Week 10: Sequential design, one method

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Goal. Design any sequential circuit with the same truth-table method you already use for combinational logic. No new theory, no excitation tables.

The whole idea

A sequential circuit is just combinational logic plus flip-flops:

And because we use D flip-flops, the rule Q_next = D means the next state is the D input. So you never need an excitation table: whatever you want the next state to be, that is what you feed to D.

The recipe

  1. Decide the states and draw the next-state truth table: columns are present state + inputs on the left, next state + outputs on the right.
  2. For each next-state bit, read its column as a function of the present-state and input columns.
  3. Minimise it (Karnaugh map) and that expression is the D input for that flip-flop.
  4. Wire the combinational logic to the D inputs, share one clock across all flip-flops, done.

It is the Week 4 design chain, with the present state added as inputs.

Worked example: a 2-bit counter

We want the state to step 00 → 01 → 10 → 11 → 00. Present state Q1 Q0, next state Q1+ Q0+:

Q1 Q0 Q1+ Q0+
0 0 0 1
0 1 1 0
1 0 1 1
1 1 0 0

Reading the columns: Q0+ = Q0' (it toggles every clock) and Q1+ = Q1 ⊕ Q0 (it toggles when Q0 is 1). Those become the D inputs: D0 = Q0', D1 = Q1 ⊕ Q0.

2-bit counter

▶ Open in LogicLab

Sequential design

Step the clock and watch the two LEDs count in binary.

In the lab

The 2-bit counter is the course’s sequential lab. Build it in the simulator (Lab 3) and then on a breadboard with a dual D flip-flop IC clocked by the Arduino (Lab 4). Full instructions are in the Lab Annex.

Check yourself