Sequential Circuits
Circuits whose output depends on the present input AND the stored past — they have memory.
Description
A circuit with memory: outputs depend on current inputs plus stored state. Real systems need to remember — counting, sequencing, and protocols all need history. Feed combinational logic outputs back through storage elements clocked in time.
- Combinational: output = f(inputs only); no memory.
- Sequential: output = f(inputs, present state); has memory.
- Structure = combinational logic + storage elements in a feedback loop.
- Synchronous: state changes only on clock edges — predictable, easy to analyze.
- Asynchronous: state can change any time inputs change — fast but hazard-prone.
- Almost all modern design is synchronous (clocked).
- What: A circuit with memory: outputs depend on current inputs plus stored state.
- Why: Real systems need to remember — counting, sequencing, and protocols all need history.
- How: Feed combinational logic outputs back through storage elements clocked in time.
- Where: Counters, controllers, CPUs, communication protocols — anything with state.
At a glance
What
A circuit with memory: outputs depend on current inputs plus stored state.
Why
Real systems need to remember — counting, sequencing, and protocols all need history.
How
Feed combinational logic outputs back through storage elements clocked in time.
Where
Counters, controllers, CPUs, communication protocols — anything with state.
When
Whenever behavior must depend on what happened before, not just now.
Think of it like…
A combinational circuit is a calculator that forgets instantly; a sequential circuit is a person with a notepad — the next action depends on what they jotted down before.
Combinational vs sequential
- Combinational: output = f(inputs only); no memory.
- Sequential: output = f(inputs, present state); has memory.
- Structure = combinational logic + storage elements in a feedback loop.
Synchronous vs asynchronous
- Synchronous: state changes only on clock edges — predictable, easy to analyze.
- Asynchronous: state can change any time inputs change — fast but hazard-prone.
- Almost all modern design is synchronous (clocked).
Two machine models
| Model | Output depends on | Output timing |
|---|---|---|
| Mealy | state + inputs | can change between edges |
| Moore | state only | changes only after edge |
Clock frequency ↔ period converter
▶ live simulatorT = 1 / f · pick any input and output unit (Hz/kHz/MHz/GHz ↔ s/ms/µs/ns/ps)
Real-world applications
The 5 Whys
- 1
Why sequential circuits? Many tasks need memory of the past.
- 2
Why memory? Counting, sequencing, and protocols are history-dependent.
- 3
Why clock it? A shared clock makes all state changes happen together.
- 4
Why simultaneous changes? Avoids races and makes timing analyzable.
- 5
Root cause: feedback through clocked storage turns logic into a state machine.
Cheat sheet
Working principle
- Feed combinational logic outputs back through storage elements clocked in time.
- A circuit with memory: outputs depend on current inputs plus stored state.
Formulas & Boolean expressions
- Combinational: output = f(inputs only); no memory.
- Sequential: output = f(inputs, present state); has memory.
- Structure = combinational logic + storage elements in a feedback loop.
Key facts
- Combinational: output = f(inputs only); no memory.
- Synchronous: state changes only on clock edges — predictable, easy to analyze.
Why it exists
- Root cause: feedback through clocked storage turns logic into a state machine.