AExE0203 Sequential logic circuit¶
Sequential logic versus combinational logic¶
- Combinational output depends only on present inputs.
- Sequential output depends on present inputs and stored state.
- Memory is commonly realized using latches, flip-flops, or registers.
Latches and flip-flops¶
| Element | Triggering style | Recognition cue |
|---|---|---|
| Latch | level-sensitive | responds while enable is active |
| Flip-flop | edge-triggered | updates only on clock edge |
The syllabus names RS flip-flops, gated flip-flops, edge-triggered flip-flops, and master-slave flip-flops. These fit the broader family below.
RS, D, JK, and T behavior¶
| Device | Main next-state idea | Trap |
|---|---|---|
| RS latch / FF | set, reset, hold | forbidden condition in basic form |
| D FF | next state follows D at active edge | simplest storage element |
| JK FF | refined RS; toggle when \(J=K=1\) | race-around concern in level triggering |
| T FF | toggles when T is 1 | useful for counters |
Basic RS meanings:
- S = 1, R = 0 -> set;
- S = 0, R = 1 -> reset;
- S = 0, R = 0 -> hold for NOR-based RS latch;
- S = 1, R = 1 is forbidden for the basic NOR latch.
Gated or clocked versions allow state changes only when the gate/clock condition is active.
Edge-triggered and master-slave operation¶
- Edge-triggered flip-flops sample input only at the transition edge.
- Positive-edge devices respond on the rising edge.
- Negative-edge devices respond on the falling edge.
- Master-slave flip-flops use two stages with opposite clock phases to prevent direct transparency.
- In the conventional positive-pulse master-slave JK arrangement, the master is enabled while the clock is HIGH and the slave while it is LOW. Other polarity implementations can reverse these levels; opposite, non-overlapping phases are the invariant.
Race-around cue:
- a level-triggered JK flip-flop can toggle repeatedly during one clock pulse when \(J=K=1\) and the pulse width is too large;
- edge-triggered or master-slave realization removes that practical problem.
Registers¶
Register = a group of flip-flops used to store multi-bit data.
Types:
| Type | Function |
|---|---|
| SISO | serial in, serial out |
| SIPO | serial in, parallel out |
| PISO | parallel in, serial out |
| PIPO | parallel in, parallel out |
| Universal shift register | can shift left, shift right, load, and hold |
Applications of shift registers:
- serial-to-parallel conversion;
- parallel-to-serial conversion;
- temporary storage;
- digital delay line;
- sequence generation and ring/Johnson counters.
Counters¶
| Counter type | Clocking | Recognition |
|---|---|---|
| Asynchronous or ripple | output of one FF clocks the next | simple, slower due to ripple delay |
| Synchronous | common clock to all FFs | faster, better controlled timing |
Key facts:
- an \(n\)-flip-flop binary counter has modulus up to \(2^n\);
- ripple counters accumulate propagation delay stage by stage;
- synchronous counters need more combinational logic but reduce cumulative delay.
Ring and Johnson cues:
- ring counter circulates a single 1 or 0;
- Johnson counter feeds inverted last stage output back to first stage, giving up to \(2n\) states with \(n\) flip-flops.
Timing and state recognition¶
MCQ cues:
- "stores one bit" -> flip-flop;
- "samples only on rising edge" -> positive-edge-triggered FF;
- "convert serial stream to byte" -> SIPO register;
- "faster counter for high-speed logic" -> synchronous counter.
Sequential-logic traps¶
- "gated" does not automatically mean edge-triggered.
- The forbidden state depends on the exact RS implementation form.
- A register stores multiple bits; a single flip-flop stores one bit.
- Counter modulus is about the number of distinct states, not just the number of flip-flops.
Sequential-logic revision box¶
- Latch is level-sensitive; flip-flop is edge-triggered in the usual exam sense.
- JK with \(J=K=1\) toggles.
- Master-slave and edge-triggered forms avoid race-around behavior.
- Register = group of flip-flops.
- Ripple counter is simpler but slower; synchronous counter is faster.
- \(n\) binary flip-flops can represent up to \(2^n\) states.