vault backup: 2025-01-09 14:07:03

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education/computer engineering/ECE1410/Binary Manipulation.md

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+- To find the magnitude of a negative twos compliment number, flip all of the bits and add one.
+- 

education/computer engineering/ECE2700/Boolean Algebra.md

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+![](./assets/logic-gate)

education/computer engineering/ECE2700/Digital Hardware.md

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+Any poduct that contains a logic circuit is classified as digital hardware. 
+- Moore's Law states that the number of a transistors on a chip doubles every two years
+	- The International Technology Roadmap for Semiconductors (ITRS) forecasts technology, including the number of transistors on a chip
+- Multiple integrated circuits can be connected using a printed circuit board, or PCB.
+- *Standard chips* conform to an agreed upon standard for functionality and physical configuration. They are usually less than 100 transistors in size, and provide basic building blocks for logic.
+	- These chips are combined to form a larger logic circuit
+	- They were popular until the 1980s
+	- As ICs improved, it became inefficient space-wise to have separate chips for each logical building block
+	- The functionality of these chips is fixed, and they do not change.
+# Programmable Logic Devices
+Programmable logic devices (PLDs) include a number of programmable switches that can configure the internal circuitry of a chip
+- The most common type of PLD is a Field Programmable Gate Array (FPGA)
+- FPGAs are widely available, but come with the drawback that they're limited in speed and performance
+
+# Application Specific Integrated Circuits
+Application Specific Integrated Circuits (ASICs) have higher maximum performance and transistor density compared to FPGAs, but the cost of production is very high.
+- A logic circuit is made of connected logic gates
+
+# Binary Numbers
+In base 10, a value is expressed by an n-tuple with n digits
+$$ D = d_{n-1}d_{n-2} \cdots d_1 d_0 $$
+This represents the value
+$$ V(D) = d_{n-1} * 10^{n-1} + d_{n - 2} * 10^{n-2} + \cdots + d_1 * 10^1 + d_0 * 10^0 $$
+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.
+$$ V(B) = b_{n-1} * 2^{n-1} + b_{n-2} * 2^{n-2} \cdots b_{1} * 2^1 + b_0 * 2^0 $$
+- 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
+## Conversions
+### Base 10 to Binary
+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 |
+| --------------- | --------- |
+| $857 / 2 = 428$ | $1$       |
+| $428 / 2 = 214$ | $0$       |
+| $214 / 2 = 107$ | $0$       |
+| $107 / 2 = 53$  | $1$       |
+| $53 / 2 = 26$   | $1$       |
+| $26 / 2 = 13$   | $0$       |
+| $13 / 2 = 6$    | $1$       |
+| $6 / 2 = 3$     | $0$       |
+| $3 / 2 = 1$     | $1$       |
+| $1 / 2 = 0$     | $1$       |
+
+The final answer is $1101011001$.
+# Definitions
+- **Xtor** is an abbreviation for *transistor*
+- **Moore's Law** states that the number of transistors on a chip doubles every two years.
+- A tuple is a finite and ordered list of things

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

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+# Introduction
+Every mathematical function can be thought of as a set of ordered pairs, or an input value and an output value.
+- Examples include $f(x) = x^2 + 2x + 1$, and $\{(1, 3), (2, 5), (4, 7)\}$.
+
+**A limit describes how a function behaves *near* a point, rather than *at* that point.***
+- As an example, given a *well behaved function* $f(x)$ and the fact that:
+	- $f(1.9) = 8.41$
+	- $f(1.999) = 8.99401$
+	- $f(2.1) = 9.61$
+	- $f(2.01) = 9.061$
+	- $f(2.0001) = 9.0006$
+	We can note that the smaller the distance of the input value $x$ to $2$, the smaller the distance of the output to $9$. This is most commonly described in the terms "As $x$ approaches $2$, $f(x)$ approaches $9$", or "As $x \to 2$, $f(x) \to 9$."
+
+Limits are valuable because they can be used to describe a point on a graph, even if that point is not present.
+# Standard Notation
+The standard notation for a limit is:
+$$ \lim_{x \to a} f(x) = L $$
+- As $x$ approaches $a$, the output of $f(x)$ draws closer to $L$. In the above notation, $x$ and $a$ are not necessarily equal.
+- When plotted, the hole is located at $(a, L)$.
+# Definitions
+
+| Term                  | Definition                                                                    |
+| --------------------- | ----------------------------------------------------------------------------- |
+| Well behaved function | A function that is continuous, has a single value, and is defined everywhere. |
+
+
+
+

education/nutrition/Review.md

@@ -113,4 +113,25 @@ Leptin's primary role is to regulate long-term energy balance. High leptin level
 ## Exprimental
 - A systematic way of testing a hypothesis
 ## Epidemiological
-- Observations of the occurrence, distribution, and associations
+- Observations of the occurrence, distribution, and associations
+
+# Practice Final
+- To reduce blood pressure, one should follow the DASH diet
+- Bleeding gums, easy bruising, and poor wound healing that characterize scurvey are all related to vitamin C's role in synthesis of collagen.
+- Vitamin K is a fat soluble vitamin that can be made in the GI tract
+- Parathyroid hormone enhances the body's ability to retain calcium.
+- Males have a higher basal metabolic rate than females
+- On the intuitive eating spectrum, awareness, balance, moderation, and variety would exist in the middle. Apathy is on the left and anxiety is on the right
+- The term appetite describes a biological need for food
+
+- The 10 principals of intuitive eating are:
+ 1. Reject Diet Culture
+2. Honor Your Hunger
+3. Make Peace with Food
+4. Discover the Satisfaction Factor
+5. Feel Your Fullness
+6. Challenge the Food Police
+7. Cope with Your Emotions with Kindness
+8. Respect Your Body
+9. Movement -- Feel the Difference
+10. Honor Your Health with Gentle Nutrition