📗 -> 01/13/25: ECS154A-L4
🎤 Vocab
❗ Unit and Larger Context
✒️ -> Scratch Notes
N-type an P-type Doping
N-Type - Extra electron
-
- charge
P-Type -
- Lots of holes?
VLSI - Very Large Scale Integration
Karnaugh Map
- Every box in a Karnaugh Box has a Hamming Distance (bit difference) of 1 from another adjacent box
- Left, right, up, down. No diagonals. No upper dimensional funny business. Just go left-right across borders.
- Represents a combination of ABC activation in binary as in integer
| A | A | |||
|---|---|---|---|---|
| 000: 0 | 010: 2 | 110: 6 | 100: 4 | |
| C | 001: 1 | 011: 3 | 111: 7 | 101: 5 |
| B | B |
- ABC
| A | A | ||||
|---|---|---|---|---|---|
| 0000: 0 | 0100: 4 | 1100: 12 | 1000: 8 | ||
| 0001: 1 | 0101: 5 | 1101: 13 | 1001: 9 | D | |
| C | 0011: 3 | 0111: 7 | 1111: 15 | 1011: 11 | D |
| C | 0010: 2 | 0110: 6 | 1110: 14 | 1010: 10 | |
| B | B |
- ABCD
Literal - One of variables
Implicant - Where there is a 1
Cover - Collection of implicants that cover all 1s
Prime Implicant - Largest possible implicant
Cost - Number of gat inputs
- Generate prime implicants
- Find set of essential PI’s
- Pick non-essential min-cost PI’s that cover function
| A | A | ||||
|---|---|---|---|---|---|
| 1 | 1 | ||||
| 1 | D | ||||
| C | 1 | 1 | 1 | D | |
| C | 1 | 1 | |||
| B | B |
- Smallest Possible expression:
- Bottom right + Top horizontal + Middle vertical
- To find the smallest possible expression, circle adjacent groups with Hamming distance of 1 between adjacent members. IE a rectangle with an area that is a power of 2.
- In the above, we circled the top horizontal 2, the middle vertical 2, and the bottom right 2x2 square, then expressed those areas logically
| A | A | ||||
|---|---|---|---|---|---|
| 1 | 1 | 1 | |||
| 1 | D | ||||
| C | 1 | D | |||
| C | 1 | 1 | 1 | ||
| B | B |
- Horizontal strip + Corners
- not(BD) wraps all of the corners since they are each a hamming distance of 1 from each other.
Suppose you have an E-lock that has three buttons (LMR)
Lock opens when right-most 2 buttons pressed, trapdoor over alligators if anything else
| L | L | |||
|---|---|---|---|---|
| 1 | 1 | 1 | ||
| R | 1 | 1 | 1 | |
| M | M |
- Equation for trapdoor:
- Wont open if nothing done.
- Solution to lock is more exclusive:
- Solution to lock is more exclusive:
🧪 -> Refresh the Info
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🔗 -> Links
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Connections
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