1. SEQUENTIAL LOGIC By Tom Fitch

2. Types of Circuits Combinational: Gates Combinational: Gates Sequential: Flip-Flops Sequential: Flip-Flops

3. Sequential Circuits Why are they so important? Why are they so important? they have memory they have memory the memory is based on the inputs AKA “feedback” the memory is based on the inputs AKA “feedback” the previous state is the input/memory control the previous state is the input/memory control used in all kinds of finite state machines used in all kinds of finite state machines

4. Clocks and Flip-Flops The Clock The Clock output is based on the clock, Q and Q’ are not always the same output is based on the clock, Q and Q’ are not always the same

5. Clock Edge Trigger Positive Edge vs. Negative Edge Positive Edge vs. Negative Edge when does the circuit test the inputs? when does the circuit test the inputs?

6. S-R Flip-Flop An SR Flip Flop is an arrangements of logic gates that maintains a stable output even after the inputs are turned off. This simple flip flop circuit has a set input (S) and a reset input (R). The set input causes the output of 0 (top output) and 1 (bottom output). The reset input causes the opposite to happen (top = 1, bottom =0). Once the outputs are established, the wiring of the circuit is maintained until S or R go high, or power is turned of to the circuit. An SR Flip Flop is an arrangements of logic gates that maintains a stable output even after the inputs are turned off. This simple flip flop circuit has a set input (S) and a reset input (R). The set input causes the output of 0 (top output) and 1 (bottom output). The reset input causes the opposite to happen (top = 1, bottom =0). Once the outputs are established, the wiring of the circuit is maintained until S or R go high, or power is turned of to the circuit. This is a simple model of how a bit of RAM can be perpetuated. There are many issues not shown here such as timing inputs and synchronization, but the simplicity of the circuit gives you an idea of how RAM operates. This is a simple model of how a bit of RAM can be perpetuated. There are many issues not shown here such as timing inputs and synchronization, but the simplicity of the circuit gives you an idea of how RAM operates. Definition: Definition:

7. S-R Flip-Flop Implementation: Implementation: notice that the output is based on the previous state of the circuit notice that the output is based on the previous state of the circuit output = S OR (R’ AND state) output = S OR (R’ AND state)

8. Remember Those Flip-Flops? They’re just a function of the output, same as an S-R Flip-Flop They’re just a function of the output, same as an S-R Flip-Flop this is how sequential circuits are based on the output this is how sequential circuits are based on the output

9. D Flip-Flop Example How does a clocked D Flip-Flop work? How does a clocked D Flip-Flop work? one input, and the clock one input, and the clock but you get the outputs by NOR’ing with the other output! but you get the outputs by NOR’ing with the other output!

10. T Flip-Flop Example Implementing a clocked T Flip-Flop Implementing a clocked T Flip-Flop one input, and the clock one input, and the clock need to do more work this time… outputs AND with the input need to do more work this time… outputs AND with the input

11. Is This For Real? Finite State Machines Finite State Machines Adders Adders Registers Registers