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8c346a674b
27
.obsidian/plugins/obsidian-git/data.json
vendored
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.obsidian/plugins/obsidian-git/data.json
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{
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"commitMessage": "vault backup: {{date}}",
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"autoCommitMessage": "vault backup: {{date}}",
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"commitDateFormat": "YYYY-MM-DD HH:mm:ss",
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"autoSaveInterval": 5,
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"autoPushInterval": 0,
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"autoPullInterval": 5,
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"autoPullOnBoot": true,
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"disablePush": false,
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"pullBeforePush": true,
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"disablePopups": false,
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"listChangedFilesInMessageBody": false,
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"showStatusBar": true,
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"updateSubmodules": false,
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"syncMethod": "merge",
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"customMessageOnAutoBackup": false,
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"autoBackupAfterFileChange": false,
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"treeStructure": false,
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"refreshSourceControl": true,
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"basePath": "",
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"differentIntervalCommitAndPush": false,
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"changedFilesInStatusBar": false,
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"showedMobileNotice": true,
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"refreshSourceControlTimer": 7000,
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"showBranchStatusBar": true,
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"setLastSaveToLastCommit": false
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}
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@ -24,9 +24,7 @@ $$ V(D) = d_{n-1} * 10^{n-1} + d_{n - 2} * 10^{n-2} + \cdots + d_1 * 10^1 + d_0
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In a binary or base 2 number system, each digit can be a zero or one, called a *bit*.
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In a binary or base 2 number system, each digit can be a zero or one, called a *bit*.
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$$ D = d_{n-1}d_{n-2} \cdots d_1 d_0 $$
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$$ D = d_{n-1}d_{n-2} \cdots d_1 d_0 $$
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To determine the integer value, a very similar formula can be used.
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To determine the integer value, a very similar formula can be used.
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$$ V(B) = b_{n-1} * 2^{n-1} + b_{n-2} * 2^{n-2} \cdots b_{1} * 2^1 + b_0 * 2^0 $$This formula can be generalized as:
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$$ V(B) = b_{n-1} * 2^{n-1} + b_{n-2} * 2^{n-2} \cdots b_{1} * 2^1 + b_0 * 2^0 $$
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*For radix $r$*:
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$$ k = k_{n-1} k_{n-2} \cdots k_1 k_0$$
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- 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 $(10)_2$.
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- 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 $(10)_2$.
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- The *least significant bit* (LSB) is usually the right-most bit. The highest value bit, or the *most significant bit* (MSB).
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- The *least significant bit* (LSB) is usually the right-most bit. The highest value bit, or the *most significant bit* (MSB).
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- A nibble is 4 bits, and a byte is 8 bits
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- A nibble is 4 bits, and a byte is 8 bits
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@ -36,18 +34,18 @@ Repeatedly divide by 2, and track the remainder.
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As an example, the below table shows how one might convert from $(857)_{10}$ to base 2.
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As an example, the below table shows how one might convert from $(857)_{10}$ to base 2.
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| Equation | Remainder | |
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| Equation | Remainder |
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| --------------- | --------- | --- |
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| --------------- | --------- |
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| $857 / 2 = 428$ | $1$ | |
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| $857 / 2 = 428$ | $1$ |
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| $428 / 2 = 214$ | $0$ | |
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| $428 / 2 = 214$ | $0$ |
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| $214 / 2 = 107$ | $0$ | |
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| $214 / 2 = 107$ | $0$ |
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| $107 / 2 = 53$ | $1$ | |
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| $107 / 2 = 53$ | $1$ |
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| $53 / 2 = 26$ | $1$ | |
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| $53 / 2 = 26$ | $1$ |
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| $26 / 2 = 13$ | $0$ | |
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| $26 / 2 = 13$ | $0$ |
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| $13 / 2 = 6$ | $1$ | |
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| $13 / 2 = 6$ | $1$ |
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| $6 / 2 = 3$ | $0$ | |
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| $6 / 2 = 3$ | $0$ |
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| $3 / 2 = 1$ | $1$ | |
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| $3 / 2 = 1$ | $1$ |
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| $1 / 2 = 0$ | $1$ | |
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| $1 / 2 = 0$ | $1$ |
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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.
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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.
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# Definitions
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# Definitions
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@ -18,7 +18,6 @@
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- Standardized in 1995
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- Standardized in 1995
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- Originally intended for simulation of logic networks, later adapted to synthesis
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- Originally intended for simulation of logic networks, later adapted to synthesis
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- Behavioral Verilog describes broader behavior, at a higher level
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```verilog
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```verilog
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// V---V---v--v-----portlist (not ordered)
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// V---V---v--v-----portlist (not ordered)
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module example1(x1, x2, s, f);
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module example1(x1, x2, s, f);
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@ -35,25 +34,6 @@ module example1(x1, x2, s, f);
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endmodule
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endmodule
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```
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```
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```verilog
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- Behavioral Verilog describes broader behavior, at a higher level
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// V---V---v--v-----portlist (not ordered)
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module example1(x1, x2, s, f);
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// Defining the types of the various ports
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input x1, x2, s;
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output f;
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// You can also do this
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assign f = (~s & x1) | (s & x2);
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// Or this
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always @(a, b)
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// always @(....) says "do this stuff whenever any of the values inside of @(...) change"
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{s1, s0} = a + b;
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endmodule
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```
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- Structural Verilog describes how things are laid out at a logic level
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- Structural Verilog describes how things are laid out at a logic level
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## Testbench Layout
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- Define UUT module
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- Initialize Inputs
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- Wait
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- Test every possible combination of inputs and validate that the outputs are correct
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- Debug output can be displayed with `$display("Hello world");`
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@ -18,21 +18,4 @@ The above formula can be used to find the *derivative*. This may also be referre
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## Secant Line
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## Secant Line
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A **Secant Line** connects two points on a graph.
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A **Secant Line** connects two points on a graph.
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A **Tangent Line** represents the rate of change or slope at a single point on the graph.
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A **Tangent Line** represents the rate of change or slope at a single point on the graph.
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# Notation
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Given the equation $y = f(x)$, the following are all notations used to represent the derivative of $f$ at $x$:
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- $f'(x)$
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- $\dfrac{d}{dx}f(x)$
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- $y'$
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- $\dfrac{dy}{dx}$
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- $\dfrac{df}{dx}$
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- "Derivative of $f$ with respect to $x$"
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# Functions that are not differentiable at a given point
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- Where a function is not defined
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- Where a sharp turn takes place
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- If the slope of the tangent line is vertical
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# Higher Order Differentials
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- Take the differential of a differential
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