vault backup: 2025-01-28 11:24:36

.obsidian/plugins/obsidian-git/data.json

@@ -0,0 +1,27 @@
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+  "autoCommitMessage": "vault backup: {{date}}",
+  "commitDateFormat": "YYYY-MM-DD HH:mm:ss",
+  "autoSaveInterval": 5,
+  "autoPushInterval": 0,
+  "autoPullInterval": 5,
+  "autoPullOnBoot": true,
+  "disablePush": false,
+  "pullBeforePush": true,
+  "disablePopups": false,
+  "listChangedFilesInMessageBody": false,
+  "showStatusBar": true,
+  "updateSubmodules": false,
+  "syncMethod": "merge",
+  "customMessageOnAutoBackup": false,
+  "autoBackupAfterFileChange": false,
+  "treeStructure": false,
+  "refreshSourceControl": true,
+  "basePath": "",
+  "differentIntervalCommitAndPush": false,
+  "changedFilesInStatusBar": false,
+  "showedMobileNotice": true,
+  "refreshSourceControlTimer": 7000,
+  "showBranchStatusBar": true,
+  "setLastSaveToLastCommit": false
+}

education/computer engineering/ECE2700/Digital Hardware.md

@@ -24,7 +24,9 @@ $$ V(D) = d_{n-1} * 10^{n-1} + d_{n - 2} * 10^{n-2} + \cdots + d_1 * 10^1 + d_0
 In a binary or base 2 number system, each digit can be a zero or one, called a *bit*. 
 $$ D = d_{n-1}d_{n-2} \cdots d_1 d_0 $$
 To determine the integer value, a very similar formula can be used.
-$$ V(B) = b_{n-1} * 2^{n-1} + b_{n-2} * 2^{n-2} \cdots b_{1} * 2^1 + b_0 * 2^0 $$
+$$ V(B) = b_{n-1} * 2^{n-1} + b_{n-2} * 2^{n-2} \cdots b_{1} * 2^1 + b_0 * 2^0 $$This formula can be generalized as:
+*For radix $r$*:
+$$ k = k_{n-1} k_{n-2} \cdots k_1 k_0$$
 - The base of a number is often notated in the format of $(n)_b$, EG a base 10 number might be $(14)_{10}$, and a binary number might be $(10)_2$. 
 - The *least significant bit* (LSB) is usually the right-most bit. The highest value bit, or the *most significant bit* (MSB).
 - A nibble is 4 bits, and a byte is 8 bits
@@ -34,18 +36,18 @@ Repeatedly divide by 2, and track the remainder.
 
 As an example, the below table shows how one might convert from $(857)_{10}$ to base 2.
 
-| Equation        | Remainder |
-| --------------- | --------- |
-| $857 / 2 = 428$ | $1$       |
-| $428 / 2 = 214$ | $0$       |
-| $214 / 2 = 107$ | $0$       |
-| $107 / 2 = 53$  | $1$       |
-| $53 / 2 = 26$   | $1$       |
-| $26 / 2 = 13$   | $0$       |
-| $13 / 2 = 6$    | $1$       |
-| $6 / 2 = 3$     | $0$       |
-| $3 / 2 = 1$     | $1$       |
-| $1 / 2 = 0$     | $1$       |
+| Equation        | Remainder |     |
+| --------------- | --------- | --- |
+| $857 / 2 = 428$ | $1$       |     |
+| $428 / 2 = 214$ | $0$       |     |
+| $214 / 2 = 107$ | $0$       |     |
+| $107 / 2 = 53$  | $1$       |     |
+| $53 / 2 = 26$   | $1$       |     |
+| $26 / 2 = 13$   | $0$       |     |
+| $13 / 2 = 6$    | $1$       |     |
+| $6 / 2 = 3$     | $0$       |     |
+| $3 / 2 = 1$     | $1$       |     |
+| $1 / 2 = 0$     | $1$       |     |
 
 The final answer is $1101011001$. The least significant bit is the remainder of the first division operation, and the most significant bit is the remainder of the last operation.
 # Definitions

education/computer engineering/ECE2700/Verilog.md

@@ -18,6 +18,7 @@
 - Standardized in 1995
 - Originally intended for simulation of logic networks, later adapted to synthesis
 
+- Behavioral Verilog describes broader behavior, at a higher level
 ```verilog
 //              V---V---v--v-----portlist (not ordered)
 module example1(x1, x2, s, f);
@@ -34,6 +35,25 @@ module example1(x1, x2, s, f);
 endmodule	
 ```
 
-- Behavioral Verilog describes broader behavior, at a higher level
+```verilog
+//              V---V---v--v-----portlist (not ordered)
+module example1(x1, x2, s, f);
+	// Defining the types of the various ports
+	input x1, x2, s;
+	output f;
+	// You can also do this
+	assign f = (~s & x1) | (s & x2);
+	// Or this
+	always @(a, b)
+	// always @(....) says "do this stuff whenever any of the values inside of @(...) change"
+		{s1, s0} = a + b;
+endmodule	
+```
 - Structural Verilog describes how things are laid out at a logic level
 
+## Testbench Layout
+- Define UUT module
+- Initialize Inputs
+- Wait
+- Test every possible combination of inputs and validate that the outputs are correct
+- Debug output can be displayed with `$display("Hello world");`

education/math/MATH1210 (calc 1)/Derivatives.md

@@ -18,4 +18,21 @@ The above formula can be used to find the *derivative*. This may also be referre
 ## Secant Line
 A **Secant Line** connects two points on a graph.
 
-A **Tangent Line** represents the rate of change or slope at a single point on the graph.
+A **Tangent Line** represents the rate of change or slope at a single point on the graph.
+
+# Notation
+Given the equation $y = f(x)$, the following are all notations used to represent the derivative of $f$ at $x$:
+- $f'(x)$
+- $\dfrac{d}{dx}f(x)$
+- $y'$
+- $\dfrac{dy}{dx}$
+- $\dfrac{df}{dx}$
+- "Derivative of $f$ with respect to $x$"
+
+# Functions that are not differentiable at a given point
+- Where a function is not defined
+- Where a sharp turn takes place
+- If the slope of the tangent line is vertical
+
+# Higher Order Differentials
+- Take the differential of a differential