit embedded below:

Expand All @@ -191,16 +196,17 @@ You can verify the behavior of an **NAND gate** circuit element in the live circ

## NOR Gate

NOR gate inverts the output of an OR gate. In other words, it only goes HIGH when all the inputs are LOW. Refer Table 4.30.
NOR gate inverts the output of an OR gate. In other words, it only goes HIGH when all the inputs are LOW.
**Boolean Expression:** `Y = ¬(A + B)`

Table 4.30: Two-input NOR gate truth table

| Input 1 | Input 2 | Output |
| ------- | ------- | ------ |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
| A (Input 1) | B (Input 2) | Y = (¬(A + B)) |
| ----------- | ----------- | -------------- |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |

You can verify the behavior of an **NOR gate** circuit element in the live circuit embedded below:

Expand All @@ -219,16 +225,17 @@ You can verify the behavior of an **NOR gate** circuit element in the live circu

## XNOR Gate

XNOR gate inverts the output of an XOR gate––it only goes HIGH if both the inputs are the same. Refer Table 4.31.
XNOR gate inverts the output of an XOR gate––it only goes HIGH if both the inputs are the same.
**Boolean Expression:** `Y = ¬(A ⊕ B)`

Table 4.31: Two-input XNOR gate truth table

| Input 1 | Input 2 | Output |
| ------- | ------- | ------ |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| A (Input 1) | B (Input 2) | Y = (¬(A ⊕ B)) |
| ----------- | ----------- | -------------- |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

You can verify the behavior of an **XNOR gate** circuit element in the live circuit embedded below:

Expand Down