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+# Digital Hardware and Logic Gates
+
+## Digital Hardware Concepts
+
+### Digital Hardware
+
+- Hardware (HW) means electronic circuits
+- Digital means every wire (or signal) can be in one of two (binary) states
+	- Electrically, the states are two different voltage levels (e.g. 5V and 0V)
+	- We abstractly define two logic values (1 and 0) to be associated with these two voltage levels
+	- We also use the terms "true" and "false"
+- Abstraction is key to much of this course!
+
+### Representing Information
+
+- Every signal means something (abstractly)
+- A single signal can represent some state, or be used as a means of control
+- Multiple signals can be grouped together to create a binary value
+	- Each signal is a bit (binary digit)
+- The same multi-bit value can mean different things in different contexts...
+
+### Putting values in context
+
+- The 6-bit value 101000 might mean
+	- 40, as an unsigned number, or address
+	- -24, if viewed as a 6-bit signed number
+	- "store byte", as an opcode (instruction)
+- Sometimes, leading 0's are implied
+	- 101000 as an 8-bit unsigned number is still 40
+		- But it's not still -24 as an 8-bit signed number (it's also 40)
+- With no context, the default is to interpret as an unsigned (i.e. no negatives) number
+
+---
+
+## Counting in Binary
+
+- Insight into unsigned numbers
+- When we count, we start from 0, add 1 at each step:
+	- 0+1 = 1
+	- 1+1 = 2, but we can't express 2
+- In decimal, 9+1 = 10
+	- Carry into next position and go back to 0
+	- Same with binary, but that happens at 1+1
+- 1+1 = 10, 10+1 = 11, 11+1 = 100, etc.
+- What is 111?
+
+### Counting from 0 to 15
+
+- You will need to know this range of binary numbers
+- Leading 0's: 3 as a 4-bit number is 0011
+
+|Decimal|Binary|
+|--|----|
+|0 |0   |
+|1 |1   |
+|2 |10  |
+|3 |11  |
+|4 |100 |
+|5 |101 |
+|6 |110 |
+|7 |111 |
+|8 |1000|
+|9 |1001|
+|9 |1001|
+|10|1010|
+|11|1011|
+|12|1100|
+|13|1101|
+|14|1110|
+|15|1111|
+
+---
+
+## ASCII codes
+
+- Another context for representing letters
+	- A table can be found [here](https://www.asciitable.com/)
+- ASCII codes are 7-bit values (between 0 and 127)
+
+---
+
+## Logic building blocks
+
+### Logic Circuit Building Blocks
+
+- Logic circuits are functions that generate an output based on a set of inputs
+	- Inputs and output are binary/logical values
+- Three fundamental operations
+	- AND (output is true only if all inputs are true)
+	- OR (output is true if any of the inputs are true)
+	- NOT (output is the inverse of the input)
+		- Also called INV (for inverter)
+- **All** logic functions are made by a combination of these three operations
+
+### Logic in algebraic form
+
+- Note: variable names are generic; they have no inherent meaning
+- AND
+	- Expressed as a product (multiplication)
+	- `Y = X1 * X2` (or just `X1X2`)
+- OR
+	- Expressed as a sum (addition)
+	- `Y = X1 + X2`
+- NOT
+	- `Y = !X1`
+
+### Logic Gates
+
+- Because these are HW circuits, it's useful to have a schematic abstraction
+	- We call these logic "gates"
+	- The symbols for AND, OR, and INV are below
+	- AND and OR can have more than 2 inputs
+		- Same symbol
+- Note the overbar used at the output of the inverter
+	- Just another way of expressing `!` (or `~`)
+
+![schematic](1.1.png)
+
+### Logic Circuits
+
+- If we want a function that is different than just AND or OR, or we have more than two signals to work with, we can combine gates into a larger circuit
+- Much of what we'll be covering is how to define the circuit needed to implement a given logic function
+
+![schematic](1.2.png)
+
+---
+
+[Truth tables, minterms, and simple synthesis ->](2.md)