Last Sync: 2022-06-04 17:30:04

Hardware/Logic_Gates/Logic_gates.md

@@ -9,147 +9,3 @@ tags:
 # Logic gates
 
 Logic gates are the basic building blocks of digital computing. **A logic gate is an electrical circuit that has one or more than one input and only one output.** The input controls the output and the logic is isomorphic with [Boolean connectives](../../Logic/Truth-functional_connectives.md) defined in terms of [truth-tables](../../Logic/Truth-tables.md).
-
-### Truth tables
-
-Truth-tables present the conditions under which logical propositions are true or false. To take the `AND` operator: `AND` evaluates to `true` if both of its constituent expressions are `true`, and `false` in any other circumstances (e.g. if one proposition is `true` and the other `false` (or vice versa) and if both propositions are `false` ).
-
-This is most clearly expressed in the following truth table:
-
-**Truth table for `AND`**
-
-````
-p    q   p & q
-_    _   _____
-t    t     t
-t    f     f
-f    t     f
-f    f     f   
-````
-
- The negation operator (`¬` or `~` ) switches the value of a proposition from true to false. When we put `~` before `true` it becomes false and when we put `~` before `false` it becomes `true`. We will see shortly that this corresponds to a basic on/off switch.
-
-**Truth table fo `NOT`**
-
-````
-p    ~ p
-_    __
-t    f
-f    t
-````
-
-## `AND` gate
-
-Just as we can create `NOT` logic from a NAND gate, without the `AND` conditions, we can create a circuit that exemplifies the truth conditions of `AND` without including those of `NOT`.
-
-When we attach two NAND gates in sequence connected to two switches as input this creates the following binary conditions:
-
-````
-A    B   Output
-_    _   _____
-
-0    0     0       (1)
-1    0     0       (2)
-0    1     0       (3)
-1    1     1       (4)
-````
-
-Which is identical to the truth table for `AND` :
-
-````
-p    q   p & q
-_    _   _____
-
-t    t     t      (1)
-t    f     f      (2)
-f    t     f      (3)
-f    f     f      (4)  
-````
-
-### Natural language
-
- > 
- > `AND` (`&`) is `true` when both constituent propositions are `true` and `false` in all other circumstances viz. `false false` (`¬P & ¬Q` / `0 0` ), `true false` (`P & ¬Q` / `1 0` ), `false true` (`¬P & Q` / `0 1` )
-
-AND at 0 0
-
-![Screenshot_2020-08-25_at_15.04.10 1.png](../img/Screenshot_2020-08-25_at_15.04.10%201.png)
-
-AND at 1 0 or 0 1
-![Screenshot_2020-08-25_at_15.05.20.png](../img/Screenshot_2020-08-25_at_15.05.20.png)
-
-![Screenshot_2020-08-25_at_15.05.36.png](../img/Screenshot_2020-08-25_at_15.05.36.png)
-
-### Symbol for `AND` gate
-
-It's very similar to NAND so be careful not to confuse it
-
-![Pasted image 20220319173651.png](../img/Pasted%20image%2020220319173651.png)
-
-### `OR`
-
- > 
- > `OR` (in logic known as **disjunction**) in its non-exclusive form is `true` if either of its propositions are `true` or both are `true` . It is `false` otherwise.
-
-![Pasted image 20220319173819.png](../img/Pasted%20image%2020220319173819.png)
-
-````
-p    q   p V q
-_    _   _____
-
-t    t     t      (1)
-t    f     t      (2)
-f    t     t      (3)
-f    f     f      (4)  
-````
-
-### `XOR`
-
- > 
- > `XOR` stands for **exclusive or**, also known as **exclusive conjunction**. This means it can only be `true` if one of its propositions are `true` . If both are `true` this doesn't exclude one of the propositions so the overall statement has to be `false` . This is the only change in the truth conditions from `OR` .
-
-![Pasted image 20220319173834.png](../img/Pasted%20image%2020220319173834.png)
-
-Electrical symbol for XOR
-
-````
-p    q   p X V q
-_    _   ________
-
-t    t     f      (1)
-t    f     t      (2)
-f    t     t      (3)
-f    f     f      (4)  
-````
-
-### `**NOR**`
-
- > 
- > This is equivalent to saying 'neither' in natural language. It is only `true` both propositions are `false` . If either one of the propositions is `true` the outcome is `false` . If both are `true` it is `false`
-
-![Pasted image 20220319173900.png](../img/Pasted%20image%2020220319173900.png)
-
-### `XNOR`
-
- > 
- > This one is confusing. I can see the truth conditions but don't understand them. It is `true` if both propositions are `false` like `NOR` or if both propositions are `true` and `false` otherwise.
-
-````
-p    q   p ¬V q
-_    _   ________
-
-t    t     f      (1)
-t    f     f      (2)
-f    t     f      (3)
-f    f     t      (4)  
-````
-
-````
-p    q   p X¬V q
-_    _   ________
-
-t    t     t      (1)
-t    f     f      (2)
-f    t     f      (3)
-f    f     t      (4)  
-````

Hardware/Logic_Gates/Or_gate.md

@@ -0,0 +1,25 @@
+---
+tags:
+  - Logic
+  - Electronics
+  - Hardware
+  - logic-gates
+---
+
+# OR gate
+
+ > `OR` (in logic known as **disjunction**) in its non-exclusive form is `true` if either of its propositions are `true` or both are `true` . It is `false` otherwise.
+
+![Pasted image 20220319173819.png](../../img/Pasted_image_20220319173819.png)
+
+````
+p    q   p v q
+_    _   _____
+
+t    t     t     
+t    f     t     
+f    t     t     
+f    f     f        
+````
+
+TO DO: Add circuit diagram for OR gate

Hardware/Logic_Gates/Xor_gate.md

@@ -0,0 +1,24 @@
+---
+tags:
+  - Logic
+  - Electronics
+  - Hardware
+  - logic-gates
+---
+
+# XOR gate
+
+ > `XOR` stands for **exclusive or**, also known as **exclusive conjunction**. This means it can only be `true` if one of its propositions are `true` . If both are `true` this doesn't exclude one of the propositions so the overall statement has to be `false` . This is the only change in the truth conditions from `OR` .
+
+![Pasted image 20220319173834.png](../../img/Pasted_image_20220319173834.png)
+
+
+````
+p    q   p xv q
+_    _   ________
+
+t    t     f      (1)
+t    f     t      (2)
+f    t     t      (3)
+f    f     f      (4)  
+````