Lesson 23 Flashcards — Digital Logic#
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1. Why is digital representation robust in a way analog is not?
Only two states are valid, so noise that does not push a value across the decision threshold is completely removed when the signal is regenerated. Analog noise accumulates permanently.
2. What does digital robustness cost?
You must quantize first, and quantization error never goes away. Digital trades a one-time known error for immunity to every error after it.
3. How many values can n bits represent?
\(2^n\). This is the same relationship as the ADC level count in Objective 2.5 (there we called the exponent b).
4. Name the three fundamental logic gates and when each outputs 1.
NOT when the input is 0; AND when all inputs are 1; OR when any input is 1.
5. What is special about XOR?
It outputs 1 when the inputs differ — the 'are these different?' gate. It appears throughout arithmetic and error checking.
6. How do you tell the gate symbols apart on a circuit diagram?
AND has a flat back and a D-shaped nose; OR has a curved back and a pointed nose; NOT is a triangle. A bubble on the output inverts it (NAND, NOR, XNOR), and a second arc across the back marks XOR and XNOR.
7. How many rows does a truth table with n inputs have?
\(2^n\). List them in binary counting order so you cannot miss one.
8. What does combinational mean?
The output depends only on the inputs right now, with no memory of what came before — which is why a truth table specifies it completely. Objective 2.8 adds the memory.
9. Why is the truth table considered the ground truth for a circuit?
Because it is the complete specification. Two circuits with the same truth table are functionally identical, however differently they are built.
10. How do you build a truth table for a compound circuit?
Give every intermediate wire its own column, in the order signals are produced, and fill each using only the columns to its left. Holding intermediates in your head is where errors come from. If the drawing does not name a wire, name it yourself and use that as the column head.
11. On a circuit diagram, what does a filled dot where wires meet mean?
Fan-out — one signal feeding two places, so the same value arrives at both gates and it gets one column in the truth table. Wires that merely cross with no dot are unrelated.
12. How do you write a Sum of Products expression?
For each row where the output is 1, write a product (AND) of all inputs, complementing any input that is 0 in that row. Then OR those products together.
13. How do you write a Product of Sums expression?
For each row where the output is 0, write a sum (OR) of all inputs, complementing any input that is 1 in that row. Then AND those sums together. Note the inversion is opposite to SOP.
14. When would you choose POS over SOP?
When the table has few 0s. Few 1s favors SOP, few 0s favors POS — both describe the same circuit.