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+[\<- Latches](12.md)
+
+---
+
+# Flip-flops
+
+## Motivation for flip-flops
+
+### Counting
+
+- A common example of a sequential circuit
+	- We'll learn later how this really works
+
+![diagram](13.1.png)
+
+### Time, and gate delays
+
+- All the timing diagrams we have seen show the output change as soon as the inputs change
+	- Not reality but often a fine abstraction when we only care about logical behavior
+- In reality, it takes some amount of time for a change in an input to "propagate" to a change in the output
+	- This form of propagation delay is called gate delay
+
+### Pass-thru effects
+
+- With a latch, the output can change for the entire time the CLK is asserted
+- What happens if next count logic is "faster" than the time CLK is high?
+	- Uneven counting, probably not what we want
+
+![diagram](13.2.png)
+
+### Avoiding pass-thru effects
+
+- We could shrink the time that CLK is high, but this becomes impractical
+	- Circuitry to generate and distribute CLK is cleaner if high and low phases are equal
+- Use circuit structures that are designed to react to just the "edge" of the clock
+	- Output can only change when CLK goes from low to high (rising edge) or high to low (falling edge)
+	- We call these circuits flip-flops
+
+---
+
+## Master/slave latch
+
+- Note how the clock "port" is drawn
+
+![circuit](13.3.png)
+![timing diagram](13.4.png)
+![graphical symbol](13.5.png)
+
+- The output Q can only change at the "edge" of the clock (the negative edge)
+
+---
+
+## Positive edge-triggered flip-flop
+
+- A more efficient design than master/slave
+
+![circuit](13.6.png)
+![graphical symbol](13.7.png)
+
+### How does it work?
+
+- When clock is low
+	- P1 and P2 are high, isolating Q/!Q
+	- P3 is the same as D and P4 is !D
+- As soon as Clock goes high
+	- If P3 is high (i.e., D is 1)
+		- P1 goes low, setting Q to 1
+		- Gates 1 and 3 are disabled, P4 doesn't matter
+	- If P4 is high (i.e., D is 0)
+		- P2 goes low, resetting Q to 0
+		- Gate 4 is disabled, D doesn't matter
+- When Clock goes low, P1 and P2 go to 1
+
+---
+
+## Summary of latch/flip-flop behavior
+
+### Latch vs flip-flops
+
+![circuit](13.8.png)
+![timing diagram](13.9.png)
+
+### Analogies
+
+- A latch is like a door:
+	- When CLK is high, the door is open
+		- Q does whatever D does while the door is open
+	- When CLK goes low, the door shuts
+		- Q "latches" onto whatever value was on D when the door shut
+- A flip-flop is like a camera
+	- Q is a picture of whatever is on D at the relevant edge (positive edge or negative edge)
+	- Q \*cannot\* change until the next relevant edge
+
+### Setup and Hold Time
+
+- The output "latches" when the CLK transitions (waveform is neg-edge trigger)
+- If D changes close to this time, you might not get a stable output
+	- Like taking a picture and the subject moves
+
+![diagram](13.10.png)