Lecture No. 23
Dated: 23-02-2025
A sequential circuit
We will be dealing with electrical pulses which have 2 states, on or off.
The 2 points A and B can act as digit places.
Therefore, this machine has \(2^2 = 4\) states.
\[q_0 = (A = 0, B = 0) = (0, 0)\]
\[q_1 = (A = 0, B = 1) = (0, 1)\]
\[q_2 = (A = 1, B = 0) = (1, 0)\]
\[q_3 = (A = 1, B = 1) = (1, 1)\]
The transitions of this machine are determined using the following relations
\[\text{new } B = \text{old } A\]
\[\text{new } A = (\text {input}) \, \textbf{ NAND } \, (\text{old } A \, \textbf{ AND } \text{old } B)\]
\[\text{output } = (\text{input}) \, \textbf{ OR } \, (\text{old } B)\]
| Old State | Inputting 0 | Inputting 1 | ||
|---|---|---|---|---|
| State | Output | State | Output | |
| \(q_0 \equiv (0, 0)\) | \((1, 0) \equiv q_2\) | \(0\) | \((1, 0) \equiv q_2\) | \(1\) |
| \(q_1 \equiv (0, 1)\) | \((1, 0) \equiv q_2\) | \(1\) | \((1, 0) \equiv q_2\) | \(1\) |
| \(q_2 \equiv (1,0)\) | \((1, 1) \equiv q_3\) | \(0\) | \((1, 1) \equiv q_3\) | \(1\) |
| \(q_3 \equiv (1, 1)\) | \((1, 1) \equiv q_3\) | \(1\) | \((0, 1) \equiv q_1\) | \(1\) |
Corresponding transition diagram1
Running the string2 \(01101110\) on this machine.
| Input | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | |
|---|---|---|---|---|---|---|---|---|---|
| States | \(q_0\) | \(q_2\) | \(q_3\) | \(q_1\) | \(q_2\) | \(q_3\) | \(q_1\) | \(q_2\) | \(q_3\) |
| Output | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
References
-
Read more about transition diagrams. ↩