Analysis of Combinational Circuits
Given a gate circuit, recover what function it computes.
Description
Analysis is the reverse of design: starting from a gate diagram, you derive the Boolean functions of the outputs, build the truth table, and state in words what the circuit does. Label intermediate wires, write expressions outward to the outputs, then tabulate.
- Confirm the circuit is combinational (no feedback/storage).
- Label all gate outputs that depend only on inputs.
- Label outputs of gates that depend on those, and so on.
- Write the Boolean expression for each labelled wire.
- Substitute inward until outputs are in terms of inputs.
- Build the truth table from the output expressions.
- Simplify to recognize a standard block if possible.
- Describe the operation in words.
- Cross-check a few input rows by hand.
- Spot redundant gates that minimization would remove.
At a glance
What
Determining the function(s) a given combinational circuit implements.
Why
To verify, document, or reverse-engineer existing logic.
How
Label gate outputs, write expressions stage by stage, build the truth table.
Where
Verification, reading schematics, exam analysis problems.
When
Whenever you must understand a circuit you didn't design.
Think of it like…
Analysis is tasting a finished dish to deduce the recipe; design is following a recipe to cook the dish.
Analysis procedure
- Confirm the circuit is combinational (no feedback/storage).
- Label all gate outputs that depend only on inputs.
- Label outputs of gates that depend on those, and so on.
- Write the Boolean expression for each labelled wire.
- Substitute inward until outputs are in terms of inputs.
From expression to meaning
- Build the truth table from the output expressions.
- Simplify to recognize a standard block if possible.
- Describe the operation in words.
- Cross-check a few input rows by hand.
- Spot redundant gates that minimization would remove.
Design vs analysis
| Design | Analysis |
|---|---|
| spec → circuit | circuit → spec |
| truth table first | truth table derived |
| synthesize | reverse-engineer |
Trace a gate's function
▶ live simulatorClick a terminal (A/B) to toggle it · glowing wires carry a logic 1 · the lamp is output Y
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Real-world applications
The 5 Whys
- 1
Why analyze? Understand/verify a given circuit.
- 2
Why label wires? Build expressions stage by stage.
- 3
Why a truth table? Pin down exact behavior.
- 4
Why describe in words? Confirm intent.
- 5
Root cause: working expressions outward recovers the function from the gates.
Cheat sheet
Working principle
- Label gate outputs, write expressions stage by stage, build the truth table.
- Determining the function(s) a given combinational circuit implements.
Formulas & Boolean expressions
- spec → circuit = circuit → spec
- truth table first = truth table derived
- synthesize = reverse-engineer
Key facts
- Confirm the circuit is combinational (no feedback/storage).
- Build the truth table from the output expressions.
Why it exists
- Root cause: working expressions outward recovers the function from the gates.