🌟 Combinational Logic Circuits (Design Procedure for Combinational Circuit)
Designing a combinational logic circuit is a bit like building a puzzle — every piece has to fit perfectly to get the right final picture. In this case, the picture is the desired output for every possible input.
Let’s break this topic down step-by-step, in a simple and friendly way.
🧩 What Is a Combinational Circuit?
A combinational circuit is a type of digital circuit where the output depends only on the current inputs — not on any previous values.
There’s no memory element inside it.
So, you can think of it like a vending machine that gives you a snack immediately after you press a button combination. It doesn’t care what you pressed earlier — only what you pressed right now!
⚙️ The Goal of Designing a Combinational Circuit
When we design a combinational circuit, our goal is simple:
To find the right combination of logic gates that produce the desired output for all possible input conditions.
In other words, we’re trying to create a circuit that behaves exactly as we want, no matter what inputs we feed in.
🪜 Step-by-Step Design Procedure
Here’s a friendly walk-through of the typical design steps for any combinational logic circuit.
🧠 Step 1: Understand and Define the Problem
Before touching logic gates or equations, start with what the circuit is supposed to do.
For example, do you want it to compare numbers, add them, or detect some condition?
Ask yourself:
- What are the inputs?
- What are the outputs?
- What relationship should exist between them?
Once you’re clear about that, the rest becomes easy.
Example:
You might want to design a circuit that lights up an LED only when two switches are ON.
Here, the inputs are the two switches, and the output is the LED light signal.
🗂️ Step 2: List the Inputs and Outputs
Write down all the input variables (say, J, K, L) and all the outputs (maybe one or more).
This helps you see how many combinations you’ll need to test in the truth table.
For instance, if you have 3 inputs, there will be 2³ = 8 possible combinations of inputs.
📊 Step 3: Construct the Truth Table
This is where the real fun begins.
A truth table lists all possible input combinations and shows the corresponding output for each.
Think of it as a full “recipe” of how your circuit should behave.
Example (for 2 inputs J and K):
| J | K | Output |
| – | – | —— |
| 0 | 0 | ? |
| 0 | 1 | ? |
| 1 | 0 | ? |
| 1 | 1 | ? |
You fill in the output column based on the problem statement.
🧮 Step 4: Write the Boolean Expression
Now that you have the truth table, you can express the output as a Boolean function.
There are two common ways:
- Sum of Products (SOP) — you add up all combinations where the output is 1.
- Product of Sums (POS) — you multiply combinations where the output is 0.
For example, if the output is 1 for (J=1, K=0) and (J=1, K=1),
then the SOP expression is:F = J K' + J K
This represents the output logically.
✂️ Step 5: Simplify the Boolean Expression
Once you have your Boolean equation, it might look long and complicated.
To make the circuit smaller, faster, and cheaper, you should simplify it.
This can be done using:
- Boolean algebra rules, or
- Karnaugh Maps (K-map)
Both methods help reduce unnecessary logic gates.
It’s like trimming off extra wires you don’t need.
🔧 Step 6: Draw the Logic Diagram
Now comes the creative part — drawing the circuit!
Use the simplified Boolean equation and represent each operation with a logic gate:
- AND gate for multiplication (·)
- OR gate for addition (+)
- NOT gate for inversion (′)
Connect them step-by-step according to your simplified function.
🧱 Step 7: Verify the Circuit
Finally, test your design.
You can either re-check it using the truth table or simulate it using digital tools like Logisim or Multisim.
If every output matches your intended truth table, congratulations — your circuit works perfectly!
💡 Example in Real Life
Let’s say you’re designing a security lock system that opens only when two correct buttons are pressed.
You can treat the two buttons as inputs (J and K),
and the unlock signal as output (F).
Your truth table will show that only when J=1 and K=1, the output F=1.
That’s just an AND gate circuit!
So, by following the same design steps, you’ve just created a simple digital lock logic.
🪄 Quick Recap
| Step | Description |
|---|---|
| 1 | Define the problem (know what you want the circuit to do) |
| 2 | Identify inputs and outputs |
| 3 | Build a truth table |
| 4 | Write the Boolean expression |
| 5 | Simplify the Boolean expression |
| 6 | Draw the logic diagram |
| 7 | Verify the output |
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